document_title: If I Ruled the World

question_text: who wrote the song if i ruled the world

question_tokens: who wrote the song if i ruled the world

text: If I Ruled the World

text: "If I Ruled the World" is a popular song, composed by Leslie Bricusse and Cyril Ornadel, which was originally from the 1963 West End musical Pickwick (based on Charles Dickens's The Pickwick Papers). In the context of the stage musical, the song is sung by Samuel Pickwick, when he is mistaken for an election candidate and called on by the crowd to give his manifesto.  Ornadel and Bricusse received the 1963 Ivor Novello award for Best Song Musically and Lyrically.[1]

tag: p

text: The song is usually associated with Sir Harry Secombe, who got the song to No 18 in the UK charts in 1963, but has been performed by other singers, notably Tony Bennett, Robert Goulet, James Brown, Stevie Wonder, The Supremes,  Tom Jones and Regina Belle. Tony Bennett originally recorded the song in 1965, and had a number 34 hit with it on the U.S. pop singles charts.  With Celine Dion, he returned to the song on his Grammy-winning 2006 album Duets: An American Classic.

text: Andy Hallett, the actor best known for playing the part of Lorne ('The Host') in the television series Angel, sang the song in that series' final episode.  The politician-spoofing BBC panel show If I Ruled the World was named after the song.

text: This song was featured in Spring/Summer 2009 on the Vodafone adverts in the UK.

text: Jamie Cullum also recorded a version for his album The Pursuit, and performed it at his special performance at the Late Night Prom, number Prom 55, of The Proms in London, with The Heritage Ensemble, on Thursday 26 August 2010 between 22:15 and 13.45. As shown on BBC televisions' BBC Four on the following night.[2]


document_title: Area code 352

question_text: where is area code 352 in united states

question_tokens: where is area code 352 in united states

root

text: Area code 352

text: Area code 352 is a telephone dialing area around Gainesville, Florida. It split from area code 904 in 1996.

text: It includes all of Dixie, Gilchrist, Levy, Marion, Citrus, Sumter, Lake (with the exception of Montverde, Florida), and Hernando counties, and all but the extreme north of Alachua County. It also includes the southern and eastern tips of Bradford County, the west edge of northern Putnam County, the southwestern part of Clay County, the northeast and north central parts of Pasco county, and the Steinhatchee and Tennile communities in extreme southern Taylor County.

text: Area code 352 spells FLA on most telephone keypads.


document_title: Approximations of π

question_text: what english mathematician calculated the value of pi to 707

question_tokens: what english mathematician calculated the value of pi to 707

text: Approximations of π

text: Early history[edit]

text: The best known approximations to π dating to before the Common Era were accurate to two decimal places; this was improved upon in Chinese mathematics in particular by the mid first millennium, to an accuracy of seven decimal places. After this, no further progress was made until the late medieval period.

text: Some Egyptologists[2] have claimed that the ancient Egyptians used an approximation of π as  22⁄7 from as early as the Old Kingdom.[3] This claim has met with skepticism.[4][5]

text: Babylonian mathematics usually approximated π to 3, sufficient for the architectural projects of the time (notably also reflected in the description of Solomon's Temple in the Hebrew Bible).[6] The Babylonians were aware that this was an approximation, and one Old Babylonian mathematical tablet excavated near Susa in 1936 (dated to between the 19th and 17th centuries BCE) gives a better approximation of π as 25/8=3.125, about 0.5 percent below the exact value.[7][8][9][10]

text: At about the same time, the Egyptian Rhind Mathematical Papyrus (dated to the Second Intermediate Period, c. 1600 BCE, although stated to be a copy of an older, Middle Kingdom text) implies an approximation of π as  256⁄81 ≈ 3.16 (accurate to 0.6 percent) by calculating the area of a circle by approximating the circle by an octagon.[4][11]

text: Astronomical calculations in the Shatapatha Brahmana (c. 6th century BCE) use a fractional approximation of 339/108 ≈ 3.139.[12]

text: In the 3rd century BCE, Archimedes proved the sharp inequalities  223⁄71 < π <  22⁄7, by means of regular 96-gons (accuracies of 2·10−4 and 4·10−4, respectively).

text: In the 2nd century CE, Ptolemy, used the value  377⁄120, the first known approximation accurate to three decimal places (accuracy 2·10−5).[13]

text: The Chinese mathematician Liu Hui in 263 CE computed π to between 7000314102400000000♠3.141024 and 7000314270800000000♠3.142708 by inscribing an 96-gon and 192-gon; the average of these two values is 7000314186600000000♠3.141866 (accuracy 9·10−5). He also suggested that 3.14 was a good enough approximation for practical purposes. He has also frequently been credited with a later and more accurate result π ≈ 3927/1250 = 3.1416 (accuracy 2·10−6), although some scholars instead believe that this is due to the later (5th-century) Chinese mathematician Zu Chongzhi.[14] Zu Chongzhi is known to have computed π between 3.1415926 and 3.1415927, which was correct to seven decimal places. He gave two other approximations of π: π ≈ 22/7 and π ≈ 355/113. The latter fraction is the best possible rational approximation of π using fewer than five decimal digits in the numerator and denominator. Zu Chongzhi's result surpasses the accuracy reached in Hellenistic mathematics, and would remain without improvement for close to a millennium.

text: In Gupta-era India (6th century), mathematician Aryabhata in his astronomical treatise Āryabhaṭīya calculated the value of π to five significant figures (π ≈ 62832/20000 = 3.1416).[15] using it to calculate an approximation of the Earth's circumference.[16] Aryabhata stated that his result "approximately" (āsanna "approaching") gave the circumference of a circle. His 15th-century commentator Nilakantha Somayaji (Kerala school of astronomy and mathematics) has argued that the word means not only that this is an approximation, but that the value is incommensurable (irrational).[17]

text: Middle Ages[edit]

text: By the 5th century CE, π was known to about seven digits in Chinese mathematics, and to about five in Indian mathematics. Further progress was not made for nearly a millennium, until the 14th century, when Indian mathematician and astronomer Madhava of Sangamagrama, founder of the Kerala school of astronomy and mathematics, discovered the infinite series for π, now known as the Madhava–Leibniz series,[18][19] and gave two methods for computing the value of π. One of these methods is to obtain a rapidly converging series by transforming the original infinite series of π. By doing so, he obtained the infinite series

text: and used the first 21 terms to compute an approximation of π correct to 11 decimal places as 7000314159265359000♠3.14159265359.

text: The other method he used was to add a remainder term to the original series of π. He used the remainder term

text: in the infinite series expansion of  π⁄4 to improve the approximation of π to 13 decimal places of accuracy when n = 75.

text: Jamshīd al-Kāshī (Kāshānī), a Persian astronomer and mathematician, correctly computed 2π to 9 sexagesimal digits in 1424.[20] This figure is equivalent to 17 decimal digits as

text: which equates to

text: He achieved this level of accuracy by calculating the perimeter of a regular polygon with 3 × 228 sides.[21]

text: 16th to 19th centuries[edit]

text: In the second half of the 16th century, the French mathematician François Viète discovered an infinite product that converged on Pi known as Viète's formula.

text: The German/Dutch mathematician Ludolph van Ceulen (circa 1600) computed the first 35 decimal places of π with a 262-gon. He was so proud of this accomplishment that he had them inscribed on his tombstone.

text: In Cyclometricus (1621), Willebrord Snellius demonstrated that the perimeter of the inscribed polygon converges on the circumference twice as fast as does the perimeter of the corresponding circumscribed polygon. This was proved by Christiaan Huygens in 1654. Snellius was able to obtain 7 digits of pi from a 96-sided polygon.[22]

text: In 1789, the Slovene mathematician Jurij Vega calculated the first 140 decimal places for π of which the first 126 were correct[23] and held the world record for 52 years until 1841, when William Rutherford calculated 208 decimal places of which the first 152 were correct. Vega improved John Machin's formula from 1706 and his method is still mentioned today.

text: The magnitude of such precision (152 decimal places) can be put into context by the fact that the circumference of the largest known object, the observable universe, can be calculated from its diameter (93 billion light-years) to a precision of less than one Planck length (at 6965161620000000000♠1.6162×10−35 meters, the shortest unit of length that has real meaning) using π expressed to just 62 decimal places.

text: The English amateur mathematician William Shanks, a man of independent means, spent over 20 years calculating π to 707 decimal places. This was accomplished in 1873, with the first 527 places correct. He would calculate new digits all morning and would then spend all afternoon checking his morning's work. This was the longest expansion of π until the advent of the electronic digital computer three-quarters of a century later.

text: 20th century[edit]

text: In 1910, the Indian mathematician Srinivasa Ramanujan found several rapidly converging infinite series of π, including

text: which computes a further eight decimal places of π with each term in the series. His series are now the basis for the fastest algorithms currently used to calculate π. See also Ramanujan–Sato series.

text: From the mid-20th century onwards, all calculations of π have been done with the help of calculators or computers.

text: In 1944, D. F. Ferguson, with the aid of a mechanical desk calculator, found that William Shanks had made a mistake in the 528th decimal place, and that all succeeding digits were incorrect.

text: In the early years of the computer, an expansion of π to 7005100000000000000♠100000 decimal places[24]:78 was computed by Maryland mathematician Daniel Shanks (no relation to the above-mentioned William Shanks) and his team at the United States Naval Research Laboratory in Washington, D.C. In 1961, Shanks and his team used two different power series for calculating the digits of π. For one, it was known that any error would produce a value slightly high, and for the other, it was known that any error would produce a value slightly low. And hence, as long as the two series produced the same digits, there was a very high confidence that they were correct. The first 100,265 digits of π were published in 1962.[24]:80–99 The authors outlined what would be needed to calculate π to 1 million decimal places and concluded that the task was beyond that day's technology, but would be possible in five to seven years.[24]:78

text: In 1989, the Chudnovsky brothers correctly computed π to over 1 billion decimal places on the supercomputer IBM 3090 using the following variation of Ramanujan's infinite series of π:

text: In 1999, Yasumasa Kanada and his team at the University of Tokyo correctly computed π to over 200 billion decimal places on the supercomputer HITACHI SR8000/MPP (128 nodes) using another variation of Ramanujan's infinite series of π. In October 2005, they claimed to have calculated it to 1.24 trillion places.[25]

text: Records since then have all been accomplished on personal computers using the Chudnovsky algorithm. In 2009, Fabrice Bellard computed just under 2.7 trillion digits, and from 2010 onward, all records have been set using Alexander Yee's "y-cruncher" software. As of November 2016[update], the record stands at 22,459,157,718,361 (πe×1012) digits.[26] The limitation on further expansion is primarily storage space for the computation.[27]

text: 21st century[edit]

text: In November 2002, Yasumasa Kanada and a team of 9 others used the Hitachi SR8000, a 64-node supercomputer with 1 terabyte of main memory, to calculate π to roughly 1.24 trillion digits in around 600 hours.

text: In August 2009, a Japanese supercomputer called the T2K Open Supercomputer more than doubled the previous record by calculating π to roughly 2.6 trillion digits in approximately 73 hours and 36 minutes.

text: In December 2009, Fabrice Bellard used a home computer to compute 2.7 trillion decimal digits of π. Calculations were performed in base 2 (binary), then the result was converted to base 10 (decimal). The calculation, conversion, and verification steps took a total of 131 days.[28]

text: In August 2010, Shigeru Kondo used Alexander Yee's y-cruncher to calculate 5 trillion digits of π. This was the world record for any type of calculation, but significantly it was performed on a home computer built by Kondo.[29] The calculation was done between 4 May and 3 August, with the primary and secondary verifications taking 64 and 66 hours respectively.[30]

text: In October 2011, Shigeru Kondo broke his own record by computing ten trillion (1013) and fifty digits using the same method but with better hardware.[31][32]

text: In December 2013, Kondo broke his own record for a second time when he computed 12.1 trillion digits of π.[33]

text: In October 2014, someone going by the pseudonym "houkouonchi" used y-cruncher to calculate 13.3 trillion digits of π.[1]

text: In November 2016, Peter Trueb and his sponsors computed on y-cruncher and fully verified 22.4 trillion digits of π. The computation took (with 3 interruptions) 105 days to complete.[34]

text: Practical approximations[edit]

text: Depending on the purpose of a calculation, π can be approximated by using fractions for ease of calculation. The most notable such approximations are  22⁄7 (accuracy 2·10−4) and  355⁄113 (accuracy 8·10−8).

text: Non-mathematical "definitions" of π[edit]

text:
Of some notability are legal or historical texts purportedly "defining π" to have some rational value, notably the "Indiana Pi Bill" of 1897, which stated "the ratio of the diameter and circumference is as five-fourths to four" (which would imply "π = 3.2") and a passage in the Hebrew Bible that implies that

π
=
3

{\displaystyle \pi =3}

.

text: Imputed biblical value[edit]

text: It is sometimes claimed that the Hebrew Bible implies that "π equals three", based on a passage in NKJV and NKJV giving measurements for the round basin located in front of the Temple in Jerusalem as having a diameter of 10 cubits and a circumference of 30 cubits.

text: The issue is discussed in the Talmud and in Rabbinic literature.[35] Among the many explanations and comments are these:

text:
Rabbi Nehemiah explained this in his Mishnat ha-Middot (the earliest known Hebrew text on geometry, ca. 150 CE) by saying that the diameter was measured from the outside rim while the circumference was measured along the inner rim. This interpretation implies a brim about 0.225 cubit (or, assuming an 18-inch "cubit", some 4 inches), or one and a third "handbreadths," thick (cf. NKJV and NKJV).
Maimonides states (ca. 1168 CE) that π can only be known approximately, so the value 3 was given as accurate enough for religious purposes. This is taken by some[36] as the earliest assertion that π is irrational.
Another rabbinical explanation[by whom?][year needed] invokes gematria: In NKJV the word translated 'measuring line' appears in the Hebrew text spelled QWH קַוה, but elsewhere the word is most usually spelled QW קַו. The ratio of the numerical values of these Hebrew spellings is  111⁄106. If the putative value of 3 is multiplied by this ratio, one obtains  333⁄106 = 3.141509433... – giving 5 correct digits, which is within 1/10,000 of the true value of π. For this to work, it must be assumed that the measuring line is different for the diameter and circumference.

tag: ul

text: There is still some debate on this passage in biblical scholarship.[not in citation given][37][38] Many reconstructions of the basin show a wider brim (or flared lip) extending outward from the bowl itself by several inches to match the description given in NKJV[39] In the succeeding verses, the rim is described as "a handbreadth thick; and the brim thereof was wrought like the brim of a cup, like the flower of a lily: it received and held three thousand baths" NKJV, which suggests a shape that can be encompassed with a string shorter than the total length of the brim, e.g., a Lilium flower or a Teacup.

text: The Indiana bill[edit]

text: The so-called "Indiana Pi Bill" of 1897, has often been characterized as an attempt to "legislate the value of Pi". Rather, the bill dealt with a purported solution to the problem of geometrically "Squaring the circle".[40]

text: The bill was nearly passed by the Indiana General Assembly in the U.S., and has been claimed to imply a number of different values for π, although the closest it comes to explicitly asserting one is the wording "the ratio of the diameter and circumference is as five-fourths to four", which would make π = 16/5 = 3.2, a discrepancy of nearly 2 percent. A mathematics professor who happened to be present the day the bill was brought up for consideration in the Senate, after it had passed in the House, helped to stop the passage of the bill on its second reading, after which the assembly thoroughly ridiculed it before tabling it indefinitely.

text: Development of efficient formulae[edit]

text: Polygon approximation to a circle[edit]

text: Archimedes, in his Measurement of a Circle, created the first algorithm for the calculation of π based on the idea that the perimeter of any (convex) polygon inscribed in a circle is less than the circumference of the circle, which, in turn, is less than the perimeter of any circumscribed polygon. He started with inscribed and circumscribed regular hexagons, whose perimeters are readily determined. He then shows how to calculate the perimeters of regular polygons of twice as many sides that are inscribed and circumscribed about the same circle. This is a recursive procedure which would be described today as follows: Let pk and Pk denote the perimeters of regular polygons of k sides that are inscribed and circumscribed about the same circle, respectively. Then,

text: Archimedes uses this to successively compute P12, p12, P24, p24, P48, p48, P96 and p96.[41] Using these last values he obtains

text: It is not known why Archimedes stopped at a 96-sided polygon; it only takes patience to extend the computations. Heron reports in his Metrica (about 60 CE) that Archimedes continued the computation in a now lost book, but then attributes an incorrect value to him.[42]

text: Archimedes uses no trigonometry in this computation and the difficulty in applying the method lies in obtaining good approximations for the square roots that are involved. Trigonometry, in the form of a table of chord lengths in a circle, was probably used by Claudius Ptolemy of Alexandria to obtain the value of π given in the Almagest (circa 150 CE).[43]

text: Advances in the approximation of π (when the methods are known) were made by increasing the number of sides of the polygons used in the computation. A trigonometric improvement by Willebrord Snell (1621) obtains better bounds from a pair of bounds gotten from the polygon method. Thus, more accurate results were obtained from polygons with fewer sides.[44] Viète's formula, published by François Viète in 1593, was derived by Viète using a closely related polygonal method, but with areas rather than perimeters of polygons whose numbers of sides are powers of two.[45]

text: The last major attempt to compute π by this method was carried out by Grienberger in 1630 who calculated 39 decimal places of π using Snell's refinement.[44]

text: Machin-like formula[edit]

text: For fast calculations, one may use formulae such as Machin's:

text: together with the Taylor series expansion of the function arctan(x). This formula is most easily verified using polar coordinates of complex numbers, producing:

text:
(
5
+
i

)

4

⋅
(
239
−
i
)
=

2

2

⋅

13

4

(
1
+
i
)
.

{\displaystyle (5+i)^{4}\cdot (239-i)=2^{2}\cdot 13^{4}(1+i).}

text: (Note also that {x,y} = {239, 132} is a solution to the Pell equation x2−2y2 = −1.)

text: Formulae of this kind are known as Machin-like formulae. Machin's particular formula was used well into the computer era for calculating record numbers of digits of π,[24] but more recently other similar formulae have been used as well.

text: For instance, Shanks and his team used the following Machin-like formula in 1961 to compute the first 100,000 digits of π:[24]

text:
π
4

=
6
arctan

1
8

+
2
arctan

1
57

+
arctan

1
239

{\displaystyle {\frac {\pi }{4}}=6\arctan {\frac {1}{8}}+2\arctan {\frac {1}{57}}+\arctan {\frac {1}{239}}}

text: and they used another Machin-like formula,

text:
π
4

=
12
arctan

1
18

+
8
arctan

1
57

−
5
arctan

1
239

{\displaystyle {\frac {\pi }{4}}=12\arctan {\frac {1}{18}}+8\arctan {\frac {1}{57}}-5\arctan {\frac {1}{239}}}

text: as a check.

text: The record as of December 2002 by Yasumasa Kanada of Tokyo University stood at 1,241,100,000,000 digits. The following Machin-like formulae were used for this:

text: K. Takano (1982).

text: F. C. W. Störmer (1896).

text: Other classical formulae[edit]

text: Other formulae that have been used to compute estimates of π include:

text: Liu Hui (see also Viète's formula):

text: Madhava:

text: Euler:

text: Newton / Euler Convergence Transformation:[46]

text: where (2k+1)!! denotes the product of the odd integers up to 2k+1.

text: Ramanujan:

text: David Chudnovsky and Gregory Chudnovsky:

text: Ramanujan's work is the basis for the Chudnovsky algorithm, the fastest algorithms used, as of the turn of the millennium, to calculate π.

text: Modern algorithms[edit]

text: Extremely long decimal expansions of π are typically computed with iterative formulae like the Gauss–Legendre algorithm and Borwein's algorithm. The latter, found in 1985 by Jonathan and Peter Borwein, converges extremely quickly:

text:
For

y

0

=

2

−
1
,

a

0

=
6
−
4

2

{\displaystyle y_{0}={\sqrt {2}}-1,\ a_{0}=6-4{\sqrt {2}}}

 and

text:
where

f
(
y
)
=
(
1
−

y

4

)

1

/

4

{\displaystyle f(y)=(1-y^{4})^{1/4}}

, the sequence

1

/

a

k

{\displaystyle 1/a_{k}}

 converges quartically to π, giving about 100 digits in three steps and over a trillion digits after 20 steps. However, it is known that using an algorithm such as the Chudnovsky algorithm (which converges linearly) is faster than these iterative formulae.

text: The first one million digits of π and  1⁄π are available from Project Gutenberg (see external links below). A former calculation record (December 2002) by Yasumasa Kanada of Tokyo University stood at 1.24 trillion digits, which were computed in September 2002 on a 64-node Hitachi supercomputer with 1 terabyte of main memory, which carries out 2 trillion operations per second, nearly twice as many as the computer used for the previous record (206 billion digits). The following Machin-like formulæ were used for this:

text: These approximations have so many digits that they are no longer of any practical use, except for testing new supercomputers.[47] Properties like the potential normality of π will always depend on the infinite string of digits on the end, not on any finite computation.

text: Miscellaneous approximations[edit]

text: Historically, base 60 was used for calculations. In this base, π can be approximated to eight (decimal) significant figures with the number 3:8:29:4460, which is

text: (The next sexagesimal digit is 0, causing truncation here to yield a relatively good approximation.)

text: In addition, the following expressions can be used to estimate π:

text: accurate to three digits:

text: accurate to three digits:

text: accurate to four digits:

text: accurate to four digits (or five significant figures):

text: an approximation by Ramanujan, accurate to 4 digits (or five significant figures):

text: accurate to five digits:

text: accurate to seven digits:

text: accurate to nine digits:

text: accurate to ten digits:

text: accurate to ten digits (or eleven significant figures):

text: accurate to 18 digits:

text: accurate to 30 decimal places:

text: accurate to 52 decimal places:

text: accurate to 161 decimal places:

text: The continued fraction representation of π can be used to generate successive best rational approximations. These approximations are the best possible rational approximations of π relative to the size of their denominators. Here is a list of the first thirteen of these:[53][54]

text: Summing a circle's area[edit]

text: Pi can be obtained from a circle if its radius and area are known using the relationship:

text: If a circle with radius r is drawn with its center at the point (0, 0), any point whose distance from the origin is less than r will fall inside the circle. The Pythagorean theorem gives the distance from any point (x, y) to the center:

text: Mathematical "graph paper" is formed by imagining a 1×1 square centered around each cell (x, y), where x and y are integers between −r and r. Squares whose center resides inside or exactly on the border of the circle can then be counted by testing whether, for each cell (x, y),

text: The total number of cells satisfying that condition thus approximates the area of the circle, which then can be used to calculate an approximation of π. Closer approximations can be produced by using larger values of r.

text: Mathematically, this formula can be written:

text: In other words, begin by choosing a value for r. Consider all cells (x, y) in which both x and y are integers between −r and r. Starting at 0, add 1 for each cell whose distance to the origin (0,0) is less than or equal to r. When finished, divide the sum, representing the area of a circle of radius r, by r2 to find the approximation of π. For example, if r is 5, then the cells considered are:

text:
(−5,5)
(−4,5)
(−3,5)
(−2,5)
(−1,5)
(0,5)
(1,5)
(2,5)
(3,5)
(4,5)
(5,5)

(−5,4)
(−4,4)
(−3,4)
(−2,4)
(−1,4)
(0,4)
(1,4)
(2,4)
(3,4)
(4,4)
(5,4)

(−5,3)
(−4,3)
(−3,3)
(−2,3)
(−1,3)
(0,3)
(1,3)
(2,3)
(3,3)
(4,3)
(5,3)

(−5,2)
(−4,2)
(−3,2)
(−2,2)
(−1,2)
(0,2)
(1,2)
(2,2)
(3,2)
(4,2)
(5,2)

(−5,1)
(−4,1)
(−3,1)
(−2,1)
(−1,1)
(0,1)
(1,1)
(2,1)
(3,1)
(4,1)
(5,1)

(−5,0)
(−4,0)
(−3,0)
(−2,0)
(−1,0)
(0,0)
(1,0)
(2,0)
(3,0)
(4,0)
(5,0)

(−5,−1)
(−4,−1)
(−3,−1)
(−2,−1)
(−1,−1)
(0,−1)
(1,−1)
(2,−1)
(3,−1)
(4,−1)
(5,−1)

(−5,−2)
(−4,−2)
(−3,−2)
(−2,−2)
(−1,−2)
(0,−2)
(1,−2)
(2,−2)
(3,−2)
(4,−2)
(5,−2)

(−5,−3)
(−4,−3)
(−3,−3)
(−2,−3)
(−1,−3)
(0,−3)
(1,−3)
(2,−3)
(3,−3)
(4,−3)
(5,−3)

(−5,−4)
(−4,−4)
(−3,−4)
(−2,−4)
(−1,−4)
(0,−4)
(1,−4)
(2,−4)
(3,−4)
(4,−4)
(5,−4)

(−5,−5)
(−4,−5)
(−3,−5)
(−2,−5)
(−1,−5)
(0,−5)
(1,−5)
(2,−5)
(3,−5)
(4,−5)
(5,−5)

text: The 12 cells (0, ±5), (±5, 0), (±3, ±4), (±4, ±3) are exactly on the circle, and 69 cells are completely inside, so the approximate area is 81, and π is calculated to be approximately 3.24 because 81 / 52 = 3.24. Results for some values of r are shown in the table below:

text:
r
area
approximation of π

2
13
3.25

3
29
3.22222

4
49
3.0625

5
81
3.24

10
317
3.17

20
1257
3.1425

100
31417
3.1417

1000
3141549
3.141549

text: For related results see The circle problem: number of points (x,y) in square lattice with x^2 + y^2 <= n.

text: Similarly, the more complex approximations of π given below involve repeated calculations of some sort, yielding closer and closer approximations with increasing numbers of calculations.

text: Continued fractions[edit]

text: Besides its simple continued fraction representation [3; 7, 15, 1, 292, 1, 1, ...], which displays no discernible pattern, π has many generalized continued fraction representations generated by a simple rule, including these two.

text: (Other representations are available at The Wolfram Functions Site.)

text: Trigonometry[edit]

text: Gregory–Leibniz series[edit]

text: The Gregory–Leibniz series

text:
is the power series for arctan(x) specialized to x = 1. It converges too slowly to be of practical interest. However, the power series converges much faster for smaller values of

x

{\displaystyle x}

, which leads to formulae where

π

{\displaystyle \pi }

 arises as the sum of small angles with rational tangents, known as Machin-like formulae.

text: Arctangent[edit]

text: Knowing that 4 arctan 1 = π, the formula can be simplified to get:

text: with a convergence such that each additional 10 terms yields at least three more digits.

text: Arcsine[edit]

text: Observing an equilateral triangle and noting that

text: yields

text: with a convergence such that each additional five terms yields at least three more digits.

text: The Salamin–Brent algorithm[edit]

text:
The Gauss–Legendre algorithm or Salamin–Brent algorithm was discovered independently by Richard Brent and Eugene Salamin in 1975. This can compute

π

{\displaystyle \pi }

 to

N

{\displaystyle N}

 digits in time proportional to

N

log

(
N
)

log

(
log

(
N
)
)

{\displaystyle N\,\log(N)\,\log(\log(N))}

, much faster than the trigonometric formulae.

text: Digit extraction methods[edit]

text: The Bailey–Borwein–Plouffe formula (BBP) for calculating π was discovered in 1995 by Simon Plouffe. Using base 16 math, the formula can compute any particular digit of π—returning the hexadecimal value of the digit—without having to compute the intervening digits (digit extraction).[56]

text: In 1996, Simon Plouffe derived an algorithm to extract the nth decimal digit of π (using base 10 math to extract a base 10 digit), and which can do so with an improved speed of O(n3(log n)3) time. The algorithm requires virtually no memory for the storage of an array or matrix so the one-millionth digit of π can be computed using a pocket calculator.[57] However, it would be quite tedious and impractical to do so.

text: The calculation speed of Plouffe's formula was improved to O(n2) by Fabrice Bellard, who derived an alternative formula (albeit only in base 2 math) for computing π.[58]

text: Efficient methods[edit]

text: Many other expressions for π were developed and published by Indian mathematician Srinivasa Ramanujan. He worked with mathematician Godfrey Harold Hardy in England for a number of years.

text: Extremely long decimal expansions of π are typically computed with the Gauss–Legendre algorithm and Borwein's algorithm; the Salamin–Brent algorithm which was invented in 1976 has also been used.

text: In 1997, David H. Bailey, Peter Borwein and Simon Plouffe published a paper (Bailey, 1997) on a new formula for π as an infinite series:

text: This formula permits one to fairly readily compute the kth binary or hexadecimal digit of π, without having to compute the preceding k − 1 digits. Bailey's website contains the derivation as well as implementations in various programming languages. The PiHex project computed 64-bits around the quadrillionth bit of π (which turns out to be 0).

text: Fabrice Bellard further improved on BBP with his formula:[59]

text: This converges extraordinarily rapidly. Ramanujan's work is the basis for the fastest algorithms used, as of the turn of the millennium, to calculate π.

text: Projects[edit]

text: Pi Hex[edit]

text: Pi Hex was a project to compute three specific binary digits of π using a distributed network of several hundred computers. In 2000, after two years, the project finished computing the five trillionth (5*1012), the forty trillionth, and the quadrillionth (1015) bits. All three of them turned out to be 0.[citation needed]

text: Software for calculating π[edit]

text: Over the years, several programs have been written for calculating π to many digits on personal computers.

text: General purpose[edit]

text: Most computer algebra systems can calculate π and other common mathematical constants to any desired precision.

text: Functions for calculating π are also included in many general libraries for arbitrary-precision arithmetic, for instance Class Library for Numbers and MPFR.

text: Special purpose[edit]

text: Programs designed for calculating π may have better performance than general-purpose mathematical software. They typically implement checkpointing and efficient disk swapping to facilitate extremely long-running and memory-expensive computations.

text:
y-cruncher by Alexander Yee[1] is the program which Shigeru Kondo used to compute the current world record number of digits. y-cruncher can also be used to calculate other constants and holds world records for several of them.
PiFast by Xavier Gourdon was the fastest program for Microsoft Windows in 2003. According to its author, it can compute one million digits in 3.5 seconds on a 2.4 GHz Pentium 4.[60] PiFast can also compute other irrational numbers like e and √2. It can also work at lesser efficiency with very little memory (down to a few tens of megabytes to compute well over a billion (109) digits). This tool is a popular benchmark in the overclocking community. PiFast 4.4 is available from Stu's Pi page. PiFast 4.3 is available from Gourdon's page.
QuickPi by Steve Pagliarulo for Windows is faster than PiFast for runs of under 400 million digits. Version 4.5 is available on Stu's Pi Page below. Like PiFast, QuickPi can also compute other irrational numbers like e, √2, and √3. The software may be obtained from the Pi-Hacks Yahoo! forum, or from Stu's Pi page.
Super PI by Kanada Laboratory[61] in the University of Tokyo is the program for Microsoft Windows for runs from 16,000 to 33,550,000 digits. It can compute one million digits in 40 minutes, two million digits in 90 minutes and four million digits in 220 minutes on a Pentium 90 MHz. Super PI version 1.1 is available from Super PI 1.1 page.

text: Notes[edit]

text:
^ Jump up to: a b c Yee, Alexander J. (2016). "y-cruncher: A Multi-Threaded Pi Program". Retrieved 28 March 2017.
Jump up ^ Petrie, W.M.F. Wisdom of the Egyptians (1940)
Jump up ^ Based on the Great Pyramid of Giza, supposedly built so that the circle whose radius is equal to the height of the pyramid has a circumference equal to the perimeter of the base (it is 1760 cubits around and 280 cubits in height). Verner, Miroslav. The Pyramids: The Mystery, Culture, and Science of Egypt's Great Monuments. Grove Press. 2001 (1997). ISBN 0-8021-3935-3
^ Jump up to: a b Rossi, Corinna Architecture and Mathematics in Ancient Egypt, Cambridge University Press. 2007. ISBN 978-0-521-69053-9.
Jump up ^ Legon, J. A. R. On Pyramid Dimensions and Proportions (1991) Discussions in Egyptology (20) 25-34 [1]
Jump up ^ See #Imputed biblical value. There has been concern over the apparent biblical statement of π ≈ 3 from the early times of rabbinical Judaism, addressed by Rabbi Nehemiah in the 2nd century. Petr Beckmann, A History of Pi, St. Martin's (1971).[page needed]
Jump up ^ David Gilman Romano, Athletics and Mathematics in Archaic Corinth: The Origins of the Greek Stadion, American Philosophical Society, 1993, p. 78. "A group of mathematical clay tablets from the Old Babylonian Period, excavated at Susa in 1936, and published by E.M. Bruins in 1950, provide the information that the Babylonian approximation of π was 3 1/8 or 3.125."
Jump up ^ E. M. Bruins, Quelques textes mathématiques de la Mission de Suse, 1950.
Jump up ^ E. M. Bruins and M. Rutten, Textes mathématiques de Suse, Mémoires de la Mission archéologique en Iran vol. XXXIV (1961).
Jump up ^ See also Beckmann 1971, pp. 12, 21–22 "in 1936, a tablet was excavated some 200 miles from Babylon. ... The mentioned tablet, whose translation was partially published only in 1950, ... states that the ratio of the perimeter of a regular hexagon to the circumference of the circumscribed circle equals a number which in modern notation is given by 57/60+36/(60)2 [i.e. π = 3/0.96 = 25/8]".
Jump up ^ Katz, Victor J. (ed.), Imhausen, Annette et al. The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton University Press. 2007. ISBN 978-0-691-11485-9
Jump up ^ Chaitanya, Krishna. A profile of Indian culture. Indian Book Company (1975). P. 133.
Jump up ^ http://uzweb.uz.ac.zw/science/maths/zimaths/pi.htm[permanent dead link]
Jump up ^ Lam, Lay Yong; Ang, Tian Se (1986), "Circle measurements in ancient China", Historia Mathematica, 13 (4): 325–340, MR 875525, doi:10.1016/0315-0860(86)90055-8 . Reprinted in Berggren, J. L.; Borwein, Jonathan M.; Borwein, Peter, eds. (2004), Pi: A Source Book, Springer, pp. 20–35, ISBN 9780387205717 . See in particular pp. 333–334 (pp. 28–29 of the reprint).
Jump up ^ Āryabhaṭīya (gaṇitapāda 10):

chaturadhikam śatamaṣṭaguṇam dvāśaṣṭistathā sahasrāṇām ayutadvayaviṣkambhasyāsanno vr̥ttapariṇahaḥ.
"Add four to one hundred, multiply by eight and then add sixty-two thousand. The result is approximately the circumference of a circle of diameter twenty thousand. By this rule the relation of the circumference to diameter is given."

In other words, (4 + 100) × 8 + 62000 is the circumference of a circle with diameter 20000. This provides a value of π ≈ 62832/20000 = 3.1416, Jacobs, Harold R. (2003). Geometry: Seeing, Doing, Understanding (Third Edition). New York: W.H. Freeman and Company. p. 70.
Jump up ^ "Aryabhata the Elder". University of St Andrews, School of Mathematics and Statistics. Retrieved 20 July 2011.
Jump up ^ S. Balachandra Rao (1998). Indian Mathematics and Astronomy: Some Landmarks. Bangalore: Jnana Deep Publications. ISBN 81-7371-205-0.
Jump up ^ George E. Andrews, Ranjan Roy; Richard Askey (1999). Special Functions. Cambridge University Press. p. 58. ISBN 0-521-78988-5.
Jump up ^ Gupta, R. C. (1992). "On the remainder term in the Madhava–Leibniz's series". Ganita Bharati. 14 (1-4): 68–71.
Jump up ^ Al-Kashi, author: Adolf P. Youschkevitch, chief editor: Boris A. Rosenfeld, p. 256
Jump up ^ Azarian, Mohammad K. (2010), "al-Risāla al-muhītīyya: A Summary", Missouri Journal of Mathematical Sciences, 22 (2): 64–85
Jump up ^ https://docs.google.com/viewer?a=v&q=cache:NTSdP7wNFA8J:www.ijpam.eu/contents/2003-7-2/4/4.pdf+&hl=en&gl=uk&pid=bl&srcid=ADGEESjTAd8gQzDqGaN7fo99joDgBNmLm4PCsT69_vWR13A0nR6yT0T-RZFFSpqN-djir-w4lBOV2Juacul9apQNCW2KMOxf0csRinFDa-1DOSRpxTk83Cg4i8qAxvylfWoLRM04qjE8&sig=AHIEtbSw0AiTGzbt4uLFRLrbOXiXNknJCg
Jump up ^ Sandifer, Edward (2007). "Why 140 Digits of Pi Matter" (PDF). Jurij baron Vega in njegov čas: Zbornik ob 250-letnici rojstva [Baron Jurij Vega and His Times: Celebrating 250 Years]. Ljubljana: DMFA. p. 17. ISBN 978-961-6137-98-0. LCCN 2008467244. OCLC 448882242. We should note that Vega's value contains an error in the 127th digit. Vega gives a 4 where there should be an [6], and all digits after that are incorrect.
^ Jump up to: a b c d e Shanks, D.; Wrench, Jr., J. W. (1962). "Calculation of π to 100,000 decimals". Mathematics of Computation. American Mathematical Society. 16 (77): 76–99. JSTOR 2003813. doi:10.2307/2003813. .
Jump up ^ Announcement at the Kanada lab web site.
Jump up ^ Treub, Peter (30 November 2016). "Digit Statistics of the First 22.4 Trillion Decimal Digits of Pi". arXiv:1612.00489  [math.NT].
Jump up ^ Yee, Alexander J.; Kondo, Shigeru (December 2013). "12.1 Trillion Digits of Pi, And we're out of disk space...".
Jump up ^ "Pi Computation Record".
Jump up ^ McCormick Grad Sets New Pi Record Archived 28 September 2011 at the Wayback Machine.
Jump up ^ "Pi - 5 Trillion Digits".
Jump up ^ By Glenn (2011-10-19). "Short Sharp Science: Epic pi quest sets 10 trillion digit record". Newscientist.com. Retrieved 2016-04-18.
Jump up ^ Alexander J. Yee; Shigeru Kondo (22 October 2011). "Round 2... 10 Trillion Digits of Pi".
Jump up ^ Alexander J. Yee; Shigeru Kondo (28 December 2013). "12.1 Trillion Digits of Pi".
Jump up ^ "y-cruncher - A Multi-Threaded Pi Program". www.numberworld.org. Retrieved 2016-11-29.
Jump up ^ Tsaban, Boaz; Garber, David (February 1998). "On the rabbinical approximation of π" (PDF). Historia Mathematica. 25 (1): 75–84. ISSN 0315-0860. doi:10.1006/hmat.1997.2185. Retrieved 14 July 2009.
Jump up ^ Wilbur Richard Knorr, The Ancient Tradition of Geometric Problems, New York: Dover Publications, 1993.
Jump up ^ Aleff, H. Peter. "Ancient Creation Stories told by the Numbers: Solomon's Pi". recoveredscience.com. Archived from the original on 14 October 2007. Retrieved 30 October 2007.
Jump up ^ O'Connor, J J; E F Robertson (August 2001). "A history of Pi". Archived from the original on 30 October 2007. Retrieved 30 October 2007.
Jump up ^ Math Forum – Ask Dr. Math
Jump up ^ "Indiana's squared circle" by Arthur E. Hallerberg (Mathematics Magazine, vol. 50 (1977), pp. 136–140)
Jump up ^ Eves 1992, p. 131
Jump up ^ Beckmann 1971, p. 66
Jump up ^ Eves 1992, p. 118
^ Jump up to: a b Eves 1992, p. 119
Jump up ^ Beckmann 1971, pp. 94–95
Jump up ^ "Pi Formulas - from Wolfram MathWorld". Mathworld.wolfram.com. 2016-04-13. Retrieved 2016-04-18.
Jump up ^ "What can you do with a supercomputer? - ExtremeTech".
Jump up ^ Gardner, Martin (1995). "New Mathematical Diversions". Mathematical Association of America: 92 .
Jump up ^ A nested radical approximation for π Archived 6 July 2011 at the Wayback Machine.
Jump up ^ "Lost notebook page 16" ,Ramanujan
Jump up ^ Hoffman, D.W. College Mathematics Journal, 40 (2009) 399
Jump up ^ "Mathematics".
Jump up ^ "Sloane's A002485 : Numerators of convergents to Pi". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Jump up ^ "Sloane's A002486 : Denominators of convergents to Pi". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Jump up ^ "Fractional Approximations of Pi".
Jump up ^ MathWorld: BBP Formula Wolfram.com
Jump up ^ Simon Plouffe, On the computation of the n'th decimal digit of various transcendental numbers, November 1996; Revised December 2009
Jump up ^ Bellard's Website: Bellard.org
Jump up ^ "The world of Pi - Bellard". Pi314.net. 2013-04-13. Retrieved 2016-04-18.
Jump up ^ "PiFast timings"
Jump up ^ Takahashi, Daisuke; Kanada, Yasumasa (10 August 2010). "Kanada Laboratory home page". University of Tokyo. Archived from the original on 24 August 2011. Retrieved 1 May 2011.


document_title: Blu-ray

question_text: what was the first blu ray movie released

question_tokens: what was the first blu ray movie released

text: Blu-ray

text: History[edit]

text: Early history[edit]

text: The information density of the DVD format was limited by the wavelength of the laser diodes used. Following protracted development, blue laser diodes operating at 405 nanometers became available on a production basis, allowing for development of a more-dense storage format that could hold higher-definition media. Sony started two projects in collaboration with Philips[13] applying the new diodes: UDO (Ultra Density Optical),[14] and DVR Blue (together with Pioneer),[15] a format of rewritable discs that would eventually become Blu-ray Disc (more specifically, BD-RE). The core technologies of the formats are similar. The first DVR Blue prototypes were unveiled at the CEATEC exhibition in October 2000 by Sony.[16] A trademark for the "Blue Disc" logo was filed February 9, 2001.[17] On February 19, 2002, the project was officially announced as Blu-ray Disc,[18][19] and Blu-ray Disc Founders was founded by the nine initial members.

text: The first consumer device arrived in stores on April 10, 2003: the Sony BDZ-S77, a US$3,800 BD-RE recorder that was made available only in Japan.[20] But there was no standard for prerecorded video, and no movies were released for this player. Hollywood studios insisted that players be equipped with digital rights management before they would release movies for the new format, and they wanted a new DRM system that would be more secure than the failed Content Scramble System (CSS) used on DVDs. On October 4, 2004, the name "Blu-ray Disc Founders" was officially changed to the Blu-ray Disc Association (BDA), and 20th Century Fox joined the BDA's Board of Directors.[21] The Blu-ray Disc physical specifications were completed in 2004.[22]

text: In January 2005, TDK announced that they had now developed an ultra-hard yet very thin polymer coating ("Durabis") for Blu-ray discs; this was a significant technical advance because a far tougher protection was desired in the consumer market to protect bare discs against scratching and damage compared to DVD, while technically Blu-ray Disc required a much thinner layer for the denser and higher frequency blue laser.[23] Cartridges, originally used for scratch protection, were no longer necessary and were scrapped. The BD-ROM specifications were finalized in early 2006.[24]

text: AACS LA, a consortium founded in 2004,[25] had been developing the DRM platform that could be used to securely distribute movies to consumers. However, the final AACS standard was delayed,[26] and then delayed again when an important member of the Blu-ray Disc group voiced concerns.[27] At the request of the initial hardware manufacturers, including Toshiba, Pioneer, and Samsung, an interim standard was published that did not include some features, such as managed copy.[28]

text: Launch and sales developments[edit]

text: The first BD-ROM players (Samsung BD-P1000) were shipped in mid-June 2006, though HD DVD players beat them to market by a few months.[29][30] The first Blu-ray Disc titles were released on June 20, 2006: 50 First Dates, The Fifth Element, Hitch, House of Flying Daggers, Underworld: Evolution, xXx (all Sony), Twister (Warner Bros.), and MGM's The Terminator.[31] The earliest releases used MPEG-2 video compression, the same method used on standard DVDs. The first releases using the newer VC-1 and AVC formats were introduced in September 2006.[32] The first movies using 50 GB dual-layer discs were introduced in October 2006.[33] The first audio-only albums were released in May 2008.[34][35]

text: The first mass-market Blu-ray Disc rewritable drive for the PC was the BWU-100A, released by Sony on July 18, 2006.[36] It recorded both single and dual-layer BD-Rs as well as BD-REs and had a suggested retail price of US $699. As of  June 2008[update], more than 2,500 Blu-ray Disc titles were available in Australia and the United Kingdom, with 3,500 in the United States and Canada.[37] In Japan, as of  July 2010[update], more than 3,300 titles have been released.[38]

text: Competition from HD DVD[edit]

text: The DVD Forum, chaired by Toshiba, was split over whether to develop the more expensive blue laser technology. In March 2002 the forum approved a proposal, which was endorsed by Warner Bros. and other motion picture studios. The proposal involved compressing high-definition video onto dual-layer standard DVD-9 discs.[39][40] In spite of this decision, however, the DVD Forum's Steering Committee announced in April that it was pursuing its own blue-laser high-definition video solution. In August, Toshiba and NEC announced their competing standard, Advanced Optical Disc.[41] It was finally adopted by the DVD Forum and renamed HD DVD the next year,[42] after being voted down twice by DVD Forum members who were also Blu-ray Disc Association members—a situation that drew preliminary investigations by the U.S. Department of Justice.[43]

text: HD DVD had a head start in the high-definition video market, as Blu-ray Disc sales were slow to gain market share. The first Blu-ray Disc player was perceived as expensive and buggy, and there were few titles available.[44]

text: The appearance of the Sony PlayStation 3, which contained a Blu-ray Disc player for primary storage, helped support Blu-ray.[45] Sony also ran a more thorough and influential marketing campaign for the format.[46] AVCHD camcorders were also introduced in 2006. These recordings can be played back on many Blu-ray Disc players without re-encoding but are not compatible with HD DVD players. By January 2007, Blu-ray Discs had outsold HD DVDs,[47] and during the first three quarters of 2007, BD outsold HD DVD by about two to one. At CES 2007, Warner proposed Total Hi Def—a hybrid disc containing Blu-ray on one side and HD DVD on the other, but it was never released.

text:
In a June 28, 2007, press release, Twentieth Century Fox cited Blu-ray Disc's adoption of the BD+ anticopying system as key to their decision to support the Blu-ray Disc format.[48][49]
On January 4, 2008, a day before CES 2008, Warner Bros. (the only major studio still releasing movies in both HD DVD and Blu-ray Disc format) announced that it would release only in Blu-ray Disc after May 2008.[50] This effectively included other studios that came under the Warner umbrella, such as New Line Cinema and HBO—though in Europe, HBO distribution partner, the BBC, announced it would, while keeping an eye on market forces, continue to release product on both formats. This led to a chain reaction in the industry, with major U.S. retailers such as Best Buy, Walmart, and Circuit City and Canadian chains such as Future Shop dropping HD DVD in their stores. A then major European retailer, Woolworths, dropped HD DVD from its inventory.[51] Netflix and Blockbuster—major DVD rental companies—said they would no longer carry HD DVD.

text: Following these new developments, on February 19, 2008, Toshiba announced it would end production of HD DVD devices,[52] allowing Blu-ray Disc to become the industry standard for high-density optical discs. Universal Studios, the sole major movie studio to back HD DVD since its inception, said shortly after Toshiba's announcement: "While Universal values the close partnership we have shared with Toshiba, it is time to turn our focus to releasing new and catalog titles on Blu-ray Disc."[53] Paramount Pictures, which started releasing movies only in HD DVD format during late 2007, also said it would start releasing in Blu-ray Disc. Both studios announced initial Blu-ray lineups in May 2008. With this, all major Hollywood studios supported Blu-ray.[54]

text: Future scope and market trends[edit]

text: This article needs to be updated. Please update this article to reflect recent events or newly available information. (April 2018)

tag: table

text: According to Media Research, high-definition software sales in the US were slower in the first two years than DVD software sales.[10] 16.3 million DVD software units were sold in the first two years (1997–98) compared to 8.3 million high-definition software units (2006–07).[10][55] One reason given for this difference was the smaller marketplace (26.5 million HDTVs in 2007 compared to 100 million SDTVs in 1998).[55] Former HD DVD supporter Microsoft did not make a Blu-ray Disc drive for the Xbox 360.[56] The 360's successor Xbox One features a Blu-ray drive, as does the PS4, with both supporting 3D Blu-ray after later firmware updates.[57][58]

text: Shortly after the "format war" ended, Blu-ray Disc sales began to increase. A study by The NPD Group found that awareness of Blu-ray Disc had reached 60% of U.S. households. Nielsen VideoScan sales numbers showed that for some titles, such as 20th Century Fox's Hitman, up to 14% of total disc sales were from Blu-ray, although the average Blu-ray sales for the first half of the year were only around 5%. In December 2008, the Blu-ray Disc version of The Dark Knight sold 600,000 copies on the first day of its launch in the United States, Canada, and the United Kingdom.[59] A week after the launch, The Dark Knight BD had sold over 1.7 million copies worldwide, making it the first Blu-ray Disc title to sell over a million copies in the first week of release.[60]

text:
Blu-ray Disc sales in United States and Canada

Year

Cumulative sales (millions)

2006
1.2[61]

2007
19.2[61]

2008
82.9[61]

2009
177.2[61]

2010
350[62]

text: According to Singulus Technologies AG, Blu-ray is being adopted faster than the DVD format was at a similar period in its development. This conclusion was based on the fact that Singulus Technologies has received orders for 21 Blu-ray dual-layer machines during the first quarter of 2008, while 17 DVD machines of this type were made in the same period in 1997.[63] According to GfK Retail and Technology, in the first week of November 2008, sales of Blu-ray recorders surpassed DVD recorders in Japan.[64] According to the Digital Entertainment Group, the number of Blu-ray Disc playback devices (both set-top box and game console) sold in the U.S. had reached 28.5 million by the end of 2010.[62]

text: Blu-ray faces competition from video on demand[65] and from new technologies that allow access to movies on any format or device, such as Digital Entertainment Content Ecosystem or Disney's Keychest.[66] Some commentators have suggested that renting Blu-ray will play a vital part in keeping the technology affordable while allowing it to move forward.[67] In an effort to increase sales, studios are releasing movies in combo packs with Blu-ray Discs and DVDs as well as digital copies that can be played on computers and mobile devices. Some are released on "flipper" discs with Blu-ray on one side and DVD on the other. Other strategies are to release movies with the special features only on Blu-ray Discs and none on DVDs.

text: Beyond Blu-ray Disc[edit]

text: The Holographic Versatile Disc (HVD), described in the ECMA-377 standard, has been in development by The Holography System Development (HSD) Forum using a green writing/reading laser (532 nm) and a red positioning/addressing laser (650 nm). It is to offer MPEG-2, MPEG-4 AVC (H.264), HEVC (H.265), and VC-1 encoding, supporting a maximum storage capacity of 6TB.[68] No systems corresponding to the Ecma International HVD standard have been released.[69] Because the Blu-ray Disc format is upgradable it poses challenges to the adoption of the HVD format. 4K Blu-ray discs and players became available in the first quarter of 2016, having a storage capacity of up to 100 GB.[70][71]

text: Ongoing development[edit]

text: Although the Blu-ray Disc specification has been finalized, engineers continue to work on advancing the technology. By 2005, quad-layer (128 GB) discs had been demonstrated on a drive with modified optics[72] and standard unaltered optics.[73] Hitachi stated that such a disc could be used to store 7 hours of 32 Mbit/s video (HDTV) or 3 hours and 30 minutes of 64 Mbit/s video (ultra-high-definition television). In August 2006, TDK announced that they had created a working experimental Blu-ray Disc capable of holding 200 GB of data on a single side, using six 33 GB data layers.[74]

text: Also, behind closed doors at CES 2007, Ritek revealed that they had successfully developed a high-definition optical disc process that extends the disc capacity to ten layers, which increases the capacity of the discs to 250 GB. However, they noted that the major obstacle is that current read/write technology does not allow additional layers.[75] JVC has developed a three-layer technology that allows putting both standard-definition DVD data and HD data on a BD/(standard) DVD combination.[76] This would have enabled the consumer to purchase a disc that can be played on DVD players and can also reveal its HD version when played on a BD player.[77] Japanese optical disc manufacturer Infinity announced the first "hybrid" Blu-ray Disc/(standard) DVD combo, to be released February 18, 2009. This disc set of the TV series "Code Blue" featured four hybrid discs containing a single Blu-ray Disc layer (25 GB) and two DVD layers (9 GB) on the same side of the disc.[78]

text:
In January 2007, Hitachi showcased a 100 GB Blu-ray Disc, consisting of four layers containing 25 GB each.[79] Unlike TDK's and Panasonic's 100 GB discs, they claim this disc is readable on standard Blu-ray Disc drives that are currently in circulation, and it is believed that a firmware update is the only requirement to make it readable to current players and drives.[80]
In December 2008, Pioneer Corporation unveiled a 400 GB Blu-ray Disc (containing 16 data layers, 25 GB each) that will be compatible with current players after a firmware update. Its planned launch was in the 2009–10 time frame for ROM and 2010–13 for rewritable discs. Ongoing development was underway to create a 1 TB Blu-ray Disc.[81]

text: At CES 2009, Panasonic unveiled the DMP-B15, the first portable Blu-ray Disc player, and Sharp introduced the LC-BD60U and LC-BD80U series, the first LCD HDTVs with integrated Blu-ray Disc players. Sharp has also announced that they will sell HDTVs with integrated Blu-ray Disc recorders in the United States by the end of 2009. Set-top box recorders were not being sold in the U.S. for fear of unauthorized copying. However, personal computers with Blu-ray recorder drives were available. On January 1, 2010, Sony, in association with Panasonic, announced plans to increase the storage capacity on their Blu-ray Discs from 25 GB to 33.4 GB via a technology called i-MLSE (Maximum likelihood Sequence Estimation). The higher-capacity discs, according to Sony, would be readable on existing Blu-ray Disc players with a firmware upgrade.[82] This technology is later used on BDXL discs.[83]

text: On July 20, 2010, the research team of Sony and Japanese Tohoku University announced the joint development of a blue-violet laser,[84] to help create Blu-ray discs with a capacity of 1 TB using only two layers (and potentially more than 1 TB with additional layering). By comparison, the first blue laser was invented in 1996, with the first prototype discs coming four years later.

text: On January 7, 2013, Sony announced that it would release "Mastered in 4K" Blu-ray Disc titles which are sourced at 4K and encoded at 1080p.[85] "Mastered in 4K" Blu-ray Disc titles can be played on existing Blu-ray Disc players and have a larger color space using xvYCC.[85][86] On January 14, 2013, Blu-ray Disc Association president, Andy Parsons, stated that a task force was created three months prior to conduct a study concerning an extension to the Blu-ray Disc specification that would add the ability to contain 4K Ultra HD video.[87][88]

text: On August 5, 2015, The Blu-ray Disc Association (BDA) announced it will commence licensing the Ultra HD Blu-ray format starting August 24, 2015. The Ultra HD Blu-ray format delivered high dynamic range content that significantly expanded the range between the brightest and darkest elements, expanded color range, high frame rate (up to 60fps) and up to 3840×2160 resolution, object-based sound formats, and an optional "digital bridge" feature. New players were required to play this format, which were able to play both DVDs, traditional Blu-rays and the new format. New Ultra HD Blu-ray discs hold up to 66 GB and 100 GB of data on dual- and triple-layer discs, respectively.[89]

text: Physical media[edit]

text:
Type

Diameter(cm)

Layers

Capacity

Bytes

Standard disc size, single layer
12
1
25,025,314,816

Standard disc size, dual layer
12
2
50,050,629,632

Standard disc size, XL 3 layer[90]
12
3
100,103,356,416

Standard disc size, XL 4 layer[90]
12
4
128,001,769,472

Mini disc size, single layer
8
1
7,791,181,824

Mini disc size, dual layer
8
2
15,582,363,648

text: Laser and optics[edit]

text: While a DVD uses a 650 nm red laser, Blu-ray Disc uses a 405 nm "blue" laser diode. Although the laser is called "blue", its color is actually in the violet range. The shorter wavelength can be focused to a smaller area, thus enabling it to read information recorded in pits that are less than half the size of those on a DVD, and can consequently be spaced more closely, resulting in a shorter track pitch, enabling a Blu-ray Disc to hold about five times the amount of information that can be stored on a DVD. The lasers are GaN (gallium nitride) laser diodes that produce 405 nm light directly, that is, without frequency doubling or other nonlinear optical mechanisms.[91] Conventional DVDs use 650 nm red lasers, and CDs use 780 nm near-infrared lasers.

text: The minimum "spot size" on which a laser can be focused is limited by diffraction and depends on the wavelength of the light and the numerical aperture of the lens used to focus it. By decreasing the wavelength, increasing the numerical aperture from 0.60 to 0.85, and making the cover layer thinner to avoid unwanted optical effects, designers can cause the laser beam to focus on a smaller spot, which effectively allows more information to be stored in the same area.[92] For Blu-ray Disc, the spot size is 580 nm.[93] This allows a reduction of the pit size from 400 nm for DVD to 150 nm for Blu-ray Disc, and of the track pitch from 740 nm to 320 nm.[92] See compact disc for information on optical discs' physical structure. In addition to the optical improvements, Blu-ray Discs feature improvements in data encoding that further increase the amount of content that can be stored.[94]

text: Hard-coating technology[edit]

text: Since the Blu-ray Disc data layer is closer to the surface of the disc compared to the DVD standard, it was more vulnerable to scratches in early designs.[95] The first discs were therefore housed in cartridges for protection, resembling Professional Discs introduced by Sony in 2003. Using a cartridge would increase the price of an already expensive medium, so designers chose hard-coating of the pickup surface instead. TDK was the first company to develop a working scratch-protection coating for Blu-ray Discs, naming it Durabis. In addition, both Sony's and Panasonic's replication methods include proprietary hard-coat technologies. Sony's rewritable media are spin-coated, using a scratch-resistant and antistatic coating. Verbatim's recordable and rewritable Blu-ray Discs use their own proprietary technology, called Hard Coat.[96]

text: The Blu-ray Disc specification requires the testing of resistance to scratches by mechanical abrasion.[92] In contrast, DVD media are not required to be scratch-resistant, but since development of the technology, some companies, such as Verbatim, implemented hard-coating for more expensive lines of recordable DVDs.

text: Drive speeds[edit]

text:
BD drive speeds

Drive speed

Data rate

~Write time (minutes)

Mbit/s
MB/s
Single-Layer
Dual-Layer

1×
36
4.5
90
180

2×
72
9
45
90

4×
144
18
22.5
45

6×
216
27
15
30

8×
288
36
11.25
22.5

10×
360
45
9
18

12×

432
54
7.5
15

14×

504
63
6.5
13

16×

576
72
5.7
11.5

text: The table shows the speeds available. Even the lowest speed (1×) is sufficient to play and record real-time 1080p video; the higher speeds are relevant for general data storage and more sophisticated handling of video. BD discs are designed to cope with at least 5000rpm of rotational speed.

text: The usable data rate of a Blu-ray Disc drive can be limited by the capacity of the drive's data interface. With a USB 2.0 interface, the maximum exploitable drive speed is 288 Mbit/s or 36 MB/s (also called 8× speed).[97] A USB 3.0 interface (with proper cabling) does not have this limitation,[98] nor do even the oldest version of Serial ATA (SATA, 150 MB/s)[99] nor the latest Parallel ATA (133 MB/s) standards. Blu-ray drives that are integrated into a computer (as opposed to physically separate and connected via a cable) typically have a SATA interface.[100]

text: Packaging[edit]

text: Pre-recorded Blu-ray Disc titles usually ship in packages similar to but slightly smaller (18.5 mm shorter and 2 mm thinner: 135 mm × 171.5 mm × 13 mm[101]), as well as more rounded than a standard DVD keep case, generally with the format prominently displayed in a horizontal stripe across the top of the case (translucent blue for Blu-ray video discs, clear for Blu-ray 3D video releases, red for PlayStation 3 Greatest Hits Games, transparent for regular PlayStation 3 games, transparent dark blue for PlayStation 4 games, transparent green for Xbox One games and black for Ultra HD Blu-ray video releases). Warren Osborn and The Seastone Media Group, LLC created the package that was adopted worldwide following the Blu-ray versus HD DVD market adoption choice.[102] Because of the fact that Blu-ray cases are smaller than DVD cases, more Blu-Rays than DVDs can fit on a shelf, making Blu-ray an arguably better choice for situations with limited storage space.

text: Variants[edit]

text: Mini Blu-ray Disc[edit]

text: The "Mini Blu-ray Disc" (also, "Mini-BD" and "Mini Blu-ray") is a compact 8-centimetre-diameter (~3 in) variant of the Blu-ray Disc that can store 7.8 GB of data in its single layer configuration, or 15.6 GB on a dual layer disc.[103] It is similar in concept to the MiniDVD and MiniCD. Recordable (BD-R) and rewritable (BD-RE) versions of Mini Blu-ray Disc have been developed specifically for compact camcorders and other compact recording devices.[104]

text: Blu-ray Disc recordable[edit]

text: "Blu-ray Disc recordable" refers to two optical disc formats that can be recorded with an optical disc recorder. BD-Rs can be written to once, whereas BD-REs can be erased and re-recorded multiple times. The current practical maximum speed for Blu-ray Discs is about 12× (54 MB/s).[105](1.7) Higher speeds of rotation (10,000+ rpm) cause too much wobble for the discs to be written properly,[citation needed] as with the 20× (27.7 MB/s) and 52× (7.8 MB/s) maximum speeds, respectively, of standard DVDs and CDs. Since September 2007, BD-RE is also available in the smaller 8 cm Mini Blu-ray Disc size.[104][106]

text: On September 18, 2007, Pioneer and Mitsubishi codeveloped BD-R LTH ("Low to High" in groove recording), which features an organic dye recording layer that can be manufactured by modifying existing CD-R and DVD-R production equipment, significantly reducing manufacturing costs.[107] In February 2008, Taiyo Yuden, Mitsubishi, and Maxell released the first BD-R LTH Discs,[108] and in March 2008, Sony's PlayStation 3 officially gained the ability to use BD-R LTH Discs with the 2.20 firmware update.[109] In May 2009 Verbatim/Mitsubishi announced the industry's first 6X BD-R LTH media, which allows recording a 25 GB disc in about 16 minutes.[110] Unlike with the previous releases of 120 mm optical discs (i.e. CDs and standard DVDs), Blu-ray recorders hit the market almost simultaneously with Blu-ray's debut.

text: BD9 and BD5[edit]

text: The BD9 format was proposed to the Blu-ray Disc Association by Warner Home Video as a cost-effective alternative to the 25/50 GB BD-ROM discs. The format was supposed to use the same codecs and program structure as Blu-ray Disc video but recorded onto less expensive 8.5 GB dual-layer DVD. This red-laser media could be manufactured on existing DVD production lines with lower costs of production than the 25/50 GB Blu-ray media.[111]

text: Usage of BD9 for releasing content on "pressed" discs never caught on. With the end of the format war, manufacturers ramped production of Blu-ray Discs and lowered prices to compete with DVDs. On the other hand, the idea of using inexpensive DVD media became popular among individual users. A lower-capacity version of this format that uses single-layer 4.7 GB DVDs has been unofficially called BD5. Both formats are being used by individuals for recording high-definition content in Blu-ray format onto recordable DVD media.[112][113] Despite the fact that the BD9 format has been adopted as part of the BD-ROM basic format, none of the existing Blu-ray player models explicitly claim to be able to read it. Consequently, the discs recorded in BD9 and BD5 formats are not guaranteed to play on standard Blu-ray Disc players. AVCHD and AVCREC also use inexpensive media like DVDs, but unlike BD9 and BD5 these formats have limited interactivity, codec types, and data rates. As of March 2011, BD9 was removed as an official BD-ROM disc.[114]

text: BDXL[edit]

text: The BDXL format allows 100 GB and 128 GB write-once discs,[115][116] and 100 GB rewritable discs for commercial applications. It was defined in June 2010.[citation needed] BD-R 3.0 Format Specification (BDXL) defined a multi-layered disc recordable in BDAV format with the speed of 2× and 4×, capable of 100/128 GB and usage of UDF2.5/2.6.[117] BD-RE 4.0 Format Specification (BDXL) defined a multi-layered disc rewritable in BDAV with the speed of 2× and 4×, capable of 100 GB and usage of UDF2.5 as file system.[118]

text: IH-BD[edit]

text: The IH-BD (Intra-Hybrid Blu-ray) format includes a 25 GB rewritable layer (BD-RE) and a 25 GB write-once layer (BD-ROM), designed to work with existing Blu-ray Discs.[115][116]

text: Data format standards[edit]

text: Filesystem[edit]

text: Blu-ray Disc specifies the use of Universal Disk Format (UDF) 2.50 as a convergent-friendly format for both PC and consumer electronics environments. It is used in the latest specifications of BD-ROM, BD-RE, and BD-R.[119][120][121] In the first BD-RE specification (defined in 2002), the BDFS (Blu-ray Disc File System) was used. The BD-RE 1.0 specification was defined mainly for the digital recording of high-definition television (HDTV) broadcast television. The BDFS was replaced by UDF 2.50 in the second BD-RE specification in 2005, in order to enable interoperability among consumer electronics Blu-ray recorders and personal computer systems. These optical disc recording technologies enabled PC recording and playback of BD-RE.[121][122][123] BD-R can use UDF 2.50/2.60.[124]

text: The Blu-ray Disc application for recording of digital broadcasting has been developed as System Description Blu-ray Rewritable Disc Format part 3 Audio Visual Basic Specifications (BDAV). The requirements related with computer file system have been specified in System Description Blu-ray Rewritable Disc Format part 2 File System Specifications version 1.0 (BDFS).[125] Initially, the BD-RE version 1.0 (BDFS) was specifically developed for recording of digital broadcasts using the Blu-ray Disc application (BDAV application). But these requirements are superseded by the Blu-ray Rewritable Disc File System Specifications version 2.0 (UDF) (a.k.a. RE 2.0) and Blu-ray Recordable Disc File System Specifications version 1.0 (UDF) (a.k.a. R 1.0). Additionally, a new application format, BDMV (System Description Blu-ray Disc Prerecorded Format part 3 Audio Visual Basic Specifications) for High Definition Content Distribution was developed for BD-ROM. The only file system developed for BDMV is the System Description Blu-ray Read-Only Disc Format part 2 File System Specifications version 1.0 (UDF) which defines the requirements for UDF 2.50.[121][125]

text: Application format[edit]

text:
BDAV or BD-AV (Blu-ray Disc Audio/Visual):[121][125][126][127] a consumer-oriented Blu-ray video format used for audio/video recording (defined in 2002).
BDMV or BD-MV (Blu-ray Disc Movie):[119][120][121][125][127][128] a Blu-ray video format with menu capability commonly used for movie releases.
BDMV Recording specification (defined in September 2006 for BD-RE and BD-R).[120][129]
RREF (Realtime Recording and Editing Format): a subset of BDMV designed for real-time recording and editing applications.[129]
HFPA (High Fidelity Pure Audio): A high definition audio disc using the Blu-ray format

text: Directory and file structure[edit]

text: All BDMV application files are stored under a "BDMV" directory.[130][131][132][133]

text:
BDMV directory: contains the PLAYLIST, CLIPINF, STREAM, AUXDATA and BACKUP directories.
PLAYLIST directory: contains the Database files for Movie PlayLists.
xxxxx.mpls files: store information corresponding to Movie PlayLists. One file is created for each Movie PlayList. The filenames of these files are in the form "xxxxx.mpls", where "xxxxx" is a 5-digit number corresponding to the Movie PlayList.
CLIPINF directory: contains the Database files for Clips.
zzzzz.clpi files: store Clip information associated with a Clip AV stream file. The filenames of these files are in the form "zzzzz.clpi", where "zzzzz" is a 5-digit number corresponding to the Clip.
STREAM directory: contains AV stream files.
zzzzz.m2ts file: contains a BDAV MPEG-2 transport stream. The names of these files are in the form "zzzzz.m2ts", where "zzzzz" is a 5-digit number corresponding to the Clip. The same 5-digit number "zzzzz" is used for an AV stream file and its associated Clip information file.
SSIF directory: If used, Stereoscopic Interleaved files shall be placed under this directory.
zzzzz.ssif file: is a Stereoscopic Interleaved file that is composed from two BDAV MPEG-2 transport streams. Both of the streams include an MPEG-4 MVC view video stream for left eye or right eye respectively. This file is used only when 3D video is played back. The 5-digit number "zzzzz" is the same as the number used for the AV stream file "zzzzz.m2ts" that includes the MPEG-4 MVC Base view video stream.
AUXDATA directory: contains Sound data files and Font files.
sound.bdmv file: stores data relating to one or more sounds associated with HDMV Interactive Graphic streams applications. This file may or may not exist under the AUXDATA directory. If it exists, there shall be only one sound.bdmv file.
aaaaa.otf file: stores the font information associated with Text subtitle applications. The names of these files are in the form "aaaaa.otf", where "aaaaa" is a 5-digit number corresponding to the Font.
BACKUP directory: contains copies of the "index.bdmv" file, the "MovieObject.bdmv" file, all the files in the PLAYLIST directory and all files in the CLIPINF directory.
index.bdmv file: stores information describing the contents of the BDMV directory. There is only one index.bdmv file under the BDMV directory.
MovieObject.bdmv file: stores information for one or more Movie Objects. There is only one MovieObject.bdmv under the BDMV directory.

text: Media format[edit]

text: Container format[edit]

text: Audio, video, and other streams are multiplexed and stored on Blu-ray Discs in a container format based on the MPEG transport stream. It is also known as BDAV MPEG-2 transport stream and can use filename extension .m2ts.[130][134] Blu-ray Disc titles authored with menus are in the BDMV (Blu-ray Disc Movie) format and contain audio, video, and other streams in BDAV container.[135][136] There is also the BDAV (Blu-ray Disc Audio/Visual) format, the consumer oriented alternative to the BDMV format used for movie releases. The BDAV format is used on BD-REs and BD-Rs for audio/video recording.[136] BDMV format was later defined also for BD-RE and BD-R (in September 2006, in the third revision of BD-RE specification and second revision of BD-R specification).[119][120]

text: Blu-ray Disc employs the MPEG transport stream recording method. That enables transport streams of digital broadcasts to be recorded as they are broadcast, without altering the format.[137] It also enables flexible editing of a digital broadcast that is recorded as is and where the data can be edited just by rewriting the playback stream. Although it is quite natural, a function for high-speed and easy-to-use retrieval is built in.[137][138] Blu-ray Disc Video use MPEG transport streams, compared to DVD's MPEG program streams. An MPEG transport stream contains one or more MPEG program streams, so this allows multiple video programs to be stored in the same file so they can be played back simultaneously (e.g. with "picture-in-picture" effect).

text: Codecs[edit]

text: The BD-ROM specification mandates certain codec compatibilities for both hardware decoders (players) and movie software (content).[134][139] Windows Media Player does not come with the codecs required to play Blu-ray discs.[140]

text: Video[edit]

text: Originally BD-ROMs stored video up to 1920×1080 pixel resolution at up to 60 (59.94) fields per second. Currently with UHD BD-ROM videos can be stored at a maximum of 3840×2160 pixel resolution at up to 60 (59.94) frames per second, progressively scanned. While most current Blu-ray players and recorders can read and write 1920×1080 video at the full 59.94p and 50p progressive format, new players for the UHD specifications will be able to read at 3840×2160 video at either 59.94p and 50p formats.

text:
Supported video formats[141][142]

Format
Resolution andframe rate
Display aspect ratio

4K UHD [a]

3840×2160 60p
16:9

3840×2160 59.94p
16:9

3840×2160 50p
16:9

3840×2160 25p
16:9

3840×2160 24p
16:9

3840×2160 23.976p
16:9

HD [a]

1920×1080 60p
16:9

1920×1080 59.94p
16:9

1920×1080 50p
16:9

1920×1080 25p
16:9

HD

1920×1080 59.94i [b]
16:9

1920×1080 50i [b]
16:9

1920×1080 24p
16:9

1920×1080 23.976p
16:9

1440×1080 59.94i [b][c]
16:9 [d]

1440×1080 50i [b][c]
16:9 [d]

1440×1080 24p [c]
16:9 [d]

1440×1080 23.976p [c]
16:9 [d]

1280×720 59.94p
16:9

1280×720 50p
16:9

1280×720 24p
16:9

1280×720 23.976p
16:9

SD

720×480 59.94i [b]
4:3 or 16:9 [d]

720×576 50i [b]
4:3 or 16:9 [d]

text:
^ a Only supported on UltraHD Blu-Ray with HEVC video compression standard.
^ b Interlaced formats are listed in fields per second.
^ c MPEG-2 at 1440×1080 was previously not included in a draft version of the specification from March 2005.[143]
^ d These resolutions are stored anamorphically, i.e. they are stretched to the display aspect ratio by the player or display.

text: For video, all players are required to process H.262/MPEG-2 Part 2, H.264/MPEG-4 Part 10: AVC, and SMPTE VC-1.[144] BD-ROM titles with video must store video using one of the three mandatory formats; multiple formats on a single title are allowed. Blu-ray Disc allows video with a bit depth of 8-bits per color YCbCr with 4:2:0 chroma subsampling.[145][146] The choice of formats affects the producer's licensing/royalty costs as well as the title's maximum run time, due to differences in compression efficiency. Discs encoded in MPEG-2 video typically limit content producers to around two hours of high-definition content on a single-layer (25 GB) BD-ROM. The more-advanced video formats (VC-1 and MPEG-4 AVC) typically achieve a video run time twice that of MPEG-2, with comparable quality.

text: MPEG-2 was used by many studios (including Paramount Pictures, which initially used the VC-1 format for HD DVD releases) for the first series of Blu-ray Discs, which were launched throughout 2006.[147] Modern releases are now often encoded in either MPEG-4 AVC or VC-1, allowing film studios to place all content on one disc, reducing costs and improving ease of use. Using these formats also frees a lot of space for storage of bonus content in HD (1080i/p), as opposed to the SD (480i/p) typically used for most titles. Some studios, such as Warner Bros., have released bonus content on discs encoded in a different format than the main feature title. For example, the Blu-ray Disc release of Superman Returns uses VC-1 for the feature film and MPEG-2 for some of its bonus content.[148] Today, Warner and other studios typically provide bonus content in the video format that matches the feature.

text: Audio[edit]

text: For audio, BD-ROM players are required to implement Dolby Digital (AC-3), DTS, and linear PCM. Players may optionally implement Dolby Digital Plus and DTS-HD High Resolution Audio as well as lossless formats Dolby TrueHD and DTS-HD Master Audio.[149] BD-ROM titles must use one of the mandatory schemes for the primary soundtrack. A secondary audiotrack, if present, may use any of the mandatory or optional codecs.

text:
Specification of BD-ROM Primary audio streams[150]

LPCM (uncompressed)
Dolby Digital
Dolby Digital Plus
Dolby TrueHD (lossless)
DTS Digital Surround
DTS-HD Master Audio (lossless)
DRA
DRA extension

Max. bitrate
27.648 Mbit/s
640 kbit/s
4.736 Mbit/s
18.64 Mbit/s
1.524 Mbit/s
24.5 Mbit/s
1.5 Mbit/s
3.0 Mbit/s

Max. channel
8 (48 kHz, 96 kHz), 6 (192 kHz)
5.1
7.1
8 (48 kHz, 96 kHz), 6 (192 kHz)
5.1
8 (48 kHz, 96 kHz), 6 (192 kHz)
5.1
7.1

Bits/sample
16, 20, 24
16, 24
16, 24
16, 24
16, 20, 24
16, 24
16
16

Sample frequency
48 kHz, 96 kHz, 192 kHz
48 kHz
48 kHz
48 kHz, 96 kHz, 192 kHz
48 kHz
48 kHz, 96 kHz, 192 kHz
48 kHz
48 kHz, 96 kHz

text: Bit rate[edit]

text: For users recording digital television programming, the recordable Blu-ray Disc standard's initial data rate of 36 Mbit/s is more than adequate to record high-definition broadcasts from any source (IPTV, cable/satellite, or terrestrial). BD Video movies have a maximum data transfer rate of 54 Mbit/s, a maximum AV bitrate of 48 Mbit/s (for both audio and video data), and a maximum video bit rate of 40 Mbit/s. This compares to HD DVD movies, which have a maximum data transfer rate of 36 Mbit/s, a maximum AV bitrate of 30.24 Mbit/s, and a maximum video bitrate of 29.4 Mbit/s.[151]

text: Java software interface[edit]

text: At the 2005 JavaOne trade show, it was announced that Sun Microsystems' Java cross-platform software environment would be included in all Blu-ray Disc players as a mandatory part of the standard.[152] Java is used to implement interactive menus on Blu-ray Discs, as opposed to the method used on DVD-video discs. DVDs use pre-rendered MPEG segments and selectable subtitle pictures, which are considerably more primitive and rarely seamless. At the conference, Java creator James Gosling suggested that the inclusion of a Java virtual machine, as well as network connectivity in some BD devices, will allow updates to Blu-ray Discs via the Internet, adding content such as additional subtitle languages and promotional features not included on the disc at pressing time.[153] This Java Version is called BD-J and is built on a profile of the Globally Executable MHP (GEM) standard; GEM is the worldwide version of the Multimedia Home Platform standard.

text: Player profiles[edit]

text: The BD-ROM specification defines four Blu-ray Disc player profiles, including an audio-only player profile (BD-Audio) that does not require video decoding or BD-J. All of the video-based player profiles (BD-Video) are required to have a full implementation of BD-J.

text:
Feature

BD-Audio

BD-Video

Grace Period[d]

Bonus View

BD-Live[e]

Blu-ray 3D

Profile 3.0[c]

Profile 1.0

Profile 1.1

Profile 2.0

Profile 5.0

Built-in persistent memory

Unneeded

64 KB

64 KB

64 KB

64 KB?

Local storage capability[a]

Unneeded

Optional

256 MB

1 GB

1 GB

Secondary video decoder (PiP)

No video

Optional

Mandatory

Mandatory

Mandatory

Secondary audio decoder[b]

Optional

Optional

Mandatory

Mandatory

Mandatory

Virtual file system

Unneeded

Optional

Mandatory

Mandatory

Mandatory

Internet connection capability

No

No

No

Mandatory

Mandatory

text:
^ a This is used for storing audio/video and title updates. It can either be built-in memory or removable media, such as a memory card or USB flash memory.
^ b A secondary audio decoder is typically used for interactive audio and commentary.
^ c Profile 3.0 is a separate audio-only player profile. The first Blu-ray Disc album to be released was Divertimenti, by record label Lindberg Lyd, and it has been confirmed to work on the PS3.[154][155]^ d Also known as Initial Standard profile.
^ e Also known as Final Standard profile.

text: On November 2, 2007, the Grace Period Profile was superseded by Bonus View as the minimum profile for new BD-Video players released to the market.[156] When Blu-ray Disc software not authored with interactive features dependent on Bonus View or BD-Live hardware capabilities is played on Profile 1.0 players, it is able to play the main feature of the disc, but some extra features may not be available or will have limited capability.[157]

text: BD-Live[edit]

text: The biggest difference between Bonus View and BD-Live is that BD-Live requires the Blu-ray Disc player to have an Internet connection to access Internet-based content. BD-Live features have included Internet chats, scheduled chats with the director, Internet games, downloadable featurettes, downloadable quizzes, and downloadable movie trailers.[158][159][160] While some Bonus View players may have an Ethernet port, it is used for firmware updates and is not used for Internet-based content.[161] In addition, Profile 2.0 also requires more local storage in order to handle this content.

text: Profile 1.0 players are not eligible for Bonus View or BD-Live compliant upgrades and do not have the function or capability to access these upgrades, with the exception of the latest players and the PlayStation 3. Internet is required to use.[162][163][164]

text: Region codes[edit]

text: As with the implementation of region codes for DVDs, Blu-ray Disc players sold in a specific geographical region are designed to play only discs authorized by the content provider for that region. This is intended to permit content providers (motion picture studios, television production company etc.) to enact regional price discrimination and/or exclusive content licensing. According to the Blu-ray Disc Association, all Blu-ray Disc players and Blu-ray Disc-equipped computer systems are required to enforce regional coding. However, content providers need not use region playback codes.[166] Some current estimates suggest 70% of available [movie] Blu-ray Discs from the major studios are region-code-free and can, therefore, be played on any Blu-ray Disc player, in any region.[167]

text: Movie distributors have different region coding policies. Among major U.S. studios, Walt Disney Pictures, Warner Bros., Paramount Pictures, Universal Studios, and Sony Pictures have released most of their titles region-free.[168][169][170][171][172][173] MGM and Lions Gate Entertainment have released a mix of region-free and region-coded titles.[174][175] 20th Century Fox has released most of their titles region-coded.[176] Vintage film restoration and distribution company The Criterion Collection uses US region coding in all Blu-ray releases.[177][178]

text: The Blu-ray Disc region coding scheme divides the world into three regions, labeled A, B, and C.

text:
Region code

Area

A

The Americas and their dependencies, Taiwan, Hong Kong, Macau, Japan, Korea and Southeast Asia; excludes instances that fall under Region C

B

Africa, Middle East, Southwest Asia, most of Europe, United Kingdom of Great Britain and Northern Ireland, Australia, New Zealand, and their dependencies; excludes instances that fall under Region C

C

Central Asia, mainland China, Mongolia, South Asia, Belarus, Russia, Ukraine, Kazakhstan, Moldova, and their dependencies

FREE

Informal term meaning "worldwide". Region free is not an official setting; discs that bear the region FREE symbol either have no flags set or have all three flags set. Discs with no flags set may not play in some non-compliant players.

ABC

text: In circumvention of region coding restrictions, stand-alone Blu-ray Disc players are sometimes modified by third parties to allow for playback of Blu-ray Discs (and DVDs) with any region code.[179] Instructions ("hacks") describing how to reset the Blu-ray region counter of computer player applications to make them multi-region indefinitely are also regularly posted to video enthusiast websites and forums. Unlike DVD region codes, Blu-ray region codes are verified only by the player software, not by the optical drive's firmware.

text: The latest types of Blu-Ray players, suitable for UltraHD content, is region-free.[180]

text: Digital rights management[edit]

text: The Blu-ray Disc format employs several layers of digital rights management (DRM) which restrict the usage of the discs.[181][182] This has led to extensive criticism of the format by organizations opposed to DRM, such as the Free Software Foundation,[183] and consumers because new releases require player firmware updates to allow disc playback.[184][185]

text: High-bandwidth Digital Content Protection[edit]

text: Blu-ray equipment is required to implement the High-bandwidth Digital Content Protection (HDCP) system to encrypt the data sent by players to rendering devices through physical connections. This is aimed at preventing the copying of copyrighted content as it travels across cables. Through a protocol flag in the media stream called the Image Constraint Token (ICT), a Blu-ray Disc can enforce its reproduction in a lower resolution whenever a full HDCP-compliant link is not used. In order to ease the transition to high definition formats, the adoption of this protection method was postponed until 2011.[186]

text: Advanced Access Content System[edit]

text: The Advanced Access Content System (AACS) is a standard for content distribution and digital rights management. It was developed by AS Licensing Administrator, LLC (AACS LA), a consortium that includes Disney, Intel, Microsoft, Panasonic, Warner Bros., IBM, Toshiba, and Sony. Since the appearance of the format on devices in 2006, several successful attacks have been made on it. The first known attack relied on the trusted client problem. In addition, decryption keys have been extracted from a weakly protected player (WinDVD). Since keys can be revoked in newer releases,[187] this is only a temporary attack, and new keys must continually be discovered in order to decrypt the latest discs.

text: BD+[edit]

text: BD+ was developed by Cryptography Research Inc. and is based on their concept of Self-Protecting Digital Content.[188] BD+, effectively a small virtual machine embedded in authorized players, allows content providers to include executable programs on Blu-ray Discs. Such programs can:[181]

text:
Examine the host environment to see if the player has been tampered with. Every licensed playback device manufacturer must provide the BD+ licensing authority with memory footprints that identify their devices.
Verify that the player's keys have not been changed
Execute native code, possibly to patch an otherwise insecure system
Transform the audio and video output. Parts of the content will not be viewable without letting the BD+ program unscramble it.

text: If a playback device manufacturer finds that its devices have been hacked, it can potentially release BD+ code that detects and circumvents the vulnerability. These programs can then be included in all new content releases.[189] The specifications of the BD+ virtual machine are available only to licensed device manufacturers. A list of licensed commercial adopters is available from the BD+ website.

text: The first titles using BD+ were released in October 2007. Since November 2007, versions of BD+ protection have been circumvented by various versions of the AnyDVD HD program.[190][191] Other programs known to be capable of circumventing BD+ protection are DumpHD (versions 0.6 and above, along with some supporting software),[192] MakeMKV,[193] and two applications from DVDFab (Passkey and HD Decrypter[194]).

text: BD-ROM Mark[edit]

text: BD-ROM Mark is a small amount of cryptographic data that is stored separately from normal Blu-ray Disc data, aiming to prevent replication of the discs. The cryptographic data is needed to decrypt the copyrighted disc content protected by AACS.[195] A specially licensed piece of hardware is required to insert the ROM Mark into the media during mastering. During replication, this ROM Mark is transferred together with the recorded data to the disc. In consequence, any copies of a disc made with a regular recorder will lack the ROM Mark data and will be unreadable on standard players.

text: Backward compatibility[edit]

text: The Blu-ray Disc Association recommends but does not require that Blu-ray Disc drives be capable of reading standard DVDs and CDs, for backward compatibility.[196] Most Blu-ray Disc players are capable of reading both CDs and DVDs; however, a few of the early Blu-ray Disc players released in 2006, such as the Sony BDP-S1, could play DVDs but not CDs.[197][198][199] In addition, Blu-ray players cannot play HD DVDs, and HD DVD players cannot play Blu-ray discs. Some Blu-ray players can also play Video CDs, and all 4K Blu-ray players can play regular Blu-ray Discs, and most can play DVDs and CDs. The PlayStation 4 does not support CDs.

text: Variations[edit]

text: High Fidelity Pure Audio (BD-A)[edit]

text: High Fidelity Pure Audio (HFPA) is a marketing initiative, spearheaded by the Universal Music Group, for audio-only Blu-ray optical discs. Launched in 2013 as a potential successor to the compact disc, it has been compared with DVD-A and SACD, which had similar aims.

text: AVCHD[edit]

text: AVCHD was originally developed as a high definition format for consumer tapeless camcorders. Derived from the Blu-ray Disc specification, AVCHD shares a similar random access directory structure but is restricted to lower audio and video bitrates, simpler interactivity, and the use of AVC-video and Dolby AC-3 (or linear PCM) audio. Being primarily an acquisition format, AVCHD playback is not recognized by all devices that play Blu-ray Disc. Nevertheless, many such devices are capable of playing AVCHD recordings from removable media, such as DVDs, SD/SDHC memory cards, "Memory Stick" cards, and hard disk drives.[200]

text: AVCREC[edit]

text: AVCREC uses a BDAV container to record high definition content on conventional DVDs.[201] Presently AVCREC is tightly integrated with the Japanese ISDB broadcast standard and is not marketed outside of Japan. AVCREC is used primarily in set-top digital video recorders and in this regard is comparable to HD REC.

text: Blu-ray 3D[edit]

text: The Blu-ray Disc Association (BDA) created a task force made up of executives from the film industry and the consumer electronics and IT sectors to help define standards for putting 3D film and 3D television content on a Blu-ray Disc.[202] On December 17, 2009, the BDA officially announced 3D specs for Blu-ray Disc, allowing backward compatibility with current 2D Blu-ray players.[203] The BDA has said, "The Blu-ray 3D specification calls for encoding 3D video using the "Stereo High" profile defined by Multiview Video Coding (MVC), an extension to the ITU-T H.264 Advanced Video Coding (AVC) codec currently implemented by all Blu-ray Disc players. MPEG4-MVC compresses both left and right eye views with a typical 50% overhead compared to equivalent 2D content, and can provide full 1080p resolution backward compatibility with current 2D Blu-ray Disc players."[204] This means the MVC (3D) stream is backward compatible with H.264/AVC (2D) stream, allowing older 2D devices and software to decode stereoscopic video streams, ignoring additional information for the second view.

text: Sony added Blu-ray 3D support to its PlayStation 3 console via a firmware upgrade on 21 September 2010.[205] The console had previously gained 3D gaming capability via an update on 21 April 2010.[206] Since the version 3.70 software update on August 9, 2011, the PlayStation 3 can play DTS-HD Master Audio and DTS-HD High Resolution Audio while playing 3D Blu-ray.[207] Dolby TrueHD is used on a small minority of Blu-ray 3D releases, and bitstreaming implemented in slim PlayStation 3 models only (original "fat" PS3 models decode internally and send audio as LPCM).[208] As of 2018, most major home entertainment studios, such as Walt Disney Studios, Sony Pictures, etc. have discontinued the Blu-ray 3D format in North America and other regions.

text: Ultra HD Blu-ray[edit]

text: Ultra HD Blu-ray is a new disc format, incompatible with existing Blu-ray Disc players, that supports 60fps 4K UHD video encoded in HEVC with 10-bit HDR and a wider color gamut.