document_title: Economic bubble

question_text: during the 1920s the united states economy move through which phase of the business cycle

root

text: Economic bubble

text: History and origin of term[edit]

text: The term "bubble", in reference to financial crisis, originated in the 1711–1720 British South Sea Bubble, and originally referred to the companies themselves, and their inflated stock, rather than to the crisis itself. This was one of the earliest modern financial crises; other episodes were referred to as "manias", as in the Dutch tulip mania. The metaphor indicated that the prices of the stock were inflated and fragile – expanded based on nothing but air, and vulnerable to a sudden burst, as in fact occurred.

tag: p

text: Some later commentators have extended the metaphor to emphasize the suddenness, suggesting that economic bubbles end "All at once, and nothing first, / Just as bubbles do when they burst,"[13] though theories of financial crises such as debt-deflation and the Financial Instability Hypothesis suggest instead that bubbles burst progressively, with the most vulnerable (most highly-leveraged) assets failing first, and then the collapse spreading throughout the economy.

text: Impact[edit]

text: The impact of economic bubbles is debated within and between schools of economic thought; they are not generally considered beneficial, but it is debated how harmful their formation and bursting is.

text: Within mainstream economics, many believe that bubbles cannot be identified in advance, cannot be prevented from forming, that attempts to "prick" the bubble may cause financial crisis, and that instead authorities should wait for bubbles to burst of their own accord, dealing with the aftermath via monetary policy and fiscal policy.

text: Political economist Robert E. Wright argues that bubbles can be identified before the fact with high confidence.[14]

text: In addition, the crash which usually follows an economic bubble can destroy a large amount of wealth and cause continuing economic malaise; this view is particularly associated with the debt-deflation theory of Irving Fisher, and elaborated within Post-Keynesian economics.

text: A protracted period of low risk premiums can simply prolong the downturn in asset price deflation as was the case of the Great Depression in the 1930s for much of the world and the 1990s for Japan. Not only can the aftermath of a crash devastate the economy of a nation, but its effects can also reverberate beyond its borders.

text: Effect upon spending[edit]

text: Another important aspect of economic bubbles is their impact on spending habits. Market participants with overvalued assets tend to spend more because they "feel" richer (the wealth effect). Many observers quote the housing market in the United Kingdom, Australia, New Zealand, Spain and parts of the United States in recent times, as an example of this effect. When the bubble inevitably bursts, those who hold on to these overvalued assets usually experience a feeling of reduced wealth and tend to cut discretionary spending at the same time, hindering economic growth or, worse, exacerbating the economic slowdown.

text: In an economy with a central bank, the bank may therefore attempt to keep an eye on asset price appreciation and take measures to curb high levels of speculative activity in financial assets.[citation needed] This is usually done by increasing the interest rate (that is, the cost of borrowing money). (Historically, this is not the only approach taken by central banks. It has been argued [15] that they should stay out of it and let the bubble, if it is one, take its course.)

text: Possible causes[edit]

text: In the 1970s, excess monetary expansion after the U.S. came off the gold standard (August 1971) created massive commodities bubbles. These bubbles only ended when the U.S. Central Bank (Federal Reserve) finally reined in the excess money, raising federal funds interest rates to over 14%.[citation needed] The commodities bubble popped and prices of oil and gold, for instance, came down to their proper levels. Similarly, low interest rate policies by the U.S. Federal Reserve in the 2001–2004 are believed to have exacerbated housing and commodities bubbles. The housing bubble popped as subprime mortgages began to default at much higher rates than expected, which also coincided with the rising of the fed funds rate.

text: It has also been variously suggested that bubbles may be rational,[16] intrinsic,[17] and contagious.[18] To date, there is no widely accepted theory to explain their occurrence.[5] Recent computer-generated agency models suggest excessive leverage could be a key factor in causing financial bubbles.[19]

text: Puzzlingly for some, bubbles occur even in highly predictable experimental markets, where uncertainty is eliminated and market participants should be able to calculate the intrinsic value of the assets simply by examining the expected stream of dividends.[7] Nevertheless, bubbles have been observed repeatedly in experimental markets, even with participants such as business students, managers, and professional traders. Experimental bubbles have proven robust to a variety of conditions, including short-selling, margin buying, and insider trading.[5][1]

text: While there is no clear agreement on what causes bubbles, there is evidence[citation needed] to suggest that they are not caused by bounded rationality or assumptions about the irrationality of others, as assumed by greater fool theory. It has also been shown that bubbles appear even when market participants are well-capable of pricing assets correctly.[9] Further, it has been shown that bubbles appear even when speculation is not possible[8] or when over-confidence is absent.[9]

text: More recent theories of asset bubble formation suggest that they are likely sociologically-driven events, thus explanations that merely involve fundamental factors or snippets of human behavior are incomplete at best. For instance, qualitative researchers Preston Teeter and Jorgen Sandberg argue that market speculation is driven by culturally-situated narratives that are deeply embedded in and supported by the prevailing institutions of the time.[5] They cite factors such as bubbles forming during periods of innovation, easy credit, loose regulations, and internationalized investment as reasons why narratives play such an influential role in the growth of asset bubbles.

text: Liquidity[edit]

text: One possible cause of bubbles is excessive monetary liquidity in the financial system, inducing lax or inappropriate lending standards by the banks, which makes markets vulnerable to volatile asset price inflation caused by short-term, leveraged speculation.[19] For example, Axel A. Weber, the former president of the Deutsche Bundesbank, has argued that "The past has shown that an overly generous provision of liquidity in global financial markets in connection with a very low level of interest rates promotes the formation of asset-price bubbles."[20]

text: According to the explanation, excessive monetary liquidity (easy credit, large disposable incomes) potentially occurs while fractional reserve banks are implementing expansionary monetary policy (i.e. lowering of interest rates and flushing the financial system with money supply); this explanation may differ in certain details according to economic philosophy. Those who believe the money supply is controlled exogenously by a central bank may attribute an 'expansionary monetary policy' to said bank and (should one exist) a governing body or institution; others who believe that the money supply is created endogenously by the banking sector may attribute such a 'policy' with the behavior of the financial sector itself, and view the state as a passive or reactive factor. This may determine how central or relatively minor/inconsequential policies like fractional reserve banking and the central bank's efforts to raise or lower short-term interest rates are to one's view on the creation, inflation and ultimate implosion of an economic bubble. Explanations focusing on interest rates tend to take on a common form, however: When interest rates are set excessively low, (regardless of the mechanism by which it is accomplished) investors tend to avoid putting their capital into savings accounts. Instead, investors tend to leverage their capital by borrowing from banks and invest the leveraged capital in financial assets such as stocks and real estate. Risky leveraged behavior like speculation and Ponzi schemes can lead to an increasingly fragile economy, and may also be part of what pushes asset prices artificially upward until the bubble pops.

text:
But these [ongoing economic crises] aren’t just a series of unrelated accidents. Instead, what we’re seeing is what happens when too much money is chasing too few investment opportunities.

Paul Krugman[21]

tag: div

text: Simply put, economic bubbles often occur when too much money is chasing too few assets, causing both good assets and bad assets to appreciate excessively beyond their fundamentals to an unsustainable level. Once the bubble bursts, the fall in prices causes the collapse of unsustainable investment schemes (especially speculative and/or Ponzi investments, but not exclusively so), which leads to a crisis of consumer (and investor) confidence that may result in a financial panic and/or financial crisis; if there is monetary authority like a central bank, it may be forced to take a number of measures in order to soak up the liquidity in the financial system or risk a collapse of its currency. This may involve actions like bailouts of the financial system, but also others that reverse the trend of monetary accommodation, commonly termed forms of 'contractionary monetary policy'.

text: Some of these measures may include raising interest rates, which tends to make investors become more risk averse and thus avoid leveraged capital because the costs of borrowing may become too expensive; others may include certain countermeasures that may be taken pre-emptively during periods of strong economic growth include having the central monetary authority increase capital reserve requirements and attempting to implement regulation that checks and/or prevents processes leading to over-expansion and excessive leveraging of debt. Ideally, such countermeasures lessen the impact of a downturn by strengthening financial institutions while the economy is strong.

text: Advocates of perspectives stressing the role of credit money in an economy often refer to (such) bubbles as "credit bubbles," and look at such measures of financial leverage as debt to GDP ratios to identify bubbles. Typically the collapse of any economic bubble results in an economic contraction termed (if less severe) a recession or (if more severe) a depression; what economic policies to follow in reaction to such a contraction is a hotly debated perennial topic of political economy.

text: The importance of liquidity was derived in a mathematical setting[22] and in an experimental setting[23][24] (see Section "Experimental and mathematical economics").

text: Social psychology factors[edit]

text: Greater fool theory[edit]

text: Greater fool theory states that bubbles are driven by the behavior of a perennially optimistic market participants (the fools) who buy overvalued assets in anticipation of selling it to other speculators (the greater fools) at a much higher price. According to this explanation, the bubbles continue as long as the fools can find greater fools to pay up for the overvalued asset. The bubbles will end only when the greater fool becomes the greatest fool who pays the top price for the overvalued asset and can no longer find another buyer to pay for it at a higher price. This theory is popular among laity but has not yet been fully confirmed by empirical research.[8][9]

text: Extrapolation[edit]

text:
The term “bubble” should indicate a price that no reasonable future outcome can justify.

Clifford Asness[25]

text: Extrapolation is projecting historical data into the future on the same basis; if prices have risen at a certain rate in the past, they will continue to rise at that rate forever. The argument is that investors tend to extrapolate past extraordinary returns on investment of certain assets into the future, causing them to overbid those risky assets in order to attempt to continue to capture those same rates of return.

text: Overbidding on certain assets will at some point result in uneconomic rates of return for investors; only then the asset price deflation will begin. When investors feel that they are no longer well compensated for holding those risky assets, they will start to demand higher rates of return on their investments.

text: Herding[edit]

text: Another related explanation used in behavioral finance lies in herd behavior, the fact that investors tend to buy or sell in the direction of the market trend.[26][27] This is sometimes helped by technical analysis that tries precisely to detect those trends and follow them, which creates a self-fulfilling prophecy.

text: Investment managers, such as stock mutual fund managers, are compensated and retained in part due to their performance relative to peers. Taking a conservative or contrarian position as a bubble builds results in performance unfavorable to peers. This may cause customers to go elsewhere and can affect the investment manager's own employment or compensation. The typical short-term focus of U.S. equity markets exacerbates the risk for investment managers that do not participate during the building phase of a bubble, particularly one that builds over a longer period of time. In attempting to maximize returns for clients and maintain their employment, they may rationally participate in a bubble they believe to be forming, as the risks of not doing so outweigh the benefits.[28]

text: Moral hazard[edit]

text: Moral hazard is the prospect that a party insulated from risk may behave differently from the way it would behave if it were fully exposed to the risk. A person's belief that they are responsible for the consequences of their own actions is an essential aspect of rational behavior. An investor must balance the possibility of making a return on their investment with the risk of making a loss – the risk-return relationship. A moral hazard can occur when this relationship is interfered with, often via government policy.

text: A recent example is the Troubled Asset Relief Program (TARP), signed into law by U.S. President George W. Bush on 3 October 2008 to provide a Government bailout for many financial and non-financial institutions who speculated in high-risk financial instruments during the housing boom condemned by a 2005 story in The Economist titled "The worldwide rise in house prices is the biggest bubble in history".[29] A historical example was intervention by the Dutch Parliament during the great Tulip Mania of 1637.

text: Other causes of perceived insulation from risk may derive from a given entity's predominance in a market relative to other players, and not from state intervention or market regulation. A firm – or several large firms acting in concert (see cartel, oligopoly and collusion) – with very large holdings and capital reserves could instigate a market bubble by investing heavily in a given asset, creating a relative scarcity which drives up that asset's price. Because of the signaling power of the large firm or group of colluding firms, the firm's smaller competitors will follow suit, similarly investing in the asset due to its price gains.

text: However, in relation to the party instigating the bubble, these smaller competitors are insufficiently leveraged to withstand a similarly rapid decline in the asset’s price. When the large firm, cartel or de facto collusive body perceives a maximal peak has been reached in the traded asset's price, it can then proceed to rapidly sell or "dump" its holdings of this asset on the market, precipitating a price decline that forces its competitors into insolvency, bankruptcy or foreclosure.

text: The large firm or cartel – which has intentionally leveraged itself to withstand the price decline it engineered – can then acquire the capital of its failing or devalued competitors at a low price as well as capture a greater market share (e.g., via a merger or acquisition which expands the dominant firm's distribution chain). If the bubble-instigating party is itself a lending institution, it can combine its knowledge of its borrowers’ leveraging positions with publicly available information on their stock holdings, and strategically shield or expose them to default.

text: Other possible causes[edit]

text: Some regard bubbles as related to inflation and thus believe that the causes of inflation are also the causes of bubbles. Others take the view that there is a "fundamental value" to an asset, and that bubbles represent a rise over that fundamental value, which must eventually return to that fundamental value. There are chaotic theories of bubbles which assert that bubbles come from particular "critical" states in the market based on the communication of economic factors. Finally, others regard bubbles as necessary consequences of irrationally valuing assets solely based upon their returns in the recent past without resorting to a rigorous analysis based on their underlying "fundamentals".

text: Experimental and mathematical economics[edit]

text: Bubbles in financial markets have been studied not only through historical evidence, but also through experiments, mathematical and statistical works. Smith, Suchanek and Williams[7] designed a set of experiments in which an asset that gave a dividend with expected value 24 cents at the end of each of 15 periods (and were subsequently worthless) was traded through a computer network. Classical economics would predict that the asset would start trading near $3.60 (15 times $0.24) and decline by 24 cents each period. They found instead that prices started well below this fundamental value and rose far above the expected return in dividends. The bubble subsequently crashed before the end of the experiment. This laboratory bubble has been repeated hundreds of times in many economics laboratories in the world, with similar results.

text: The existence of bubbles and crashes in such a simple context was unsettling for the economics community that tried to resolve the paradox on various features of the experiments. To address these issues Porter and Smith[30] and others performed a series of experiments in which short selling, margin trading, professional traders all led to bubbles a fortiori.

text: Much of the puzzle has been resolved through mathematical modeling and additional experiments. In particular, starting in 1989, Gunduz Caginalp and collaborators[22][31] modeled the trading with two concepts that are generally missing in classical economics and finance. First, they assumed that supply and demand of an asset depended not only on valuation, but on factors such as the price trend. Second, they assumed that the available cash and asset are finite (as they are in the laboratory). This is contrary to the “infinite arbitrage” that is generally assumed to exist, and to eliminate deviations from fundamental value. Utilizing these assumptions together with differential equations, they predicted the following: (a) The bubble would be larger if there was initial undervaluation. Initially, “value-based” traders would buy the undervalued asset creating an uptrend, which would then attract the “momentum” traders and a bubble would be created. (b) When the initial ratio of cash to asset value in a given experiment was increased, they predicted that the bubble would be larger.

text: An epistemological difference between most microeconomic modeling and these works is that the latter offer an opportunity to test implications of their theory in a quantitative manner. This opens up the possibility of comparison between experiments and world markets.

text: These predictions were confirmed in experiments[23][24] that showed the importance of “excess cash” (also called liquidity, though this term has other meanings), and trend-based investing in creating bubbles. When price collars were used to keep prices low in the initial time periods, the bubble became larger. In experiments in which L= (total cash)/(total initial value of asset) were doubled, the price at the peak of the bubble nearly doubled. This provided valuable evidence for the argument that “cheap money fuels markets.”

text: Caginalp's asset flow differential equations provide a link between the laboratory experiments and world market data. Since the parameters can be calibrated with either market, one can compare the lab data with the world market data.

text: The asset flow equations stipulate that price trend is a factor in the supply and demand for an asset that is a key ingredient in the formation of a bubble. While many studies of market data have shown a rather minimal trend effect, the work of Caginalp and DeSantis[32] on large scale data adjusts for changes in valuation, thereby illuminating a strong role for trend, and providing the empirical justification for the modeling.

text: The asset flow equations have been used to study the formation of bubbles from a different standpoint in [33] where it was shown that a stable equilibrium could become unstable with the influx of additional cash or the change to a shorter time scale on the part of the momentum investors. Thus a stable equilibrium could be pushed into an unstable one, leading to a trajectory in price that exhibits a large “excursion” from either the initial stable point or the final stable point. This phenomenon on a short time scale may be the explanation for flash crashes.

text: Identifying asset bubbles[edit]

text: Economic or asset price bubbles are often characterized by one or more of the following:

text:
Unusual changes in single measures, or relationships among measures (e.g., ratios) relative to their historical levels. For example, in the housing bubble of the 2000s, the housing prices were unusually high relative to income.[34] For stocks, the price to earnings ratio provides a measure of stock prices relative to corporate earnings; higher readings indicate investors are paying more for each dollar of earnings.[35]
Elevated usage of debt (leverage) to purchase assets, such as purchasing stocks on margin or homes with a lower down payment.
Higher risk lending and borrowing behavior, such as originating loans to borrowers with lower credit quality scores (e.g., subprime borrowers), combined with adjustable rate mortgages and "interest only" loans.
Rationalizing borrowing, lending and purchase decisions based on expected future price increases rather than the ability of the borrower to repay.[36]
Rationalizing asset prices by increasingly weaker arguments, such as "this time it's different" or "housing prices only go up."
A high presence of marketing or media coverage related to the asset.[5]
Incentives that place the consequences of bad behavior by one economic actor upon another, such as the origination of mortgages to those with limited ability to repay because the mortgage could be sold or securitized, moving the consequences from the originator to the investor.
International trade (current account) imbalances, resulting in an excess of savings over investments, increasing the volatility of capital flow among countries. For example, the flow of savings from Asia to the U.S. was one of the drivers of the 2000s housing bubble.[37]
A lower interest rate environment, which encourages lending and borrowing.[38]

text: Asset Bubbles[edit]

text:
Tipper and See-Saw Time (1621)
Tulip mania (Holland) (1634-1637)
South Sea Company (British) (1720)
Mississippi Company (France) (1720)
Canal Mania (UK) (1790s-1810s)
Panic of 1819 (US) (1815-1818) Prices of US land in the south and west, cotton (US main export at the time), wheat, corn and tobacco grew into a bubble following the end of the Napoleonic Wars in 1815 as the European economy was beginning to recover from wars and demand was high for agricultural goods from America. The Second Bank of the US called in loans for specie beginning in August 1818 popped the speculative land bubble. Prices of prices of agricultural commodities declined by almost -50% during 1819-1821 post bubble. A credit contraction caused by a financial crisis in England drained specie out of the U.S. The Bank of the United States also contracted its lending. [39]
Panic of 1837 (1834-1837) (US) Prices of US land, cotton, and slaves grew into bubbles with easy bank credit by the mid-1830s. Ended in financial crisis starting with the Specie Circular of 1836. Five year recession followed along with currency in the United States contracting by about 34% with prices falling by 33%. The magnitude of this contraction is only matched by the Great Depression.[40]
Railway Mania (UK) (1840s)
Panic of 1857 Land and railroad boom in US following discovery of gold in California in 1849. Resulted in large expansion of US money supply. Railroads boomed as people moved west. Railroad stocks peaks in July 1857. The failure of Ohio Life in August 1857 brought attention to the financial state of the railroad industry and land markets, thereby causing the financial panic to become a more public issue. Since banks had financed the railroads and land purchases, they began to feel the pressures of the falling value of railroad securities and many went bankrupt. Ended in worldwide crisis.
Melbourne Australia land and real estate bubble (1883-1889, crash in 1890-91) [41]
Encilhamento ("Mounting") (1886–1892)
US farm bubble and crisis - (1914-1918, crash 1919-1920) prices rapidly escalated during WWI and crash after war's end.
Roaring Twenties stock-market bubble (US) (1921–1929)
Florida speculative building bubble (US)(1922-1926)
Poseidon bubble (Australia)(1969-1970)
Gold and Silver bubble (1976-1980)

Silver Thursday 1980

The dot-com bubble (US)(1995–2000)
Japanese asset price bubble (1986-1990) Japan real estate and stock market boom
1997 Asian financial crisis (1997)
United States housing bubble (US) (2002-2006)
China stock and property bubble (China) (2003-2007)
The 2000s commodity bubbles (2002-2008)

Uranium bubble of 2007
Rhodium bubble of 2008 (increase from $500/oz to $9000/oz in July 2008, then down to $1000/oz in January 2009)[42]

Bitcoin bubbles of 2013 and 2017.

tag: ul

text: --- Real Estate Bubbles --

text:
Real estate bubble

Australian first home buyer (FHB) property bubble (as of 2009[update])
Indian property bubble (as of 2005[update])
Irish property bubble (as of 2006[update])
Spanish property bubble (as of 2006[update])
Romanian property bubble (as of 2008[update])

text: Other goods which have produced bubbles include: postage stamps and coin collecting.

text: Examples of aftermaths of bubbles[edit]

text:
Panic of 1837
Great Depression
Early 2000s recession
Great Recession


document_title: Avenged Sevenfold

question_text: when did avenged sevenfold release their first album

text: Avenged Sevenfold

text: History

text: Formation and Sounding the Seventh Trumpet (1999–2002)

text: The band was formed in 1999 in Huntington Beach, California with original members M. Shadows, Zacky Vengeance, The Rev and Matt Wendt. M Shadows came up with the name as a reference to the story of Cain and Abel from The Bible, which can be found in Genesis 4:24, although they are not a religious band.[5] Upon its formation, each member of the band also took on a pseudonym which were already nicknames of theirs from high school.[6] Matt Wendt was later replaced by Justin 'Sane' Meacham who was previously the bassist for Suburban Legends.

text: Before the release of their debut album, the band recorded two demos in 1999 and 2000.[7][8] In mid-2001, it was reported that Meacham had attempted suicide[9] by drinking excessive amounts of cough syrup.[10] The attempt affected the band's Take Action Tour.[9] During his hospitalization he remained in poor condition and was replaced by Dameon Ash.[10] In an interview, lead singer M. Shadows said of Meacham that "he perma-fried his brain and was in a mental institution for a long time, and when you have someone in your band who does that, it ruins everything that's going on all around you, and it makes you want to do something to prevent it from happening to other people."[10] Avenged Sevenfold's debut album, Sounding the Seventh Trumpet, was recorded when the band members were in their late teens and still in high school. It was originally released on their first label, Good Life Recordings in 2001.[11] When lead guitarist Synyster Gates joined the band after the album was released, the introductory track "To End the Rapture" was re-recorded featuring a full band element. The album was subsequently re-released on Hopeless Records in 2002. The band started to receive recognition, performing with bands such as Mushroomhead and Shadows Fall and playing on the Take Action Tour.[12][13]

text: Waking the Fallen and City of Evil (2003–05)

text: Having found a new bassist, Johnny Christ, the group released their second studio album titled Waking the Fallen on Hopeless Records in August 2003. The album featured a more refined and mature sound production in comparison to their previous album. The band received profiles in Billboard and The Boston Globe, and played in the Vans Warped Tour.[14][15] In 2004, Avenged Sevenfold toured again on the Vans Warped Tour and recorded a video for their song "Unholy Confessions" which went into rotation on MTV2's Headbanger's Ball.[16] Shortly after the release of Waking the Fallen, Avenged Sevenfold left Hopeless Records and were signed to Warner Bros. Records.

text: City of Evil, the band's third album and major label debut, was released on June 7, 2005 and debuted at No.30 on the Billboard 200 chart, selling over 30,000 copies in its first week of release.[17][18] It utilized a more classic metal sound than Avenged Sevenfold's previous albums, which had been grouped into the metalcore genre.[19][20] The album is also notable for the absence of screamed and growled vocals; M. Shadows worked with vocal coach Ron Anderson—whose clients have included Axl Rose and Chris Cornell—for months before the album's release to achieve a sound that had "grit while still having the tone".[19][21] The album received positive reviews from several magazines and websites and is credited for propelling the band into international popularity.

text: Avenged Sevenfold (2006–08)

text: After playing Ozzfest in 2006, Avenged Sevenfold memorably beat out R&B Singers Rihanna and Chris Brown, Panic! at the Disco, Angels & Airwaves and James Blunt for the title of Best New Artist at the MTV Video Music Awards, thanks in part to their Fear and Loathing in Las Vegas-inspired song "Bat Country."[22] They returned to the Vans Warped Tour, this time headlining and then continued on their own "Cities of Evil Tour."[23] In addition, their lead single "Bat Country" reached No.2 on the Billboard Mainstream Rock Charts, No.6 on the Billboard Modern Rock Charts and the accompanying video made it to No.1 on MTV's Total Request Live.[24] Propelled by this success, the album sold well and became Avenged Sevenfold's first gold record.[25] It was later certified platinum in August 2009.

text: Avenged Sevenfold was invited to join Ozzfest tour on the main stage, alongside other well known rock/heavy metal acts such as DragonForce, Lacuna Coil, Hatebreed, Disturbed and System of a Down for the first time in 2006.[26] That same year they also completed a worldwide tour, including the US, The United Kingdom (as well as mainland Europe), Japan, Australia and New Zealand. After a sixteen-month promotion of City of Evil, the band announced that they were cancelling their Fall 2006 tour to record new music.[27] In the interim, the band released their first DVD titled All Excess on July 17, 2007.[28] All Excess, which debuted as the No.1 DVD in the USA, included live performances and backstage footage that spanned the band's eight-year career. Two tribute albums, Strung Out on Avenged Sevenfold: Bat Wings and Broken Strings and Strung Out on Avenged Sevenfold: The String Tribute were also released in October 2007.

text: On October 26, 2007, Avenged Sevenfold released their self-titled album, the band's fourth studio album. It debuted at No. 4 on the Billboard 200 with over 90,000 copies sold.[29] Two singles, "Critical Acclaim" and "Almost Easy" were released prior to the album's debut. In December 2007, an animated video was made for "A Little Piece of Heaven". Due to the song's controversial subject matter, however, Warner Brothers only released it to registered MVI users over the internet. The third single, "Afterlife" and its video was released in January 2008. Their fourth single, "Dear God", was released on June 15, 2008. Although critical reception was generally mixed the self-titled album went on to sell over 500,000 copies and was awarded "Album of the Year" at the Kerrang! Awards.[30]

text: Avenged Sevenfold headlined the 2008 Taste of Chaos tour with Atreyu, Bullet for My Valentine, Blessthefall and Idiot Pilot.[31] They used the footage from their last show in Long Beach for Live in the LBC & Diamonds in the Rough, a two-disc B-sides CD and live DVD which was released on September 16, 2008. They also recorded numerous covers, including Pantera's "Walk", Iron Maiden's "Flash of the Blade" and Black Sabbath's "Paranoid".[31][32][33]

text: The death of The Rev and Nightmare (2009–11)

text: In January 2009, M. Shadows confirmed that the band was writing the follow-up to their self-titled fourth album within the upcoming months.[34] They also played at Rock on the Range, from May 16–17, 2009.[35] On April 16, they performed a version of Guns N' Roses' "It's So Easy" onstage with Slash, at the Nokia Theater in Los Angeles.[36] On December 28, 2009, the band's drummer James "The Rev" Sullivan was found dead at his home at the age of 28.[37] Autopsy results were inconclusive,[38] but on June 9, 2010, the cause of death was revealed to have been an "acute polydrug intoxication due to combined effects of Oxycodone, Oxymorphone, Diazepam/Nordiazepam and ethanol".[39] In a statement by the band, they expressed their grief over the death of The Rev and later posted a message from Sullivan's family which expressed their gratitude to his fans for their support.[40][41] The band members admitted in a number of interviews that they considered disbanding at this point in time.[42][43] However, on February 17, 2010, Avenged Sevenfold stated that they had entered the studio, along with now-former Dream Theater drummer Mike Portnoy, to drum for the album, in place of The Rev.[44]

text: The single "Nightmare" was digitally released on May 18, 2010.[45][46] A preview for the song was released on May 6, 2010 on Amazon.com, but was removed soon after for unknown reasons.[46] Mixing for the album had been completed in New York City, and Nightmare was finally released worldwide on July 27, 2010.[47] It met with mixed to positive reviews from music critics but was well received by the fans. Nightmare beat sales projections easily, debuting at number one on the Billboard 200 with sales of 163,000 units in its first week.[48] After finishing recording, in December, Portnoy and the band posted simultaneous statements on their websites stating that he would not be their replacement for The Rev. However, Portnoy did travel with the band overseas in December 2010 for three shows in Iraq and Kuwait sponsored by the USO. They played for U.S. Soldiers at Camp Adder, Camp Beuhring, and Balad Air Base.[49] On January 20, 2011, Avenged Sevenfold announced via Facebook that former Confide drummer Arin Ilejay would begin touring with them that year. He was not yet considered a full-time member at this point.[50][51]

text: Avenged Sevenfold performed at the Rock am Ring and Rock im Park festivals on June 3–5, 2011 alongside other bands such as Alter Bridge, System of a Down, and In Flames.[52] On April 2011, the band headlined the Golden God Awards held by Metal Hammer. The same night the band won three awards for "Best Vocalist" (M. Shadows), "Epiphone Best Guitarist(s)" (Synyster Gates and Zacky Vengeance) and "Affliction's Album of The Year: " for Nightmare, while Mike Portnoy won the award for "Drum Workshop's Best Drummer" for his work on the album.

text: Avenged Sevenfold headlined the 2011 Uproar Festival with supporting acts Three Days Grace, Seether, Bullet for My Valentine, Escape The Fate, among others.[53] In November and December 2011, the band went on their "Buried Alive" tour with supporting acts Hollywood Undead, Asking Alexandria, and Black Veil Brides.[54]

text: Hail to the King and Waking the Fallen: Resurrected (2012–14)

text: On April 11, 2012, Avenged Sevenfold won the award for "Best Live Band" and "Most Dedicated Fans" at the Revolver Golden Gods awards.[55] The band toured through Asia into April and early May, and played at the Orion Music + More, Festival on June 23 and 24 in Atlantic City, New Jersey alongside Metallica and Cage the Elephant among many others.[56]

text: On September 24, 2012, Avenged Sevenfold released a new song, titled "Carry On"; it was featured in the video game Call of Duty: Black Ops II.[57] On November 15, 2012, vocalist M. Shadows said that the band had been working on a new album since the recording of "Carry On" in August 2012.[58] The band began recording material for the album in January 2013.[59] The band then started streaming snippets of the album in May 2013 on their new radio app.[60] There, Arin Ilejay was confirmed as an official band member and replacement of deceased The Rev. M. Shadows said that the album would sound more blues rock-influenced and more like classic rock/metal like Black Sabbath and Led Zeppelin.[61]

text: The band was confirmed to play at the 2013 Rock in Rio festival on September 22, 2013.[62] On May 24, 2013, the band have announced dates for their European tour with Five Finger Death Punch and Device serving as their support bands.

text: The album, entitled Hail to the King, was released on August 27, 2013.[63] This is the first Avenged Sevenfold album without any musical contributions from deceased The Rev. The album's lead single and title track was released on July 15, 2013. Hail to the King charted as No. 1 on the US Billboard 200, the UK albums chart, as well as the Finnish, Brazilian, Canadian, and Irish charts, and was commercially and critically acclaimed. The band headlined Monster Energy's Welcome to Rockville two-day music festival in Jacksonville, FL, April 26–27, 2014, joined by more than 25 rock acts, such as Motörhead, Rob Zombie, Chevelle, Korn, Staind, Alter Bridge, The Cult, Five Finger Death Punch, Volbeat, Black Label Society, and Seether.[64] On June 13, the band headlined the Friday night of Download Festival 2014. The band also headlined the Mayhem Festival 2014 with Korn, Asking Alexandria, and Trivium.

text: In March 2014, vocalist M. Shadows revealed in an interview with Loudwire that the band had plans in the works to put something out for the overdue 10th anniversary of Waking the Fallen.[65] Waking the Fallen: Resurrected was released August 25, 2014.[66] The reissue charted No. 10 on the US Billboard 200.[67]

text: Drummer change and The Stage (2015–present)

text: In October 2014, M. Shadows confirmed that the band will begin writing their seventh album during mid-2015.[68] In May 2015, the band posted a video on their website teasing their upcoming second live DVD/documentary, entitled This is Bat Country, which will show performances from Download Festival, Rock in Rio and Rock on the Range. As of 2016, the band hasn't released the DVD because of the ongoing lawsuit with Warner Bros.

text: In July 2015 the band announced on their website that they would part ways with drummer Arin Ilejay, due to "creative differences".[69] In October 2015, the band announced on their website that they had been working with a new drummer for over a year, making sure that it was a good fit before making sudden changes.[70] On October 21, in an interview with Kerrang! magazine, guitarist Zacky Vengeance revealed that the band had been working on the new album for the past couple of months and that a couple of songs had already been completely written.[71] On November 4, 2015, the band announced that Brooks Wackerman would replace Arin Ilejay as the drummer for Avenged Sevenfold.[72] In an interview with Kerrang! magazine on December 3, guitarist Zacky Vengeance said that the new album went in all sorts of aggressive and melodic directions and described it as very "aggro".[73]

text: On January 14, 2016, Billboard reported that Avenged Sevenfold had been sued by Warner Bros. for trying to leave the label. The band later released a statement clarifying that they wanted to leave because a majority of the executives who helped sign the band to Warner Bros were no longer at the label. They also revealed that the band was going to be entering the studio to record their new album very soon, intending to release it later in 2016.[74] On March 31, the band posted a teaser of their upcoming album on their website.[75]

text: On August 18, 2016, the band performed a free live show for 1500 people in Minnesota, marking it the first live performance with new drummer Brooks Wackerman.[76] The band was announced as support for Metallica with Volbeat in the U.S. Bank Stadium on August 20, 2016, making it the first ever rock show in the stadium.[77] The band was announced as a headliner of Monster Energy Rock Allegiance 2016, along with Alice in Chains, Slayer, The Offspring, Breaking Benjamin and others.[78] Avenged Sevenfold also performed on "Louder Than Life" festival as headliners on October 1, with Slipknot, Slayer, Disturbed, Korn and other artists.[79] On June 21, the band announced a U.S. Fall tour with Volbeat, Killswitch Engage, and Avatar.[80] The band also announced a UK tour for January 2017 with Disturbed and In Flames.[81] Avenged Sevenfold was announced as a headliner of 2016 edition of Knotfest Mexico.[82] The band also announced the European Tour for February and March 2017 along with Disturbed and Chevelle.

text: On October 3, 2016, the band's logo Deathbat started appearing as a projection in London. After that, Deathbat also started appearing in Berlin, Toronto and Paris, indicating a release of the new album. On October 12, Chris Jericho posted an Instagram photo of the Deathbat logo with a date 12/9/16 underneath it. He then revealed the supposed title of the album, Voltaic Oceans,[83] It was later revealed that the new album would actually be called The Stage, a concept album about artificial intelligence, which was released on October 28, 2016 via Capitol Records.[84] The album was released to generally favorable reviews,[85] and the band decided to make a unique stage production for it, hiring Cirque du Soleil directors for its making.[86]

text: Avenged Sevenfold was announced as the main support act on Metallica's WorldWired 2017 stadium summer tour in the US and Canada, alongside Volbeat and Gojira.[87] The band also announced a series of 2017 US headlining summer shows of The Stage World Tour, with Volbeat, Motionless in White, and A Day to Remember as special guests across various dates.[88]

text: On December 22, 2017, the band released a deluxe edition of The Stage that included one new original track, six cover songs, and four live tracks from their European tour earlier that year.

text: Style and influences

text: The band's influences include Guns N' Roses, Iron Maiden, Pantera, Bad Religion, Dream Theater, Motörhead, Megadeth,[89] Metallica, Black Sabbath, Led Zeppelin, The Rolling Stones,[90] AC/DC, NOFX, Alice in Chains, Black Flag, Corrosion of Conformity, Suicidal Tendencies, Misfits, Slayer, The Vandals, Rage Against the Machine, Korn, Deftones, and AFI.[91]

text: The band has been categorized under many genres of heavy music. Mainly categorized as heavy metal,[92][93][94][95] hard rock,[94][96][97] progressive metal[98][99][100][101] and metalcore,[94][95][102] Avenged Sevenfold's music has evolved over most of the band's career. At first, the band's debut album Sounding the Seventh Trumpet consisted almost entirely of a metalcore sound; however, there were several deviations from this genre, most notably in "Streets", which shows a punk rock style, and "Warmness on the Soul", which is a piano ballad.[103] On Waking the Fallen, the band displayed a metalcore style once more, but added more clean singing and leaned a bit more towards metal and bit less close to hardcore.[95] In the band's DVD All Excess, producer Andrew Murdock explained this transition: "When I met the band after Sounding the Seventh Trumpet had come out before they had recorded Waking the Fallen, M. Shadows said to me 'This record is screaming. The record we want to make is going to be half-screaming half-singing. I don't want to scream anymore. And the record after that is going to be all singing'."

text: On City of Evil, Avenged Sevenfold's third album, the band chose to abandon the metalcore genre,[104] using a more hard rock and heavy metal style.[105] Avenged Sevenfold's self-titled album, however, has some experiments with other music genres than that from City of Evil, most notably in "Dear God", which shows a country style and "A Little Piece of Heaven", which is circled within the influence of Broadway show tunes, using primarily brass instruments and stringed orchestra to take over most of the role of the lead and rhythm guitar.[106] Nightmare contains further deviations, including a piano ballad called "Fiction", progressive metal-oriented track "Save Me" and a heavy metal sound with extreme vocals and heavier instrumentation on "God Hates Us". The band's sixth studio album Hail to the King shows more of a classic metal sound and a riff-oriented approach. On their newest album The Stage, the band explores further into progressive metal,[98] blending it with elements of thrash metal. In the past, Avenged Sevenfold has also been described as alternative metal,[107] screamo,[108] and pop punk metal.[109]

text: The band has been criticized for "not being metal enough".[93][110] Vocalist M. Shadows responded to this with, "we play music for the sake of music, not so that we can be labeled a metal band. That's like telling us we aren't punk enough. Who cares?".[110] Avenged Sevenfold is one of the notable acts of the New Wave of American Heavy Metal.[111]

text: Members

text: Current

text:
M. Shadows – lead vocals (1999–present); piano, acoustic guitar (1999–2001)
Zacky Vengeance – rhythm & lead guitar, backing vocals (1999–present)
Synyster Gates – lead guitar, backing vocals (2001–present); piano (2001–2007)
Johnny Christ – bass, backing vocals (2002–present)
Brooks Wackerman – drums, percussion (2015–present)

text: Discography

text:
Sounding the Seventh Trumpet (2001)
Waking the Fallen (2003)
City of Evil (2005)
Avenged Sevenfold (2007)
Nightmare (2010)
Hail to the King (2013)
The Stage (2016)

text: Accolades

text: This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (September 2016) (Learn how and when to remove this template message)

tag: table

text:
Year
Nominated work
Award
Result

2006
Band: Avenged Sevenfold
MTV Music Awards: Best New Artist
Won

Band: Avenged Sevenfold
Golden God Awards: Best International Band
Won

Synyster Gates on City of Evil
Total Guitar: Guitarist of the Year
Won

Synyster Gates on City of Evil
Dimebag Darrell "Young Shredder" Award
Won

Band: Avenged Sevenfold
Kerrang! Awards: Best Band on the Planet
Nominated

2008
Band: Avenged Sevenfold
Kerrang! Awards: Best International Band
Nominated

Band: Avenged Sevenfold
Kerrang! Awards: Best Live Band
Nominated

Avenged Sevenfold
Kerrang! Awards: Album of the Year
Won

2010
The Rev on Nightmare
Golden God Awards: Best Drummer[112]
Won

Band: Avenged Sevenfold
Kerrang! Awards: Best International Band
Nominated

2011
Mike Portnoy on Nightmare
Golden God Awards: Best Drummer[113]
Won

Synyster Gates & Zacky Vengeance on Nightmare
Golden God Awards: Best Guitarists[113]
Won

M. Shadows on Nightmare
Golden God Awards: Best Vocalist[113]
Won

Nightmare
Golden God Awards: Album of the Year[113]
Won

Best Live Band
Golden God Awards: Best Live Band
Nominated

Best Live Band
Kerrang! Awards: Best Live Band
Nominated

Avenged Sevenfold
Loudwire Music Awards: Live Act of the Year
Won

Nightmare
Kerrang! Awards: Best Single
Nominated

Nightmare
Kerrang! Awards: Best Album
Nominated

Band: Avenged Sevenfold
Kerrang! Awards: Best International Band
Nominated

Buried Alive
Revolver Magazine: Song of the Year
Nominated

2012
Best Live Band
Golden God Awards: Best Live Band
Won

Most Dedicated Fans
Golden God Awards: Most Dedicated Fans
Won

2013
Carry On
Golden God Awards: Song of the Year
Nominated

Hail to the King
Loudwire Music Awards: Best Rock Song
Won

Hail to the King
Loudwire Music Awards: Rock Album of the Year
Nominated

Avenged Sevenfold
Loudwire Music Awards: Rock Band of the Year
Won

Avenged Sevenfold
Loudwire Music Awards: Most Devoted Fans
Nominated

2014
Most Dedicated Fans
Golden God Awards: Most Dedicated Fans
Won

Hail to the King
Golden God Awards: Album of the Year
Nominated

M. Shadows on Hail to the King
Golden God Awards: Best Vocalist
Nominated

Synyster Gates & Zacky Vengeance on Hail to the King
Golden God Awards: Best Guitarists
Won

Arin Ilejay on Hail to the King
Golden God Awards: Best Drummer
Won

Johnny Christ on Hail to the King
Golden God Awards: Best Bassist
Nominated

Hail to the King
Golden God Awards: Song of the Year
Nominated

Avenged Sevenfold
Golden God Awards: Best International Band
Won

2016
Synyster Gates & Zacky Vengeance on The Stage
Total Guitar: Best Metal Guitarists in the World
Won

2017
Avenged Sevenfold
Golden God Awards: Best International Band
Won


document_title: List of National Basketball Association career scoring leaders

question_text: who has made the most points in the nba

question_tokens: who has made the most points in the nba

text: Scoring leaders[edit]

text: The following is a list of National Basketball Association players by total career regular season points scored.

text:
^
Active NBA player

*
Inducted into the Naismith Memorial Basketball Hall of Fame

†
Not yet eligible for Hall of Fame consideration[2]

§
1st time nominee for Hall of Fame in 2018[3]

text:
Rank
Player
Position(s)
Team(s) played for (years)[4]
Total points
Games
played
Points
per game
average[5]
Field goals
made
Three-point
field goals
made[6]
Free
throws
made

1
Abdul-Jabbar, KareemKareem Abdul-Jabbar*[7]
C
Milwaukee Bucks (1969–1975)
Los Angeles Lakers (1975–1989)
38,387
1,560
24.6
15,837
1
6,712

2
Malone, KarlKarl Malone*
PF
Utah Jazz (1985–2003)
Los Angeles Lakers (2003–2004)
36,928
1,476
25.0
13,528
85
9,787

3
Bryant, KobeKobe Bryant†
SG
Los Angeles Lakers (1996–2016)
33,643
1,346
25.0
11,719
1,827
8,378

4
Jordan, MichaelMichael Jordan*
SG
Chicago Bulls (1984–1993, 1995–1998)
Washington Wizards (2001–2003)
32,292
1,072
30.1
12,192
581
7,327

5
Chamberlain, WiltWilt Chamberlain*
C
Philadelphia/San Francisco Warriors (1959–1965)
Philadelphia 76ers (1965–1968)
Los Angeles Lakers (1968–1973)
31,419
1,045
30.1
12,681
0
6,057

6
Nowitzki, DirkDirk Nowitzki^
PF/C
Dallas Mavericks (1999–present)
31,005
1,455
21.3
10,966
1,886
7,187

7
James, LeBronLeBron James^
SF/PF
Cleveland Cavaliers (2003–2010, 2014–present)
Miami Heat (2010–2014)
30,387
1,121
27.1
11,039
1,570
6,739

8
O'Neal, ShaquilleShaquille O'Neal*
C
Orlando Magic (1992–1996)
Los Angeles Lakers (1996–2004)
Miami Heat (2004–2008)
Phoenix Suns (2008–2009)
Cleveland Cavaliers (2009–2010)
Boston Celtics (2010–2011)
28,596
1,207
23.7
11,330
1
5,935

9
Malone, MosesMoses Malone*
C
Buffalo Braves (1976)
Houston Rockets (1976–1982)
Philadelphia 76ers (1982–1986, 1993–1994)
Washington Bullets (1986–1988)
Atlanta Hawks (1988–1991)
Milwaukee Bucks (1991–1993)
San Antonio Spurs (1994–1995)
27,409
1,329
20.6
9,435
8
8,531

10
Hayes, ElvinElvin Hayes*
PF/C
San Diego/Houston Rockets (1968–1972, 1981–1984)
Baltimore/Capital/Washington Bullets (1972–1981)
27,313
1,303
21.0
10,976
5
5,356

11
Olajuwon, HakeemHakeem Olajuwon*[8]
C
Houston Rockets (1984–2001)
Toronto Raptors (2001–2002)
26,946
1,238
21.8
10,749
25
5,423

12
Robertson, OscarOscar Robertson*
PG
Cincinnati Royals (1960–1970)
Milwaukee Bucks (1970–1974)
26,710
1,040
25.7
9,508
0
7,694

13
Wilkins, DominiqueDominique Wilkins*
SF
Atlanta Hawks (1982–1994)
Los Angeles Clippers (1994)
Boston Celtics (1994–1995)
San Antonio Spurs (1996–1997)
Orlando Magic (1999)
26,668
1,074
24.8
9,963
711
6,031

14
Duncan, TimTim Duncan†
PF/C
San Antonio Spurs (1997–2016)
26,496
1,392
19.0
10,285
30
5,896

15
Pierce, PaulPaul Pierce†
SF/SG
Boston Celtics (1999–2013)
Brooklyn Nets (2013–2014)
Washington Wizards (2014–2015)
Los Angeles Clippers (2015–2017)
26,397
1,343
19.7
8,668
2,143
6,918

16
Havlicek, JohnJohn Havlicek*
SF/SG
Boston Celtics (1962–1978)
26,395
1,270
20.8
10,513
0
5,369

17
Garnett, KevinKevin Garnett†
PF/C
Minnesota Timberwolves (1995–2007, 2015–2016)
Boston Celtics (2007–2013)
Brooklyn Nets (2013–2015)
26,071
1,462
17.8
10,505
174
4,887

18
English, AlexAlex English*
SF
Milwaukee Bucks (1976–1978)
Indiana Pacers (1978–1980)
Denver Nuggets (1980–1990)
Dallas Mavericks (1990–1991)
25,613
1,193
21.5
10,659
18
4,277

19
Miller, ReggieReggie Miller*
SG
Indiana Pacers (1987–2005)
25,279
1,389
18.2
8,241
2,560
6,237

20
West, JerryJerry West*
PG/SG
Los Angeles Lakers (1960–1974)
25,192
932
27.0
9,016
0
7,160

21
Anthony, CarmeloCarmelo Anthony^
SF
Denver Nuggets (2003–2011)
New York Knicks (2011–2017)
Oklahoma City Thunder (2017–present)
25,173
1,036
24.3
8,999
1,299
5,876

22
Ewing, PatrickPatrick Ewing*
C
New York Knicks (1985–2000)
Seattle SuperSonics (2000–2001)
Orlando Magic (2001–2002)
24,815
1,183
21.0
9,702
19
5,392

23
Carter, VinceVince Carter^
SG/SF
Toronto Raptors (1999–2004)
New Jersey Nets (2004–2009)
Orlando Magic (2009–2010)
Phoenix Suns (2010–2011)
Dallas Mavericks (2011–2014)
Memphis Grizzlies (2014–2017)
Sacramento Kings (2017–present)
24,773
1,388
17.8
8,956
2,090
4,771

24
Allen, RayRay Allen§
SG
Milwaukee Bucks (1996–2003)
Seattle SuperSonics (2003–2007)
Boston Celtics (2007–2012)
Miami Heat (2012–2014)
24,505
1,300
18.9
8,567
2,973
4,398

25
Iverson, AllenAllen Iverson*
SG/PG
Philadelphia 76ers (1996–2006, 2009–2010)
Denver Nuggets (2006–2008)
Detroit Pistons (2008–2009)
Memphis Grizzlies (2009)
24,368
914
26.7
8,467
1,059
6,375

26
Barkley, CharlesCharles Barkley*
PF
Philadelphia 76ers (1984–1992)
Phoenix Suns (1992–1996)
Houston Rockets (1996–2000)
23,757
1,073
22.1
8,435
538
6,349

27
Parish, RobertRobert Parish*
C
Golden State Warriors (1976–1980)
Boston Celtics (1980–1994)
Charlotte Hornets (1994–1996)
Chicago Bulls (1996–1997)
23,334
1,611
14.5
9,614
0
4,106

28
Dantley, AdrianAdrian Dantley*
SF
Buffalo Braves (1976–1977)
Indiana Pacers (1977)
Los Angeles Lakers (1977–1979)
Utah Jazz (1979–1986)
Detroit Pistons (1986–1989)
Dallas Mavericks (1989–1990)
Milwaukee Bucks (1991)
23,177
955
24.3
8,169
7
6,832

29
Baylor, ElginElgin Baylor*
SF
Minneapolis/Los Angeles Lakers (1958–1971)
23,149
846
27.4
8,693
0
5,763

30
Drexler, ClydeClyde Drexler*
SG
Portland Trail Blazers (1983–1995)
Houston Rockets (1995–1998)
22,195
1,086
20.4
8,335
827
4,698

31
Wade, DwyaneDwyane Wade^
SG
Miami Heat (2003–2016, 2018–present)
Chicago Bulls (2016–2017)
Cleveland Cavaliers (2017–2018)
21,900
967
22.6
7,966
457
5,511

32
Payton, GaryGary Payton*
PG
Seattle SuperSonics (1990–2003)
Milwaukee Bucks (2003)
Los Angeles Lakers (2003–2004)
Boston Celtics (2004–2005)
Miami Heat (2005–2007)
21,813
1,335
16.3
8,708
1,132
3,265

33
Bird, LarryLarry Bird*
SF/PF
Boston Celtics (1979–1992)
21,791
897
24.3
8,591
649
3,960

34
Greer, HalHal Greer*
SG/PG
Syracuse Nationals/Philadelphia 76ers (1958–1973)
21,586
1,122
19.2
8,504
0
4,578

35
Bellamy, WaltWalt Bellamy*
C
Chicago Packers/Zephyrs/Baltimore Bullets (1961–1965)
New York Knicks (1965–1968)
Detroit Pistons (1968–1970)
Atlanta Hawks (1970–1974)
New Orleans Jazz (1974)
20,941
1,043
20.1
7,914
0
5,113

36
Pettit, BobBob Pettit*
PF/C
Milwaukee/St. Louis Hawks (1954–1965)
20,880
792
26.4
7,349
0
6,182

37
Robinson, DavidDavid Robinson*
C
San Antonio Spurs (1989–2003)
20,790
987
21.1
7,365
25
6,035

38
Gervin, GeorgeGeorge Gervin*
SG/SF
San Antonio Spurs (1976–1985)
Chicago Bulls (1985–1986)
20,708
791
26.2
8,045
77
4,541

39
Gasol, PauPau Gasol^
C/PF
Memphis Grizzlies (2001–2008)
Los Angeles Lakers (2008–2014)
Chicago Bulls (2014–2016)
San Antonio Spurs (2016–present)
20,622
1,177
17.5
7,880
169
4,693

40
Durant, KevinKevin Durant^
SF/SG
Seattle SuperSonics/Oklahoma City Thunder (2007–2016)
Golden State Warriors (2016–present)
20,526
757
27.1
6,959
1,399
5,209

41
Richmond, MitchMitch Richmond*
SG
Golden State Warriors (1988–1991)
Sacramento Kings (1991–1998)
Washington Wizards (1999–2001)
Los Angeles Lakers (2001–2002)
20,497
976
21.0
7,305
1,326
4,561

42
Johnson, JoeJoe Johnson^
SG/SF
Boston Celtics (2001–2002)
Phoenix Suns (2002–2005)
Atlanta Hawks (2005–2012)
Brooklyn Nets (2012–2016)
Miami Heat (2016)
Utah Jazz (2016–2018)
Houston Rockets (2018–present)
20,302
1,258
16.1
7,783
1,967
2,769

43
Chambers, TomTom Chambers
PF
San Diego Clippers (1981–1983)
Seattle SuperSonics (1983–1988)
Phoenix Suns (1988–1993)
Utah Jazz (1993–1995)
Charlotte Hornets (1997)
Philadelphia 76ers (1997)
20,049
1,107
18.1
7,378
227
5,066

44
Jamison, AntawnAntawn Jamison
PF/SF
Golden State Warriors (1999–2003)
Dallas Mavericks (2003–2004)
Washington Wizards (2004–2010)
Cleveland Cavaliers (2010–2012)
Los Angeles Lakers (2012–2013)
Los Angeles Clippers (2013–2014)
20,042
1,083
18.5
7,679
1,163
3,521

45
Stockton, JohnJohn Stockton*
PG
Utah Jazz (1984–2003)
19,711
1,504
13.1
7,039
845
4,788

46
King, BernardBernard King*
SF
New Jersey Nets (1977–1979, 1993)
Utah Jazz (1979)
Golden State Warriors (1980–1982)
New York Knicks (1982–1985, 1987)
Washington Bullets (1987–1991)
19,655
874
22.5
7,830
23
3,972

47
Robinson, CliffordClifford Robinson
PF/SF
Portland Trail Blazers (1989–1997)
Phoenix Suns (1997–2001)
Detroit Pistons (2001–2003)
Golden State Warriors (2003–2005)
New Jersey Nets (2005–2007)
19,591
1,380
14.2
7,389
1,253
3,560

48
Davis, WalterWalter Davis
SG/SF
Phoenix Suns (1977–1988)
Denver Nuggets (1988–1991, 1991–1992)
Portland Trail Blazers (1991)
19,521
1,033
18.9
8,118
157
3,128

49
Cummings, TerryTerry Cummings
PF
San Diego Clippers (1982–1984)
Milwaukee Bucks (1984–1989, 1995–1996)
San Antonio Spurs (1989–1995)
Seattle SuperSonics (1996–1997)
Philadelphia 76ers (1997–1998)
New York Knicks (1998)
Golden State Warriors (1999–2000)
19,460
1,183
16.4
8,045
44
3,326

50
Lanier, BobBob Lanier*
C
Detroit Pistons (1970–1980)
Milwaukee Bucks (1980–1984)
19,248
959
20.1
7,761
2
3,724

text: Progressive list of scoring leaders[edit]

text: This is a progressive list of scoring leaders showing how the record increased through the years.[1]

text:
Team abbreviations
Team(s) listed is the one player was on when he established the record.

ATL
Atlanta Hawks
DET
Detroit Pistons
MIL
Milwaukee Bucks
PHX
Phoenix Suns

BOS
Boston Celtics
FTW
Fort Wayne Pistons
MIN
Minnesota Timberwolves
PHW
Philadelphia Warriors

BUF
Buffalo Braves
GSW
Golden State Warriors
MNL
Minneapolis Lakers
SAS
San Antonio Spurs

CHI
Chicago Bulls
HOU
Houston Rockets
NOJ
New Orleans Jazz
SDR
San Diego Rockets

CHS
Chicago Stags
IND
Indiana Pacers
NOP
New Orleans Pelicans
SFW
San Francisco Warriors

CLE
Cleveland Cavaliers
KCO
Kansas City-Omaha Kings
OKC
Oklahoma City Thunder
STL
St. Louis Hawks

DAL
Dallas Mavericks
LAL
Los Angeles Lakers
ORL
Orlando Magic
SYR
Syracuse Nationals

DEN
Denver Nuggets
MIA
Miami Heat
PHI
Philadelphia 76ers
UTA
Utah Jazz

text:
Scoring Leader at the end of every season

Season
Year-by-year leader
Points
Active player points leader
Total points
Career points record
Total points
Single-season points record
Points
Season

1946–47
Joe Fulks*000PHW
1,389
Joe Fulks*000PHW
1,389
Joe Fulks*000PHW
1,389
Joe Fulks*000PHW
1,389
1946–47

1947–48
Max Zaslofsky000CHS
1,007
2,338
2,338
1947–48

1948–49
George Mikan*000MNL
1,698
3,898
3,898
George Mikan*000MNL
1,698
1948–49

1949–50
1,865
4,863
4,863
1,865
1949–50

1950–51
1,932
6,099
6,099
1,932
1950–51

1951–52
Paul Arizin*000PHW
1,674
7,021
7,021
1951–52

1952–53
Neil Johnston*000PHW
1,564
George Mikan*000MNL
8,460
George Mikan*000MNL
8,460
1952–53

1953–54
1,759
9,766
9,766
1953–54

1954–55
1,631
Max Zaslofsky000FTW
7,902
1954–55

1955–56
Bob Pettit*000STL
1,849
George Mikan*000MNL
10,156
10,156
1955–56

1956–57
Paul Arizin*000PHW
1,817
Ed Macauley*000STL
10,150
1956–57

1957–58
George Yardley*000DET
2,001
Dolph Schayes*000SYR
11,764
Dolph Schayes*000SYR
11,764
George Yardley*000DET
2,001
1957–58

1958–59
Bob Pettit*000STL
2,105
13,298
13,298
Bob Pettit*000STL
2,105
1958–59

1959–60
Wilt Chamberlain*
000PHW 1959–62
000SFW 1962–65
000PHI 1965–66
2,707
14,987
14,987
Wilt Chamberlain*000PHW
2,707
1959–60

1960–61
3,033
16,855
16,855
3,033
1960–61

1961–62
4,029
17,677
17,677
4,029
1961–62

1962–63
3,586
18,304
18,304
1962–63

1963–64
2,948
Bob Pettit*000STL
19,756
Bob Pettit*000STL
19,756
1963–64

1964–65
2,534
20,880
20,880
1964–65

1965–66
2,649
Wilt Chamberlain*
000PHI 1965–68
000LAL 1968–73
21,486
Wilt Chamberlain*
000PHI 1965–68
000LAL 1968–73
21,486
1965–66

1966–67
Rick Barry*000SFW
2,775
23,442
23,442
1966–67

1967–68
Dave Bing*000DET
2,142
25,434
25,434
1967–68

1968–69
Elvin Hayes*000SDR
2,327
27,098
27,098
1968–69

1969–70
Kareem Abdul-Jabbar*000MIL
2,361
27,426
27,426
1969–70

1970–71
2,596
29,122
29,122
1970–71

1971–72
2,822
30,335
30,335
1971–72

1972–73
Tiny Archibald*000KCO
2,719
31,419
31,419
1972–73

1973–74
Bob McAdoo*000BUF
2,261
Oscar Robertson*000MIL
26,710
1973–74

1974–75
2,831
John Havlicek*000BOS
22,389
1974–75

1975–76
2,427
23,678
1975–76

1976–77
Pete Maravich*000NOJ
2,273
25,073
1976–77

1977–78
George Gervin*000SAS
2,232
26,395
1977–78

1978–79
2,365
Kareem Abdul-Jabbar*
000LAL
22,141
1978–79

1979–80
2,585
24,175
1979–80

1980–81
Adrian Dantley*000UTA
2,452
26,270
1980–81

1981–82
George Gervin*000SAS
2,551
28,088
1981–82

1982–83
Alex English*000DEN
2,326
29,810
1982–83

1983–84
Adrian Dantley*000UTA
2,418
31,527
Kareem Abdul-Jabbar*000LAL
31,527
1983–84

1984–85
Michael Jordan*000CHI
2,313
33,262
33,262
1984–85

1985–86
Alex English*000DEN
2,414
35,108
35,108
1985–86

1986–87
Michael Jordan*000CHI
3,041
36,474
36,474
1986–87

1987–88
2,868
37,639
37,639
1987–88

1988–89
2,633
38,387
38,387
1988–89

1989–90
2,753
Moses Malone*
000ATL 1989–91
000MIL 1991–93
000PHI 1993–94
000SAS 1994–95
24,868
1989–90

1990–91
2,580
25,737
1990–91

1991–92
2,404
27,016
1991–92

1992–93
2,541
27,066
1992–93

1993–94
David Robinson*000SAS
2,383
27,360
1993–94

1994–95
Shaquille O'Neal*000ORL
2,315
27,409
1994–95

1995–96
Michael Jordan*000CHI
2,491
Michael Jordan*000CHI
24,489
1995–96

1996–97
2,431
26,920
1996–97

1997–98
2,357
29,277
1997–98

1998–99
Shaquille O'Neal*000LAL
1,289
Karl Malone*
000UTA 1998–2003
000LAL 2003–04
28,946
1998–99

1999–00
2,344
31,041
1999–00

2000–01
Jerry Stackhouse00DET
2,380
32,919
2000–01

2001–02
Paul Pierce†000BOS
2,144
34,707
2001–02

2002–03
Kobe Bryant†000LAL
2,461
36,374
2002–03

2003–04
Kevin Garnett†000MIN
1,987
36,928
2003–04

2004–05
Allen Iverson*000PHI
2,302
Reggie Miller*000IND
25,279
2004–05

2005–06
Kobe Bryant†000LAL
2,832
Shaquille O'Neal*
000MIA 2005–08
000PHO 2008–09
000CLE 2009–10
000BOS 2010–11
24,764
2005–06

2006–07
2,430
25,454
2006–07

2007–08
2,323
26,286
2007–08

2008–09
Dwyane Wade^000MIA
2,386
27,619
2008–09

2009–10
Kevin Durant^000OKC
2,472
28,255
2009–10

2010–11
2,161
28,596
2010–11

2011–12
1,850
Kobe Bryant†
000LAL
29,484
2011–12

2012–13
2,280
31,617
2012–13

2013–14
2,593
31,700
2013–14

2014–15
James Harden^000HOU
2,217
32,482
2014–15

2015–16
2,376
33,643
2015–16

2016–17
Russell Westbrook^000OKC
2,558
Dirk Nowitzki^000DAL
30,260
2016–17

2017–18
James Harden^000HOU
1,565
30,963
Abdul-Jabbar*0 35 yrs
38,387
Chamberlain*059 yrs
4,029
2017–18

Season
Year-by-Year Leader
Points
Active Player Points Leader
Total points
Career Points Record
Total points
Single Season Points Record
Points
Season


document_title: Curvature

question_text: curvature of a circle of radius r is given by

question_tokens: curvature of a circle of radius r is given by

text: Curvature

text: Curvature of plane curves[edit]

text: Augustin-Louis Cauchy defined the center of curvature C as the intersection point of two infinitely close normals to the curve, the radius of curvature as the distance from the point to C, and the curvature itself as the inverse of the radius of curvature.[1]

text: Let C be a plane curve (the precise technical assumptions are given below). The curvature of C at a point is a measure of how sensitive its tangent line is to moving the point to other nearby points. There are a number of equivalent ways that this idea can be made precise.

text: One way is geometrical. It is natural to define the curvature of a straight line to be constantly zero. The curvature of a circle of radius R should be large if R is small and small if R is large. Thus the curvature of a circle is defined to be the reciprocal of the radius:[2]

text: Given any curve C and a point P on it, there is a unique circle or line which most closely approximates the curve near P, the osculating circle at P. The curvature of C at P is then defined to be the curvature of that circle or line. The radius of curvature is defined as the reciprocal of the curvature.

text: Another way to understand the curvature is physical. Suppose that a particle moves along the curve with unit speed. Taking the time s as the parameter for C, this provides a natural parametrization for the curve. The unit tangent vector T (which is also the velocity vector, since the particle is moving with unit speed) also depends on time. The curvature is then the magnitude of the rate of change of T. Symbolically,

text: This is the magnitude of the acceleration of the particle and the vector dT/ds is the acceleration vector. Geometrically, the curvature κ measures how fast the unit tangent vector to the curve rotates.[3] If a curve keeps close to the same direction, the unit tangent vector changes very little and the curvature is small; where the curve undergoes a tight turn, the curvature is large.

text: These two approaches to the curvature are related geometrically by the following observation. In the first definition, the curvature of a circle is equal to the ratio of the angle of an arc to its length. Likewise, the curvature of a plane curve at any point is the limiting ratio of dθ, an infinitesimal angle (in radians) between tangents to that curve at the ends of an infinitesimal segment of the curve, to the length of that segment ds, i.e., dθ/ds.[4] If the tangents at the ends of the segment are represented by unit vectors, it is easy to show that in this limit, the magnitude of the difference vector is equal to dθ, which leads to the given expression in the second definition of curvature.

text: Precise definition[edit]

text: Suppose that C is a twice continuously differentiable immersed plane curve, which here means that there exists a parametric representation of C by a pair of functions γ(t) = (x(t), y(t)) such that the first and second derivatives of x and y both exist and are continuous, and

text: throughout the domain. For such a plane curve, there exists a reparametrization with respect to arc length s. This is a parametrization of C such that

text: The velocity vector T(s) is the unit tangent vector. The unit normal vector N(s), the curvature κ(s), the oriented or signed curvature k(s), and the radius of curvature R(s) are given by

text: Expressions for calculating the curvature in arbitrary coordinate systems are given below.

text: Signed curvature[edit]

text: The sign of the signed curvature k indicates the direction in which the unit tangent vector rotates as a function of the parameter along the curve. If the unit tangent rotates counterclockwise, then k > 0. If it rotates clockwise, then k < 0. So, for example, the sign of the curvature of the graph of a function is the same as the sign of the second derivative (see below).

text: The signed curvature depends on the particular parametrization chosen for a curve. For example, the unit circle can be parametrised by (cos θ, sin θ) (counterclockwise, with k > 0), or by (cos(−θ), sin(−θ)) (clockwise, with k < 0). More precisely, the signed curvature depends only on the choice of orientation of an immersed curve. Every immersed curve in the plane admits two possible orientations.

text: Local expressions[edit]

text: For a plane curve given parametrically in Cartesian coordinates as γ(t) = (x(t),y(t)), the curvature is

text: where primes refer to derivatives d/dt with respect to the parameter t. The signed curvature k is

text: The expression reflects the geometric meaning discussed above, that the curvature is influenced by the change amount of the tangent vector in the direction of the normal vector, as

text: These can be expressed in a coordinate-independent manner via

text: Curvature of a graph[edit]

text: For the less general case of a plane curve given explicitly as y = f(x), and now using primes for derivatives d/dx with respect to coordinate x, the curvature is

text: and the signed curvature is

text: This quantity is common in physics and engineering; for example, in the equations of bending in beams, the one-dimensional vibration of a tense string, approximations to the fluid flow around surfaces (in aeronautics), and the free surface boundary conditions in ocean waves. In such applications, the assumption is almost always made that the slope is small compared with unity, so that the approximation:

text: may be used. This approximation yields a straightforward linear equation describing the phenomenon.

text: If a curve is defined in polar coordinates as r(θ), then its curvature is

text: where here the prime refers to differentiation with respect to θ.

text: Implicit curve[edit]

text:
For implicit curves defined by a function

F
(
x
,
y
)
=
0

{\displaystyle F(x,y)=0}

 with partial derivatives

F

x

{\displaystyle F_{x}}

,

F

y

{\displaystyle F_{y}}

,

F

x
x

{\displaystyle F_{xx}}

,

F

x
y

{\displaystyle F_{xy}}

,

F

y
y

,

{\displaystyle F_{yy},}

the curvature is given by[6]

text: Examples[edit]

text: Consider the parabola y = x2. We can parametrize the curve simply as γ(t) = (t,t2) = (x,y). If we use primes for derivatives with respect to the parameter t, then

text: Substituting and dropping unnecessary absolute values, get

text: And the same result may be obtained immediately from the above formula of the curvature of a graph, without parametrizing.

text: A Lissajous curve with a 3:2 ratio of frequencies can be parametrized in this way:

text: Applying the formula it turns out to have signed curvature:

text: Curvature of space curves[edit]

text: As in the case of curves in two dimensions, the curvature of a regular space curve C in three dimensions (and higher) is the magnitude of the acceleration of a particle moving with unit speed along a curve. Thus if γ(s) is the arc-length parametrization of C then the unit tangent vector T(s) is given by

text: and the curvature is the magnitude of the acceleration:

text: The direction of the acceleration is the unit normal vector N(s), which is defined by

text: The plane containing the two vectors T(s) and N(s) is called the osculating plane to the curve at γ(s). The curvature has the following geometrical interpretation. There exists a circle in the osculating plane tangent to γ(s) whose Taylor series to second order at the point of contact agrees with that of γ(s). This is the osculating circle to the curve. The radius of the circle R(s) is called the radius of curvature, and the curvature is the reciprocal of the radius of curvature:

text: The tangent, curvature, and normal vector together describe the second-order behavior of a curve near a point. In three-dimensions, the third order behavior of a curve is described by a related notion of torsion, which measures the extent to which a curve tends to move in a helical path in space. The torsion and curvature are related by the Frenet–Serret formulas (in three dimensions) and their generalization (in higher dimensions).

text: Local expressions[edit]

text: For a parametrically-defined space curve in three dimensions given in Cartesian coordinates by γ(t) = (x(t), y(t), z(t)), the curvature is

text: where the prime denotes differentiation with respect to the parameter t. This can be expressed independently of the coordinate system by means of the formula

text: where × is the vector cross product. Equivalently,

text: Here the T denotes the matrix transpose. This last formula is also valid for the curvature of curves in a Euclidean space of any dimension.

text: Curvature from arc and chord length[edit]

text: Given two points P and Q on C, let s(P,Q) be the arc length of the portion of the curve between P and Q and let d(P,Q) denote the length of the line segment from P to Q. The curvature of C at P is given by the limit[citation needed]

text: where the limit is taken as the point Q approaches P on C. The denominator can equally well be taken to be d(P,Q)3. The formula is valid in any dimension. Furthermore, by considering the limit independently on either side of P, this definition of the curvature can sometimes accommodate a singularity at P. The formula follows by verifying it for the osculating circle.

text: Curvature of curves on surfaces[edit]

text: When a one-dimensional curve lies on a two dimensional surface embedded in three dimensions ℝ3, further measures of curvature are available, which take the surface's unit normal vector, u into account. These are the normal curvature, geodesic curvature and geodesic torsion. Any non-singular curve on a smooth surface will have its tangent vector T lying in the tangent plane of the surface orthogonal to the normal vector. The normal curvature, kn, is the curvature of the curve projected onto the plane containing the curve's tangent T and the surface normal u; the geodesic curvature, kg, is the curvature of the curve projected onto the surface's tangent plane; and the geodesic torsion (or relative torsion), τr, measures the rate of change of the surface normal around the curve's tangent.

text: Let the curve be a unit speed curve and let t = u × T so that T, u, t form an orthonormal basis: the Darboux frame. The above quantities are related by:

text: Principal curvature[edit]

text: All curves with the same tangent vector will have the same normal curvature, which is the same as the curvature of the curve obtained by intersecting the surface with the plane containing T and u. Taking all possible tangent vectors, the maximum and minimum values of the normal curvature at a point are called the principal curvatures, k1 and k2, and the directions of the corresponding tangent vectors are called principal normal directions.

text: Curvature of surfaces[edit]

text: Normal sections[edit]

text: Curvature can be evaluated along surface normal sections, similar to § Curves on surfaces above (see, e.g., Earth radius of curvature).

text: Gaussian curvature[edit]

text: In contrast to curves, which do not have intrinsic curvature, but do have extrinsic curvature (they only have a curvature given an embedding), surfaces can have intrinsic curvature, independent of an embedding. The Gaussian curvature, named after Carl Friedrich Gauss, is equal to the product of the principal curvatures, k1k2. It has a dimension of length−2 and is positive for spheres, negative for one-sheet hyperboloids and zero for planes. It determines whether a surface is locally convex (when it is positive) or locally saddle-shaped (when it is negative).

text: Gaussian curvature is an intrinsic property of the surface, meaning it does not depend on the particular embedding of the surface; intuitively, this means that ants living on the surface could determine the Gaussian curvature. For example, an ant living on a sphere could measure the sum of the interior angles of a triangle and determine that it was greater than 180 degrees, implying that the space it inhabited had positive curvature. On the other hand, an ant living on a cylinder would not detect any such departure from Euclidean geometry; in particular the ant could not detect that the two surfaces have different mean curvatures (see below), which is a purely extrinsic type of curvature.

text: Formally, Gaussian curvature only depends on the Riemannian metric of the surface. This is Gauss's celebrated Theorema Egregium, which he found while concerned with geographic surveys and mapmaking.

text: An intrinsic definition of the Gaussian curvature at a point P is the following: imagine an ant which is tied to P with a short thread of length r. It runs around P while the thread is completely stretched and measures the length C(r) of one complete trip around P. If the surface were flat, she would find C(r) = 2πr. On curved surfaces, the formula for C(r) will be different, and the Gaussian curvature K at the point P can be computed by the Bertrand–Diguet–Puiseux theorem as

text: The integral of the Gaussian curvature over the whole surface is closely related to the surface's Euler characteristic; see the Gauss–Bonnet theorem.

text: The discrete analog of curvature, corresponding to curvature being concentrated at a point and particularly useful for polyhedra, is the (angular) defect; the analog for the Gauss–Bonnet theorem is Descartes' theorem on total angular defect.

text: Because (Gaussian) curvature can be defined without reference to an embedding space, it is not necessary that a surface be embedded in a higher-dimensional space in order to be curved. Such an intrinsically curved two-dimensional surface is a simple example of a Riemannian manifold.

text: Mean curvature[edit]

text: The mean curvature is an extrinsic measure of curvature equal to half the sum of the principal curvatures, k1 + k2/2. It has a dimension of length−1. Mean curvature is closely related to the first variation of surface area. In particular, a minimal surface such as a soap film has mean curvature zero and a soap bubble has constant mean curvature. Unlike Gauss curvature, the mean curvature is extrinsic and depends on the embedding, for instance, a cylinder and a plane are locally isometric but the mean curvature of a plane is zero while that of a cylinder is nonzero.

text: Second fundamental form[edit]

text: The intrinsic and extrinsic curvature of a surface can be combined in the second fundamental form. This is a quadratic form in the tangent plane to the surface at a point whose value at a particular tangent vector X to the surface is the normal component of the acceleration of a curve along the surface tangent to X; that is, it is the normal curvature to a curve tangent to X (see above). Symbolically,

text: where N is the unit normal to the surface. For unit tangent vectors X, the second fundamental form assumes the maximum value k1 and minimum value k2, which occur in the principal directions u1 and u2, respectively. Thus, by the principal axis theorem, the second fundamental form is

text: Thus the second fundamental form encodes both the intrinsic and extrinsic curvatures.

text: Shape operator[edit]

text: A related notion of curvature is the shape operator, which is a linear operator from the tangent plane to itself. When applied to a tangent vector X to the surface, the shape operator is the tangential component of the rate of change of the normal vector when moved along a curve on the surface tangent to X. The principal curvatures are the eigenvalues of the shape operator, and in fact the shape operator and second fundamental form have the same matrix representation with respect to a pair of orthonormal vectors of the tangent plane. The Gauss curvature is thus the determinant of the shape tensor and the mean curvature is half its trace.

text: Curvature of space[edit]

text: By extension of the former argument, a space of three or more dimensions can be intrinsically curved. The curvature is intrinsic in the sense that it is a property defined at every point in the space, rather than a property defined with respect to a larger space that contains it. In general, a curved space may or may not be conceived as being embedded in a higher-dimensional ambient space; if not then its curvature can only be defined intrinsically.

text: After the discovery of the intrinsic definition of curvature, which is closely connected with non-Euclidean geometry, many mathematicians and scientists questioned whether ordinary physical space might be curved, although the success of Euclidean geometry up to that time meant that the radius of curvature must be astronomically large. In the theory of general relativity, which describes gravity and cosmology, the idea is slightly generalised to the "curvature of spacetime"; in relativity theory spacetime is a pseudo-Riemannian manifold. Once a time coordinate is defined, the three-dimensional space corresponding to a particular time is generally a curved Riemannian manifold; but since the time coordinate choice is largely arbitrary, it is the underlying spacetime curvature that is physically significant.

text: Although an arbitrarily curved space is very complex to describe, the curvature of a space which is locally isotropic and homogeneous is described by a single Gaussian curvature, as for a surface; mathematically these are strong conditions, but they correspond to reasonable physical assumptions (all points and all directions are indistinguishable). A positive curvature corresponds to the inverse square radius of curvature; an example is a sphere or hypersphere. An example of negatively curved space is hyperbolic geometry. A space or space-time with zero curvature is called flat. For example, Euclidean space is an example of a flat space, and Minkowski space is an example of a flat spacetime. There are other examples of flat geometries in both settings, though. A torus or a cylinder can both be given flat metrics, but differ in their topology. Other topologies are also possible for curved space. See also shape of the universe.

text: Generalizations[edit]

text: The mathematical notion of curvature is also defined in much more general contexts.[7] Many of these generalizations emphasize different aspects of the curvature as it is understood in lower dimensions.

text: One such generalization is kinematic. The curvature of a curve can naturally be considered as a kinematic quantity, representing the force felt by a certain observer moving along the curve; analogously, curvature in higher dimensions can be regarded as a kind of tidal force (this is one way of thinking of the sectional curvature). This generalization of curvature depends on how nearby test particles diverge or converge when they are allowed to move freely in the space; see Jacobi field.

text: Another broad generalization of curvature comes from the study of parallel transport on a surface. For instance, if a vector is moved around a loop on the surface of a sphere keeping parallel throughout the motion, then the final position of the vector may not be the same as the initial position of the vector. This phenomenon is known as holonomy.[8] Various generalizations capture in an abstract form this idea of curvature as a measure of holonomy; see curvature form. A closely related notion of curvature comes from gauge theory in physics, where the curvature represents a field and a vector potential for the field is a quantity that is in general path-dependent: it may change if an observer moves around a loop.

text: Two more generalizations of curvature are the scalar curvature and Ricci curvature. In a curved surface such as the sphere, the area of a disc on the surface differs from the area of a disc of the same radius in flat space. This difference (in a suitable limit) is measured by the scalar curvature. The difference in area of a sector of the disc is measured by the Ricci curvature. Each of the scalar curvature and Ricci curvature are defined in analogous ways in three and higher dimensions. They are particularly important in relativity theory, where they both appear on the side of Einstein's field equations that represents the geometry of spacetime (the other side of which represents the presence of matter and energy). These generalizations of curvature underlie, for instance, the notion that curvature can be a property of a measure; see curvature of a measure.

text: Another generalization of curvature relies on the ability to compare a curved space with another space that has constant curvature. Often this is done with triangles in the spaces. The notion of a triangle makes senses in metric spaces, and this gives rise to CAT(k) spaces.


document_title: Padmavyuha

question_text: who knew the art of exiting the chakravyuh battle formation in mahabharat

text: Padmavyuha

text: Background[edit]

text: The Chakravyūha or Padmavyūha is a multi-tiered defensive formation that looks like a blooming lotus (पद्म padma) or disc (चक्र chakra) when viewed from above.[1] The warriors at each interleaving position would be in an increasingly tough position to fight. The formation was used in the battle of Kurukshetra by Dronacharya, who became commander-in-chief of the Kaurava army after the fall of Bhishma Pitamaha.

text: The various vyūhas (military formations) were studied by the Kauravas and Pandavas alike. Most of them can be beaten using a counter-measure targeted specifically against that formation. It is important to observe that in the form of battle described in the Mahabharata, it was important to place powerful fighters in positions where they could inflict maximum damage to the opposing force, or defend their own side. As per this military strategy, a specific stationary object or a moving object or person could be captured, surrounded and fully secured during battle.

text: The formation begins with two soldiers on both sides, with other soldiers following them at a distance of three hands, drawing up seven circles and culminating in the end which is the place where the captured person or object is to be kept. In order to form the Chakravyuha, the commander has to identify soldiers who will form this formation. The number of soldiers to be deployed and the size of the Chakravyuha is calculated as per the resistance estimated. Once drawn, the foremost soldiers come on either side of the opponent to be captured, engage briefly and then advance. Their place is taken up by the next soldiers on either side, who again engage the opponent briefly and then advance. In this fashion, a number of soldiers pass the enemy and proceed in a circular pattern. By the time the rear of the formation arrives, the oblivious enemy is surrounded on all sides by seven tiers of soldiers. The last soldiers of the formation give the signal of completing the Chakravyuha. On the signal, every soldier who so far has been facing outwards turns inwards to face the opponent. It is only then that the captured enemy realizes his captivity. The army maintains the circular formation and can lead away the captive as well.

text: Abhimanyu and the Chakravyūha[edit]

text: The Chakravyūha or Padmavyūha was a very special formation (vyuha), and knowledge of how to penetrate it was limited to only a handful of warriors on the Pandavas' side, namely: Abhimanyu, Arjuna, Krishna and Pradyumna, of which only Abhimanyu was present when the Kauravas used it on the battlefield. In the Mahabharata it is mentioned that Abhimanyu learnt about the Chakravyūha while in his mother's womb but he was not able to hear how to escape the formation. After Abhimanyu had penetrated the sixth tier of the formation, all the Kauravas' commanders attacked him simultaneously, which was against the righteous rules of warfare Dharmayuddha, and gradually exhausted and killed him.[2]


document_title: Adaptation to extrauterine life

question_text: when does a baby breathe for the first time

text: Adaptation to extrauterine life

text: Breathing and circulation[edit]

text: Perfusing its body by breathing independently instead of utilizing placental oxygen delivered via the umbilical cord is the first challenge of a newborn. At birth, the baby's lungs are filled with lung liquid, which is distinct from amniotic fluid.[1] When the newborn is expelled from the birth canal, its central nervous system reacts to the sudden change in temperature and environment.[2] This triggers it to take the first breath, within about 10 seconds after delivery.[2] With the first breaths, there is a fall in pulmonary vascular resistance, and an increase in the surface area available for gas exchange. Over the next 30 seconds the pulmonary blood flow increases and is oxygenated as it flows through the alveoli of the lungs. Oxygenated blood now reaches the left atrium and ventricle, and through the descending aorta reaches the umbilical arteries. Oxygenated blood now stimulates constriction of the umbilical arteries resulting in a reduction in placental blood flow. As the pulmonary circulation increases there is an equivalent reduction in the placental blood flow which normally ceases completely after about three minutes. These two changes result in a rapid redirection of blood flow into the pulmonary vascular bed, from approximately 4% to 100% of cardiac output. The increase in pulmonary venous return results in left atrial pressure being slightly higher than right atrial pressure, which closes the foramen ovale. The flow pattern changes results in a drop in blood flow across the ductus arteriosus and the higher blood oxygen content of blood within the aorta stimulates the constriction and ultimately the closure of this fetal circulatory shunt.

text: All of these cardiovascular system changes result in the adaptation from fetal circulation patterns to an adult circulation pattern. During this transition, some types of congenital heart disease that were not symptomatic in utero during fetal circulation will present with cyanosis or respiratory signs.

text: It is common obstetric practice to intervene in these changes by applying a clamp to the umbilical cord, often within 20 seconds of birth, before transition has taken place. However delayed clamping (>1min) may have benefits in terms of iron status.[3]

text: Following birth, the expression and re-uptake of surfactant, which begins to be produced by the fetus at 20 weeks gestation, is accelerated. Expression of surfactant into the alveoli is necessary to prevent alveolar closure (atelectasis). At this point, rhythmic breathing movements also commence. If there are any problems with breathing, management can include stimulation, bag and mask ventilation, intubation and ventilation. Cardiorespiratory monitoring is essential to keeping track of potential problems. Pharmacological therapy such as caffeine can also be given to treat apnea in premature newborns. A positive airway pressure should be maintained, and neonatal sepsis must be ruled out.

text: Potential neonatal respiratory problems include apnea, transient tachypnea of the newborn (TTNB), respiratory distress syndrome (RDS), meconium aspiration syndrome (MAS), airway obstruction, and pneumonia.

text: Energy metabolism[edit]

text: Energy metabolism in the fetus must be converted from a continuous placental supply of glucose to intermittent feeding. While the fetus is dependent on maternal glucose as the main source of energy, it can use lactate, free-fatty acids, and ketone bodies under some conditions. Plasma glucose is maintained by glycogenolysis.

text: Glycogen synthesis in the liver and muscle begins in the late second trimester of pregnancy, and storage is completed in the third trimester. Glycogen stores are maximal at term, but even then, the fetus only has enough glycogen available to meet energy needs for 8–10 hours, which can be depleted even more quickly if demand is high. Newborns will then rely on gluconeogenesis for energy, which requires integration, and is normal at 2–4 days of life.

text: Fat stores are the largest storage source of energy. At 27 weeks gestation, only 1% of a fetus' body weight is fat. At 40 weeks, that number increases to 16%. Inadequate available glucose substrate can lead to hypoglycemia, fetal growth restriction, preterm delivery, or other problems. Similarly, excess substrate can lead to problems, such as infant of a diabetic mother (IDM), hypothermia or neonatal sepsis.

text: Anticipating potential problems is the key to managing most neonatal problems of energy metabolism. For example, early feeding in the delivery room or as soon as possible may prevent hypoglycemia. If the blood glucose is still low, then an intravenous (IV) bolus of glucose may be delivered, with continuous infusion if necessary. Rarely, steroids or glucagon may have to be employed.

text: Temperature regulation[edit]

text: Newborns come from a warm environment to the cold and fluctuating temperatures of this world. They are naked, wet, and have a large surface-area-to-mass ratio, with variable amounts of insulation, limited metabolic reserves, and a decreased ability to shiver. Physiologic mechanisms for preserving core temperature include vasoconstriction (decrease blood flow to the skin), maintaining the fetal position (decrease the surface area exposed to the environment), jittery large muscle activity (generate muscular heat), and "non-shivering thermogenesis". The latter occurs in "brown fat" which is specialized adipose tissue with a high concentration of mitochondria designed to rapidly oxidize fatty acids in order to generate metabolic heat. The newborn capacity to maintain these mechanisms is limited, especially in premature infants. As such, it is not surprising that some newborns may have problems regulating their temperature. As early as the 1880s, infant incubators were used to help newborns maintain warmth, with humidified incubators being used as early as the 1930s.

text: Basic techniques for keeping newborns warm include keeping them dry, wrapping them in blankets, giving them hats and clothing, or increasing the ambient temperature. More advanced techniques include incubators (at 36.5 °C), humidity, heat shields, thermal blankets, double-walled incubators, and radiant warmers while the use of skin-to-skin "kangaroo care" interventions for low-birth-weight infants have started to spread worldwide after its use as a solution in developing countries.[4]