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40000 (number)
40,000 (forty thousand) is the natural number that comes after 39,999 and before 40,001. It is the square of 200. Selected numbers in the range 40001–49999 40001 to 40999 * 40320 = smallest factorial (8!) that is not a highly composite number * 40425 = square pyramidal number * 40585 = largest factorion * 40678 = pentagonal pyramidal number * 40804 = palindromic square 41000 to 41999 * 41041 = Carmichael number * 41472 = 3- smooth number * 41586 = Large Schröder number * 41616 = triangular square number * 41835 = Motzkin number * 41841 = 1/41841 = 0.0000239 is a repeating decimal with period 7. 42000 to 42999 * 42680 = octahedral number * 42875 = 353 * 42925 = square pyramidal number 43000 to 43999 * 43261 = Markov number * 43390 = number of primes \leq 2^. * 43560 = pentagonal pyramidal number * 43691 = Wagstaff prime * 43777 = smallest member of a prime sextuplet 44000 to 44999 * 44044 = palindrome of 79 after 6 iterations of the "reverse and add" iterative proce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal number, cardinal numbers'', and numbers used for ordering are called ''Ordinal number, ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports Number (sports), jersey numbers). Some definitions, including the standard ISO/IEC 80000, ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Number
A Markov number or Markoff number is a positive integer ''x'', ''y'' or ''z'' that is part of a solution to the Markov Diophantine equation :x^2 + y^2 + z^2 = 3xyz,\, studied by . The first few Markov numbers are : 1, 2, 5, 13, 29, 34, 89, 169, 194, 233, 433, 610, 985, 1325, ... appearing as coordinates of the Markov triples :(1, 1, 1), (1, 1, 2), (1, 2, 5), (1, 5, 13), (2, 5, 29), (1, 13, 34), (1, 34, 89), (2, 29, 169), (5, 13, 194), (1, 89, 233), (5, 29, 433), (1, 233, 610), (2, 169, 985), (13, 34, 1325), ... There are infinitely many Markov numbers and Markov triples. Markov tree There are two simple ways to obtain a new Markov triple from an old one (''x'', ''y'', ''z''). First, one may permute the 3 numbers ''x'',''y'',''z'', so in particular one can normalize the triples so that ''x'' ≤ ''y'' ≤ ''z''. Second, if (''x'', ''y'', ''z'') is a Markov triple then by Vieta jumping so is (''x'', ''y'', 3''xy''&n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Root Of 2
The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself, equals the number 2. It may be written in mathematics as \sqrt or 2^, and is an algebraic number. Technically, it should be called the principal square root of 2, to distinguish it from the negative number with the same property. Geometrically, the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. The fraction (≈ 1.4142857) is sometimes used as a good rational approximation with a reasonably small denominator. Sequence in the On-Line Encyclopedia of Integer Sequences consists of the digits in the decimal expansion of the square root of 2, here truncated to 65 decimal places: : History The Babylonian clay tablet YBC 7289 (c. 1800–1600 BC) gives an approximation of in four sexagesimal figures, , which is accurate to about six ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primary Pseudoperfect Number
In mathematics, and particularly in number theory, ''N'' is a primary pseudoperfect number if it satisfies the Egyptian fraction equation :\frac + \sum_\frac = 1, where the sum is over only the prime divisors of ''N''. Properties Equivalently, ''N'' is a primary pseudoperfect number if it satisfies :1 + \sum_ \frac = N. Except for the primary pseudoperfect number ''N'' = 2, this expression gives a representation for ''N'' as the sum of distinct divisors of ''N''. Therefore, each primary pseudoperfect number ''N'' (except ''N'' = 2) is also pseudoperfect. The eight known primary pseudoperfect numbers are : 2, 6, 42, 1806, 47058, 2214502422, 52495396602, 8490421583559688410706771261086 . The first four of these numbers are one less than the corresponding numbers in Sylvester's sequence, but then the two sequences diverge. It is unknown whether there are infinitely many primary pseudoperfect numbers, or whether there are any odd primary pseudoperfect number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nelson Mandela
Nelson Rolihlahla Mandela (; ; 18 July 1918 – 5 December 2013) was a South African Internal resistance to apartheid, anti-apartheid activist who served as the President of South Africa, first president of South Africa from 1994 to 1999. He was the country's first black head of state and the first elected in a Universal suffrage, fully representative democratic election. Presidency of Nelson Mandela, His government focused on dismantling the legacy of apartheid by fostering racial Conflict resolution, reconciliation. Ideologically an African nationalist and African socialism, socialist, he served as the president of the African National Congress (ANC) party from 1991 to 1997. A Xhosa people, Xhosa, Mandela was born into the Thembu people, Thembu royal family in Mvezo, Union of South Africa. He studied law at the University of Fort Hare and the University of Witwatersrand before working as a lawyer in Johannesburg. There he became involved in anti-colonial and African ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
46664
46664 was a series of AIDS benefit concerts played in honour of Nelson Mandela by South African and foreign musicians between 2003 and 2008. Origin The second time that Mandela was imprisoned on Robben Island was in 1964, and he was the 466th prisoner that year. His prison number remained 466/64 until 1982, when he was transferred to Pollsmoor Prison and given the prison number 220/82. "Prisoner 46664" continues to be used as a reverential title for him. Shortly before Joe Strummer's death, he and U2's Bono co-wrote the song " 46664" for Mandela as part of the campaign against AIDS in Africa. 46664 concerts Cape Town, South Africa On 29 November 2003, an event called the 46664 Concert was held at Green Point Stadium, Cape Town. It was hosted by Mandela and its goal was to raise awareness of the spread of HIV/ AIDS in South Africa. The following artists performed: * Anastacia *Beyoncé Knowles * Bob Geldof *Queen (Brian May and Roger Taylor) *Paul Oakenfold with Shifty She ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Number
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are: :0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. The Fibonacci numbers were first described in Indian mathematics, as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book ''Liber Abaci''. Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the ''Fibonacci Quarterly''. Applications of Fibonacci numbers include co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compact Disc
The compact disc (CD) is a Digital media, digital optical disc data storage format that was co-developed by Philips and Sony to store and play digital audio recordings. In August 1982, the first compact disc was manufactured. It was then released in October 1982 in Japan and branded as ''Compact Disc Digital Audio, Digital Audio Compact Disc''. The format was later adapted (as CD-ROM) for general-purpose data storage. Several other formats were further derived, including write-once audio and data storage (CD-R), rewritable media (CD-RW), Video CD (VCD), Super Video CD (SVCD), Photo CD, Picture CD, Compact Disc-Interactive (CD-i) and Enhanced Music CD. Standard CDs have a diameter of and are designed to hold up to 74 minutes of uncompressed stereo digital audio or about 650 mebibyte, MiB of data. Capacity is routinely extended to 80 minutes and 700 mebibyte, MiB by arranging data more closely on the same sized disc. The Mini CD has various diameters ranging from ; t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sampling Frequency
In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of "samples". A sample is a value of the signal at a point in time and/or space; this definition differs from the usage in statistics, which refers to a set of such values. A sampler is a subsystem or operation that extracts samples from a continuous signal. A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points. The original signal can be reconstructed from a sequence of samples, up to the Nyquist limit, by passing the sequence of samples through a type of low-pass filter called a reconstruction filter. Theory Functions of space, time, or any other dimension can be sampled, and similarly in two or more dimensions. For functions that vary with time, let ''S''(''t'') be a continuous function (or "signal") to be sampled, and let samp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
44,100 Hz
In digital audio, 44,100 Hz (alternately represented as 44.1 kHz) is a common sampling frequency. Analog audio is often recorded by sampling it 44,100 times per second, and then these samples are used to reconstruct the audio signal when playing it back. The 44.1 kHz audio sampling rate is widely used due to the compact disc (CD) format, dating back to its use by Sony from 1979. History The 44.1 kHz sampling rate originated in the late 1970s with PCM adaptors, which recorded digital audio on video cassettes,Specifically U-matic cassettes notably the Sony PCM-1600 introduced in 1979 and carried forward in subsequent models in this series. This then became the basis for Compact Disc Digital Audio (CD-DA), defined in the Red Book standard in 1980. Its use has continued as an option in 1990s standards such as the DVD, and in 2000s, standards such as HDMI. This sampling frequency is commonly used for MP3 and other consumer audio file formats which were origi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
79 (number)
79 (seventy-nine) is the natural number following 78 and preceding 80. In mathematics 79 is: * An odd number. * The smallest number that can not be represented as a sum of fewer than 19 fourth powers. * The 22nd prime number (between and ) * An isolated prime without a twin prime, as 77 and 81 are composite. * The smallest prime number ''p'' for which the real quadratic field Q[] has Ideal class group, class number greater than 1 (namely 3). * A cousin prime with 83. * An emirp, because the reverse of 79, 97 (number), 97, is also a prime. * A Fortunate prime. * A circular prime. * A prime number that is also a Gaussian prime (since it is of the form ). * A happy prime. * A Higgs prime. * A lucky prime. * A permutable prime, with ninety-seven. * A Pillai prime, because 23 ! + 1 is divisible by 79, but 79 is not one more than a multiple of 23. * A regular prime. * A right-truncatable prime, because when the last digit (9) is removed, the remaining number (7) is still prime. * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wagstaff Prime
In number theory, a Wagstaff prime is a prime number of the form : where ''p'' is an odd prime. Wagstaff primes are named after the mathematician Samuel S. Wagstaff Jr.; the prime pages credit François Morain for naming them in a lecture at the Eurocrypt 1990 conference. Wagstaff primes appear in the New Mersenne conjecture and have applications in cryptography. Examples The first three Wagstaff primes are 3, 11, and 43 because : \begin 3 & = , \\ pt11 & = , \\ pt43 & = . \end Known Wagstaff primes The first few Wagstaff primes are: :3, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, 2932031007403, 768614336404564651, … , known exponents which produce Wagstaff primes or probable primes are: :3, 5, 7, 11, 13, 17, 19, 23, 31, 43, 61, 79, 101, 127, 167, 191, 199, 313, 347, 701, 1709, 2617, 3539, 5807, 10501, 10691, 11279, 12391, 14479, 42737, 83339, 95369, 117239 (all known Wagstaff primes) :127031, 138937, 141079, 267017, 269987, 374321, 986191, 4031399, …, 13 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
