|
Cabtaxi Number
In mathematics, the ''n''-th cabtaxi number, typically denoted Cabtaxi(''n''), is defined as the smallest positive integer that can be written as the sum of two ''positive or negative or 0'' cubes in ''n'' ways. Such numbers exist for all ''n'', which follows from the analogous result for taxicab numbers. Known cabtaxi numbers Only 10 cabtaxi numbers are known : :\begin\mathrm(1)&=&1&=&1^3 + 0^3\end :\begin\mathrm(2)&=&91&=&3^3 + 4^3 \\&&&=&6^3 - 5^3\end :\begin\mathrm(3)&=&728&=&6^3 + 8^3 \\&&&=&9^3 - 1^3 \\&&&=&12^3 - 10^3\end :\begin\mathrm(4)&=&2741256&=&108^3 + 114^3 \\&&&=&140^3 - 14^3 \\&&&=&168^3 - 126^3 \\&&&=&207^3 - 183^3\end :\begin\mathrm(5)&=&6017193&=&166^3 + 113^3 \\&&&=&180^3 + 57^3 \\&&&=&185^3 - 68^3 \\&&&=&209^3 - 146^3 \\&&&=&246^3 - 207^3\end :\begin\mathrm(6)&=&1412774811&=&963^3 + 804^3 \\&&&=&1134^3 - 357^3 \\&&&=&1155^3 - 504^3 \\&&&=&1246^3 - 805^3 \\&&&=&2115^3 - 2004^3 \\&&&=&4746^3 - 4725^3\end :\begin\mathrm(7)&=&11302198488&=&1926^3 + 1608^3 \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface or blackboard bold \mathbb. The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the natural numbers, \mathbb is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and are not. The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taxicab Number
In mathematics, the ''n''th taxicab number, typically denoted Ta(''n'') or Taxicab(''n''), also called the ''n''th Hardy–Ramanujan number, is defined as the smallest integer that can be expressed as a sum of two ''positive'' integer cubes in ''n'' distinct ways. The most famous taxicab number is 1729 = Ta(2) = 13 + 123 = 93 + 103. The name is derived from a conversation in about 1919 involving mathematicians G. H. Hardy and Srinivasa Ramanujan. As told by Hardy: History and definition The concept was first mentioned in 1657 by Bernard Frénicle de Bessy, who published the Hardy–Ramanujan number Ta(2) = 1729. This particular example of 1729 was made famous in the early 20th century by a story involving Srinivasa Ramanujan. In 1938, G. H. Hardy and E. M. Wright proved that such numbers exist for all positive integers ''n'', and their proof is easily converted into a program to generate such numbers. However, the proof makes no claims at all about whether the thus-generated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randall L
Randall may refer to the following: Places United States *Randall, California, former name of White Hall, California, an unincorporated community * Randall, Indiana, a former town *Randall, Iowa, a city *Randall, Kansas, a city *Randall, Minnesota, a city * Randall, West Virginia, an unincorporated community *Randall, Wisconsin, a town *Randall, Burnett County, Wisconsin, an unincorporated community *Randall County, Texas * Randall Creek, in Nebraska and South Dakota *Randall's Island, part of New York City *Camp Randall, Madison, Wisconsin, a former army camp, on the National Register of Historic Places *Fort Randall, South Dakota, a former military base, on the National Register of Historic Places Elsewhere *Mount Randall, Victoria Land, Antarctica * Randall Rocks, Graham Land, Antarctica *Randall, a community in the town of New Tecumseth, Ontario, Canada Businesses *Randall Amplifiers, a manufacturer of guitar amplifiers *Randall House Publications, American publisher *Randall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel J
Daniel is a masculine given name and a surname of Hebrew origin. It means "God is my judge"Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxford University Press, 2nd edition, , p. 68. (cf. Gabriel—"God is my strength"), and derives from two early biblical figures, primary among them Daniel from the Book of Daniel. It is a common given name for males, and is also used as a surname. It is also the basis for various derived given names and surnames. Background The name evolved into over 100 different spellings in countries around the world. Nicknames (Dan, Danny) are common in both English and Hebrew; "Dan" may also be a complete given name rather than a nickname. The name "Daniil" (Даниил) is common in Russia. Feminine versions (Danielle, Danièle, Daniela, Daniella, Dani, Danitza) are prevalent as well. It has been particularly well-used in Ireland. The Dutch names "Daan" and "Daniël" are also variations of Daniel. A related surname developed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christian Boyer
Christians () are people who follow or adhere to Christianity, a monotheistic Abrahamic religion based on the life and teachings of Jesus Christ. The words ''Christ'' and ''Christian'' derive from the Koine Greek title ''Christós'' (Χριστός), a translation of the Biblical Hebrew term ''mashiach'' (מָשִׁיחַ) (usually rendered as ''messiah'' in English). While there are diverse interpretations of Christianity which sometimes conflict, they are united in believing that Jesus has a unique significance. The term ''Christian'' used as an adjective is descriptive of anything associated with Christianity or Christian churches, or in a proverbial sense "all that is noble, and good, and Christ-like." It does not have a meaning of 'of Christ' or 'related or pertaining to Christ'. According to a 2011 Pew Research Center survey, there were 2.2 billion Christians around the world in 2010, up from about 600 million in 1910. Today, about 37% of all Christians live in the Ameri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uwe Hollerbach
{{disambiguation, geo ...
Uwe or UWE may refer to * Uwe (given name) * University of the West of England, Bristol * UML-based web engineering * University Würzburg's Experimental miniaturized satellites for space research UWE-1 and UWE-2 * Uwe - Wreck in Blankenese Blankenese () is a suburban quarter in the borough of Altona in the western part of Hamburg, Germany; until 1938 it was an independent municipality in Holstein. It is located on the right bank of the Elbe river. With a population of 13,637 as of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taxicab Number
In mathematics, the ''n''th taxicab number, typically denoted Ta(''n'') or Taxicab(''n''), also called the ''n''th Hardy–Ramanujan number, is defined as the smallest integer that can be expressed as a sum of two ''positive'' integer cubes in ''n'' distinct ways. The most famous taxicab number is 1729 = Ta(2) = 13 + 123 = 93 + 103. The name is derived from a conversation in about 1919 involving mathematicians G. H. Hardy and Srinivasa Ramanujan. As told by Hardy: History and definition The concept was first mentioned in 1657 by Bernard Frénicle de Bessy, who published the Hardy–Ramanujan number Ta(2) = 1729. This particular example of 1729 was made famous in the early 20th century by a story involving Srinivasa Ramanujan. In 1938, G. H. Hardy and E. M. Wright proved that such numbers exist for all positive integers ''n'', and their proof is easily converted into a program to generate such numbers. However, the proof makes no claims at all about whether the thus-generated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Taxicab Number
In mathematics, the generalized taxicab number ''Taxicab''(''k'', ''j'', ''n'') is the smallest number — if it exists — that can be expressed as the sum of ''j'' ''k''th positive powers in ''n'' different ways. For ''k'' = 3 and ''j'' = 2, they coincide with taxicab numbers. :\mathrm(1, 2, 2) = 4 = 1 + 3 = 2 + 2. :\mathrm(2, 2, 2) = 50 = 1^2 + 7^2 = 5^2 + 5^2. :\mathrm(3, 2, 2) = 1729 = 1^3 + 12^3 = 9^3 + 10^3 — famously stated by Ramanujan. Euler showed that :\mathrm(4, 2, 2) = 635318657 = 59^4 + 158^4 = 133^4 + 134^4. However, ''Taxicab''(5, 2, ''n'') is not known for any ''n'' ≥ 2:No positive integer is known that can be written as the sum of two 5th powers in more than one way, and it is not known whether such a number exists. The largest variable of \mathrm a^5+b^5=c^5+d^5 must be at least 3450. See also *Cabtaxi number In mathematics, the ''n''-th cabtaxi number, typically denoted Cabtaxi(''n''), is defined as the smallest positive integ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
