1729 (number)

Natural number 1729 1, 7, 13, 19, 91, 133, 247, 1729 1729 is the natural number following 1728 and preceding 1730. It is the first nontrivial taxicab number, expressed as the sum of two cubic positive integers in two different ways. It is known as the Ramanujan number or Hardy–Ramanujan number after G. H. Hardy and Srinivasa Ramanujan. In mathematics 1729 is a composite number, the first nontrivial taxicab number, a Carmichael number, and a centered cube number.koshy It is also the smallest absolute Euler pseudoprime. It is palindromic in bases 12, 32, and 36. 1729 is the dimension of the Fourier transform on which the fastest known algorithm for multiplying two numbers is based.harvey This is an example of a galactic algorithm.hh 1729 can be expressed as the quadratic form. Investigating pairs of its distinct integer values that represent every integer the same number of times, Schiemann found that such quadratic forms must be in four or more variables, and the least possible discriminant of a four-variable pair is 1729.guy 1729 is the first number in the sequence of "Fermat near misses" defined, in reference to Fermat's Last Theorem, as numbers of the form which are also expressible as the sum of two other cubes.oa oeis-fermat Ramanujan number Taxicab number thumb|1729 can be expressed as a sum of two positive cubes in two ways, illustrated geometrically. Ramanujan number 1729 is also known as Ramanujan number or Hardy–Ramanujan number, named after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan who was ill in hospital.ew lozano In their conversation, Hardy stated that the number 1729 from a taxicab he rode was a "dull" number and "hopefully it is not unfavourable omen", but Ramanujan remarked that "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways".hardy This conversation led to the definition of the taxicab number as the smallest integer that can be expressed as a sum of two positive cubes in a given number of distinct ways. 1729 is the second taxicab number, expressed as and .lozano 1729 was later found in one of Ramanujan's notebooks dated years before the incident, and it was noted by French mathematician Frénicle de Bessy in 1657.kahle A commemorative plaque now appears at the site of the Ramanujan–Hardy incident, at 2 Colinette Road in Putney.mm See also 1729 - a year References Edward Graham Ward Thomas 2005 An Introduction to Number Theory https://books.google.com/books?id=yT3TOp-7YrQC&pg=PA117 117 Springer 978-1-85233-917-3 Guy Richard K. Richard K. Guy 2004 Unsolved Problems in Number Theory Springer 3rd Problem Books in Mathematics, Volume 1 1 0-387-20860-7 10.1007/978-0-387-26677-0 978-0-387-26677-0 (eBook) Ramanujan https://archive.org/details/pli.kerala.rare.37877 Hardy G. H. G. H. Hardy New York Cambridge University Press 1940 12 I remember once going to see him when he was ill at Putney. I had ridden in taxi cab No. 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways." Harvey David Hoeven Joris van der March 2019 Integer multiplication in time https://hal.archives-ouvertes.fr/hal-02070778/document HAL hal-02070778 Harvey David We've found a quicker way to multiply really big numbers https://phys.org/news/2019-04-weve-quicker-big.html 2021-11-01 phys.org en Kahle Reinhard 2018 Piazza Mario Pulcini Gabriele Truth, Existence and Explanation: FilMat 2016 Studies in the Philosophy of Mathematics Boston Studies in the Philosophy and History of Science 334 Structure and Structures https://books.google.com/books?id=mM10DwAAQBAJ&pg=PA115 115 10.1007/978-3-319-93342-9 978-3-319-93342-9 Koshy Thomas 2007 Elementary Number Theory with Applications https://books.google.com/books?id=d5Z5I3gnFh0C&pg=PA340 340 Academic Press 2nd 978-0-12-372487-8 Lozano-Robledo Álvaro 2019 Number Theory and Geometry: An Introduction to Arithmetic Geometry https://books.google.com/books?id=ESiODwAAQBAJ&pg=PA413 413 American Mathematical Society 978-1-4704-5016-8 Marshall Michael A black plaque for Ramanujan, Hardy and 1,729 https://goodthinkingsociety.org/a-black-plaque-for-ramanujan-hardy-and-1729/ Good Thinking 24 February 2017 7 March 2019 Ono Ken Aczel Amir D. 2016 My Search for Ramanujan: How I Learned to Count https://books.google.com/books?id=JZkFDAAAQBAJ&pg=PA228 228 10.1007/978-3-319-25568-2 978-3-319-25568-2 A050794 Consider the Diophantine equation () or 'Fermat near misses' External links Hardy-RamanujanNumber Hardy–Ramanujan Number Grime James 1729: Taxi Cab Number or Hardy-Ramanujan Number http://www.numberphile.com/videos/1729taxicab.html Numberphile Brady Haran Bowley, Roger 2013-04-02 https://web.archive.org/web/20170306141337/http://numberphile.com/videos/1729taxicab.html 2017-03-06 dead Why does the number 1729 show up in so many Futurama episodes?, io9.com 10 Category:Integers Category:Srinivasa Ramanujan