Back عدد تاكسيكاب Arabic Número taxicab Catalan Taxital Danish Taxicab-Zahl German Αριθμοί των Ταξί Greek Número taxicab Spanish Taxicab zenbakia Basque عدد تاکسی Persian Taksiluku Finnish Nombre taxicab French
In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), is defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways.[1] The most famous taxicab number is 1729 = Ta(2) = 13 + 123 = 93 + 103, also known as the Hardy-Ramanujan number.[2][3]
The name is derived from a conversation ca. 1919 involving mathematicians G. H. Hardy and Srinivasa Ramanujan. As told by Hardy:
I remember once going to see him [Ramanujan] when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be 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."[4][5]
- ^ "Taxicab Number". Wolfram Mathworld.
- ^ "Hardy-Ramanujan Number". Wolfram Mathworld.
- ^ Grime, James; Bowley, Roger. Haran, Brady (ed.). 1729: Taxi Cab Number or Hardy-Ramanujan Number. Numberphile.
- ^ Quotations by G. H. Hardy, MacTutor History of Mathematics Archived 2012-07-16 at the Wayback Machine
- ^ Silverman, Joseph H. (1993). "Taxicabs and sums of two cubes". Amer. Math. Monthly. 100 (4): 331–340. doi:10.2307/2324954. JSTOR 2324954.