请输入您要查询的字词:

 

单词 TaxicabNumbers
释义

taxicab numbers


The number 1729 has a reputation of its own. The reason is the famous exchange between http://www-groups.dcs.st-and.ac.uk/ history/Mathematicians/Hardy.htmlG. H. Hardy, a famous British mathematician (1877-1947), and http://www-groups.dcs.st-and.ac.uk/ history/Mathematicians/Ramanujan.htmlSrinivasa Ramanujan , one of India’s greatest mathematical geniuses (1887-1920):

In 1917, during one visit to Ramanujan in a hospital (he was ill for much of his last three years), Hardy mentioned that the number of the taxi cabthat had brought him was 1729, which, as numbers go, Hardy thoughtwas “rather a dull number”. At this, Ramanujan perked up, and said“No, it is a very interesting number; it is the smallest numberexpressible as a sum of two cubes in two different ways.”

Indeed:

1729=1+123=93+103.

Moreover, there are other reasons why 1729 is far from dull. 1729 is the third Carmichael numberMathworldPlanetmath. Even more strange, beginning at the1729th decimal digit of the transcental number e, the next tensuccessive digits of e are 0719425863. This is the first appearanceof all ten digits in a row without repititions.

More generally, the smallest natural numberMathworldPlanetmath which can be expressed as the sum of n positive cubes is called the nth taxicab numberMathworldPlanetmath. The first taxicab numbers are:

2=13+13, 1729=13+123=93+103, 87539319=1673+4363=2283+4233=2553+4143

followed by 6963472309248 (found by E. Rosenstiel, J.A. Dardis, and C.R. Rosenstiel in 1991) and 48988659276962496 (found by David Wilson on November 21st, 1997).

随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 15:14:32