## Special NumbersSeptember 21, 2011 Heraclitus, who is famous for his statement that you can't step in the same river twice, knew that there is a level at which everything is unique. Those identical M&M candies can be distinguished from each other with a sensitive enough pan balance. The trick to this game is to look far enough to find whatever makes an item special. Numbers such as pi and e are clearly special, but what makes a natural number like 1729 special? The mathematician, G.H. Hardy once visited the Indian mathematician Srinivasa Ramanujan in the hospital, and he told this story."I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable 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."[1] G.H. Hardy (left), circa 1927, from his book, "A Mathematician's Apology," and an undated photograph of Srinivasa Ramanujan (right). (Via Wikimedia Commons: (Left Image), (Right Image).
The number, 1729, is now known as the second taxicab number. The different ways are 1^{3} + 12^{3} and 9^{3} + 10^{3}. That Ramanujan was in poor enough health to be in a hospital was not unexpected. The combination of his trying to eat vegetarian in early twentieth century England and his frenetic work habits likely contributed to his early demise at age 32. We can only guess what he may have discovered in number theory if he had lived longer.
Erich Friedman, an Associate Professor of Mathematics at Stetson University has memorized the first fifty digits of pi, compared to my paltry eleven. He also has an extensive website devoted to the things that make natural numbers special.[2] Some of the reasons are quite imaginative. Here are a few examples.
## References:- Quotations of Godfrey Harold Hardy on Wikiquote.
- Erich Friedman, "What's Special About This Number?" Web Site.
Linked Keywords: Heraclitus; M&M candies; pi; e; natural number; 1729; mathematician; G. H. Hardy; Indian; Srinivasa Ramanujan; A Mathematician's Apology; Wikimedia Commons; taxicab number; vegetarian; twentieth century; England; number theory; Erich Friedman; mathematics; Stetson University; Mersenne prime; Roman numeral; lexicography; stellation; icosahedron; reciprocal; palindromic prime; Lucas number; electrical resistance; resistor; electrical engineering; computer science; homework; Schröder number; prime factor; concatenation; knight; chess; self-avoiding walk; Cuban prime; Sloane's Integer Sequence A002407. |
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