Hardy-Ramanujan Number
The smallest nontrivial Taxicab Number, i.e., the smallest number representable in two ways as a sum of twoCubes. It is given by
The number derives its name from the following story G. H. Hardy
told about Ramanujan. ``Once, in the taxi from London, Hardy noticed its number, 1729. He must have thought about it a little because he enteredthe room where Ramanujan lay in bed and, with scarcely a hello, blurted out his disappointment with it. It was, he declared,`rather a dull number,' adding that he hoped that wasn't a bad omen. `No, Hardy,' said Ramanujan, `it is a very interestingnumber. It is the smallest number expressible as the sum of two [Positive] cubes in two different ways''' (Hofstadter1989, Kanigel 1991, Snow 1993).See also Diophantine Equation--Cubic, Taxicab Number
References
Guy, R. K. ``Sums of Like Powers. Euler's Conjecture.'' §D1 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 139-144, 1994. Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, p. 68, 1959. Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books, p. 564, 1989. Kanigel, R. The Man Who Knew Infinity: A Life of the Genius Ramanujan. New York: Washington Square Press, p. 312, 1991. Snow, C. P. Foreword to Hardy, G. H. A Mathematician's Apology, reprinted with a foreword by C. P. Snow. New York: Cambridge University Press, p. 37, 1993.
- Wild Point
- Wilf-Zeilberger Pair
- Wilkie's Theorem
- Williams p+1 Factorization Method
- Wilson Plug
- Wilson Prime
- Wilson Quotient
- Douady's Rabbit Fractal
- Double Bubble
- Double Bubble Conjecture
- Double Contraction Relation
- Double Cusp
- Double Exponential Distribution
- Double Exponential Integration
- Double Factorial
- Double Folium
- Double-Free Set
- Double Gamma Function
- Double Point
- Double Sixes
- Double Sum
- Doublet Function
- Doubly Even Number
- Doubly Magic Square
- Dougall-Ramanujan Identity