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.
- Exponential Ramp
- Exponential Sum Formulas
- Exponential Sum Function
- Exponent Laws
- Exponent Vector
- Exradius
- Exsecant
- Extended Cycloid
- Extended Goldbach Conjecture
- Extended Greatest Common Divisor
- Extended Mean-Value Theorem
- Extended Riemann Hypothesis
- Extension
- Extension Problem
- Extensions Calculus
- Extent
- Exterior
- Exterior Algebra
- Exterior Angle Bisector
- Exterior Angle Theorem
- Exterior Derivative
- Exterior Dimension
- Exterior Product
- Exterior Snowflake
- Extrapolation