Ramanujan cab numbers: a recreational mathematics activity

Abstract

The story of the Indian mathematician Srinivasa Ramanujan is inspiring. He endured great hardship and rose to rarefied heights in mathematics. One inspiring story about him concerns the Ramanujan taxicab number 1729 and the sequence of numbers $n$ defined by the equation: n = x^3 + y^3 = p^3 + q^3$ where x, y, p and q are distinct positive integers. 1729 is the smallest number that can be expressed as the sum of two cubes in two different ways: 10^3 + 9^3 = 12^3 + 1^3 = 1729.

The story of Ramanujan and all the people who helped him, suggest to us how the pursuit of mathematics can bring out redeeming qualities in humans.

We introduce teaching activities and software that can inspire people and help them enjoy these beautiful mathematical creations.

We hope these resources and activities can inspire minorities and students in developing nations all over the world to better appreciate the beauty in mathematics. Ramanujan would certainly have wanted all of us to appreciate the inherent beauty in these numbers.