#### Date of Graduation

Spring 2016

#### Degree

Master of Science in Mathematics

#### Department

Mathematics

#### Committee Chair

Les Reid

#### Abstract

In 1917, the British mathematician G.H. Hardy visited the Indian mathematical genius Ramanujan in the hospital. The number of the taxicab Hardy arrived in was 1729. Ramanujan immediately recognized this as the smallest positive integer that can be expressed as the sum of two cubes in two essentially different ways. In this thesis, we use properties of conics and elliptic curves to investigate this problem, its generalization to fourth powers, and a Diophantine equation involving the distance of a point from the vertices of a regular tetrahedron (the latter extends work of Christina Bisges).

#### Keywords

Diophantine, Taxi Cab Problem, tetrahedron, elliptic curve, conic section

#### Subject Categories

Mathematics

#### Copyright

© Zachary Kyle Easley

#### Recommended Citation

Easley, Zachary Kyle, "A Geometric Approach To Ramanujan's Taxi Cab Problem And Other Diophantine Dilemmas" (2016). *MSU Graduate Theses*. 2535.

https://bearworks.missouristate.edu/theses/2535