Date of Graduation

Spring 2016

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Les Reid

Keywords

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

Subject Categories

Mathematics

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).

Copyright

© Zachary Kyle Easley

Open Access

Included in

Mathematics Commons

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