Date of Graduation
Master of Science in Mathematics
Diophantine, Taxi Cab Problem, tetrahedron, elliptic curve, conic section
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).
© Zachary Kyle Easley
Easley, Zachary Kyle, "A Geometric Approach To Ramanujan's Taxi Cab Problem And Other Diophantine Dilemmas" (2016). MSU Graduate Theses. 2535.