Conics and geometry

Conics and Geometry is a report that focuses on the development of new approaches in mathematics by breaking from the accepted norm of the time. The conics themselves have their beginning in this manner. The author uses three ancient problems in geometry to illustrate this trend. Doubling the cube, squaring the circle, and trisecting an angle have intrigued mathematicians for centuries. The author shows various approaches at solving these three problems: Hippias’ Quadratrix to trisect an angle and square the circle, Pappus’ hyperbola to trisect an angle, and Little and Harris’ simultaneous solution to all three problems. After presenting these approaches, the focus turns to the conic sections in the non-Euclidean geometry known as Taxicab geometry.