The Circumquadrance of a Cyclic Quadrilateral - Rational Geometry Math Foundations - NJ Wildberger

Explore the fascinating world of cyclic quadrilaterals in this 36-minute mathematics lecture from the Insights into Mathematics series. Delve into Parameshvara's remarkable formula for calculating the circumradius of a cyclic quadrilateral, and discover how it can be extended to non-convex cases. Learn about a new algebraic formulation that avoids transcendental quantities, instead utilizing a quadratic formula rooted in Rational Trigonometry. Gain insights into how rational alternatives to traditional real number formulations can lead to more powerful and generalizable results in geometry, applicable to finite fields and relativistic geometry. Understand the importance of rethinking modern mathematics to uncover new and improved ways of comprehending geometric concepts.

Introduction
Paramesh formula
Non convex Paramesh formula
Example
Formula