Japanese Temple Problems - Famous Math Problems 14

Explore Japanese temple geometry problems in this 46-minute lecture from the "Famous Math Problems" series. Delve into a problem posed by 13-year-old Sato Naosue in 1847, examining it from both classical and Rational Trigonometry perspectives. Discover the surprising complexity of the algebra involved and gain insights into the symmetry between a triangle's incenter and excenters. Learn about the unique relationship between incenter quadrances in a 3-4-5 triangle, providing motivation to further study Rational Trigonometry as a modern approach to geometry. Follow along with the step-by-step solution, from the initial problem statement through hints, classical solutions, and advanced algebraic manipulations.

Introduction
The Problem
Hints
Classical Solution
Triangle CDE
Linear Equations
Incenter Formula
Square Things
Algebra
Exercises
References