The Area of a Triangle and Archimedes' Formula - Famous Math Problems
Insights into Mathematics via YouTube
Overview
Explore a novel approach to calculating the area of a triangle using only the lengths of its sides in this 38-minute lecture. Learn about Archimedes' ancient problem and discover a more elegant solution based on Rational Trigonometry. Delve into the two most fundamental formulas in mathematics: Pythagoras' theorem and the Triple quad formula. Understand how this method improves upon Heron's formula by eliminating unnecessary irrationalities. Follow along as the lecturer demonstrates the solution with a practical example and provides a proof. Conclude with an intriguing application of this concept to relativistic physics.
Syllabus
Introduction
Rational trigonometry
The two most important formulas
The true formula
Example
Proof
relativistic application
Taught by
Insights into Mathematics