the anti Pythagorean theorem?
an anti Pythagorean theorem. Here is a geometry identity related to Pythagoras from 8th grade math which you may not know about. It relates the sides of a triangle where one angle is 60 degrees. It all starts with a high school problem about triangles and circles and uses the law of cosine from precalculus and leads to a special 8 7 5 triangle with integer sides. Then we'll see if there are other triangles of this form, which involves the quadratic formula. In a surprising turn of events, this is related to ellipses and lines. Special thanks goes to Ian Fowler who has introduced me to this problem. He is a retired high school math teacher and graded math competition problems at the University of Waterloo in Canada
Part 2: • Anti Pythagoras 2: the Line, Ellipse, and ...
0:00 Introduction
0:30 Problem
3:10 Special Triangles
4:50 Thirty Years Later
6:50 Miracle
Law of Cosines: • Al-Kashi's Mysterious Formula
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