Tim Richardt delves into the fascinating world of the Stern-Brocot tree and its relation to binary trees of Pythagorean triples. The classical enumeration of Pythagorean triples, ternary Barning-Hall tree, stereographic projection, turn angles, and trigonometric functions are explored. The Barning-Hall tree, a ternary tree, allows for the enumeration of triples through matrix operations. The sterographic projection of the Stern-Brocot tree unveils a new method to connect turn angles to circle points. By combining this projection with turn angles, one can compute the best approximations of trigonometric functions, revealing a unique approach to circular geometry.
https://richardt.io/stereo_stern/