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Tim Richardt's Articles

Blog articles of Tim Richardt.

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The stereographic projection of the Stern–Brocot tree

I sketch how the stereographic projection of the Stern–Brocot tree forms an ordered binary tree of Pythagorean triples, which can be used to compute best approximations of turn angles of points on the circle and finally trigonometric functions. Before that, I briefly recapitulate the classical enumeration of Pythagorean triples and the ternary Barning–Hall tree.

Shanks' logarithm on the Stern–Brocot tree

By using lazy arithmetic within Shanks' logarithm algorithm, the logarithm algorithm itself becomes lazy. This allows to handle even irrational numbers.

Some notes on the Stern–Brocot tree

After briefly recapturing the Stern–Brocot tree, I show how to count small prime omega ω(n) in it and how Shannon entropy can serve as a measure for convergence of irrationals.