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You changed the article's title to an incorrect one. The tree of primitive Pythagorean triples is ternary, not binary. Each node has three children.
by not2b 2y ago
You changed the article's title to an incorrect one. The tree of primitive Pythagorean triples is ternary, not binary. Each node has three children.
- generationP 2y agoBoth conventions are valid. You call it binary when you view it as a rooted tree, or ternary if you view it just as a graph.
- nyrikki 2y agoBut it _all_ triples? > 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 The permutation and stack problem in the page seem to indicate this is a potential method for approximations, but insufficient for _all_ That said I am reading this on mobile and may have missed something.
- not2b 2y agoThe ternary tree contains all primitive triples (where the GCD of the terms is 1), where a<b<c. So it contains (3,4,5) but not (6,8,10) or (4,3,5).
- nyrikki 2y agoYes, but the binary projection does not according to the link. 345 and 435 would require two binary trees.
- AnotherGoodName 2y agoI think skipping transposed values is fine though. You could just mirror the output at 45degrees for that if you wanted it. It does hit all distinct triples including the multiples of triples so it’s more inclusive of everything than the ternary tree.
- hakmem 2y agoYou can see both triples are contained in one binary tree using the big diagram in section 3. The triple [3 4 5] has the "path" RR. The triple [4 3 5] the path R.
- feoren 2y agoKeep reading. The Barning-Hall tree is ternary, but this article is mostly devoted to the Stern-Brocot tree, which is binary.
- ColinWright 2y agoFrom the article: "I sketch how the stereographic projection of the Stern–Brocot tree forms an ordered binary tree of Pythagorean triples ..." ... and ... "Before that, I briefly recapitulate the classical enumeration of Pythagorean triples and the ternary Barning–Hall tree." So this article is about the binary tree representation.