New Orleans teenagers found a new proof of the Pythagorean Theorem
I have read about this proof for a bit and this is the first write-up that gives the slightest details. The phrase "using trigonometry" is confusing. What they do is assume functions sine and cosine exist, as normally defined, as ratios of triangle values, without assuming these have the various Pythagorean-theorem derived properties. They then construct an infinite series of nested triangles and use the formula for the sum of geometric series' to derive the length of the original triangle's hypotenuse. It certainly seems clever.<p>I'm still confused what axioms they're effectively using relative to the usual Pythagorean theorem proofs - most of these use the formula for area of a right triangle and this seemingly doesn't. On the other hand, it seems an infinite construct would require things like the axiom of induction, which may or may not be included in axiom of axiomatic geometry.