4 ms·

I think you can sidestep trigonometry (and the Law of Sines) completely. You can decompose any triangle A, B, C using their construction to create smaller trian

I think you can sidestep trigonometry (and the Law of Sines) completely. You can decompose any triangle A, B, C using their construction to create smaller triangle a, b, c where A = 2abc/(b² - a²), C = c(b² + a²)/(b² - a²), and B = c. This can be shown with only similar triangles (it seems like they unnecessarily use sines in the article). It is then just algebra to show A² + B² = c²(b² + a²)²/(b² - a²)² = C². edit: any right triangle A, B, C using their construction to create smaller right triangle a, b, c

erehweb 4y ago
Well sure, there are other proofs of Pythagorean theorem. The interesting part is that this is a new proof.
- agurjal 4y ago
  I'm certainly no expert on proofs of the Pythagorean theorem, but if their construction is novel, then the above may be too.
  - jonahx 4y ago
    It’s the infinite geometric series idea which makes it potentially novel.
hgsgm 4y ago
The Law of Sines is proven using similar triangles. This is a convenient way to bookkeep similar triangles. Does your version using the infinite series, or only the waffle cone shape?
- agurjal 4y ago
  It uses the infinite geometric series which is how A and C are determined in terms of a, b, and c (as shown in the article). I think the infinite geometric series is definitely the coolest part of their proof!