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I like the infinite triangles construct. Once A and C can be constructed from a,b,c, the theorem can be proven by proving A^2 +c^2 = C^2 with expanding/reducing
by marcusphi 4y ago
I like the infinite triangles construct. Once A and C can be constructed from a,b,c, the theorem can be proven by proving A^2 +c^2 = C^2 with expanding/reducing the equation to 4a^2b^2c^2 - 2a^2b^2c^2 = 2a^2b^2c^2, which is true. No sin rule required.
- teo_zero 4y agoThat would only prove that, given a triangle abc, you can construct another, different triangle for which the PT holds, not that the PT is valid for the given triangle.