Acknowledgement
This study was supported by a Young Researcher Grant from Umeå University.
Notes
1. The algebraic detail for the last step of the proof is as follows: Let A, B, and C be the areas on the sides a, b, and c, respectively. Then A/a 2=B/b 2=C/c 2, which implies A+B=a 2 C/c 2+b 2 C/c 2. Since A+B=C, it follows that (a 2+b 2)/c 2=1 which implies a 2+b 2=c 2.