设△ABC,a=m²-n²,b=m²+n²,c=2mn
有a²=（m²-n²）²=m^4-2m²n²+n^4
b²=(m²+n²)²=m^4+2m²n²+n^4
c²=4m²n²
∴a²+c²=m^4-2m²n²+n^4+4m²n²
=m^4+2m²n²+n^4
即a²+c²=b²,a,c是两条直角边,b是直角三角形斜边.
证毕.