Garfield's Ghost Revisited - by Tony Foster

Tony Foster posted a proof of the Pythagrean Theorem at the CutTheKnotMath facebook page, with a reference to that of President J. Garfield

A short essay accompanied the above derivation:

I call this one Garfield's ghost Pythagorean theorem proof. It looks like Garfield's original proof but it isn't...Far be it for me to criticize the former President's proof or make comparisons, but one of the advantages of this proof I developed is you actually see C². Sometimes, students get confused with Garfield's proof because they don't actually see C². What's seen is C²/2 in Garfield's original proof, and they wonder how the pythagorean theorem is derived from that. The visual messes with people a little until they understand the algebra part and how it's based on sides A & B. This proof gets around that confusion and shows C². Also, the trapezoid is easier to figure out with this one.. You can actually visualize the area of the trapezoid without using the trapezoid formula. It's quick ...