Not 100% sure, but it seems that the "ab"s that you have should be ab/2....
I have a book that contains something like 450-500 separate proofs of Mr. Pythagoras' idea. Not many were printed, so if you want one, it's used bookstore city.
Euclid's proof is arguably the toughest to understand--until you lay it out, preferably color-coding the equal triangles. Then it's really quite clever.
Ah-- my RA's dad noticed the problem in the nice diagrams too. I told him nobody had caught it yet, but I was wrong! Good for you.
I'll probably be posting on the Pythagorean Theorem in a few weeks, since I'll be teaching it. Today, the 2nd grade teacher was sick, so I combined classes again. I had the second graders try to sound out how to say "Euclid" and "Pythagorean", with somewhat humorous results.
Not 100% sure, but it seems that the "ab"s that you have should be ab/2....
I have a book that contains something like 450-500 separate proofs of Mr. Pythagoras' idea. Not many were printed, so if you want one, it's used bookstore city.
Euclid's proof is arguably the toughest to understand--until you lay it out, preferably color-coding the equal triangles. Then it's really quite clever.
I think you are right on the ab triangles being 1/2*ab in area.
Ah-- my RA's dad noticed the problem in the nice diagrams too. I told him nobody had caught it yet, but I was wrong! Good for you.
I'll probably be posting on the Pythagorean Theorem in a few weeks, since I'll be teaching it. Today, the 2nd grade teacher was sick, so I combined classes again. I had the second graders try to sound out how to say "Euclid" and "Pythagorean", with somewhat humorous results.