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I know you can use the second diagram to prove the theorem, but it requires an algebraic argument (the other two squares aren't shown). Unless the text says som
by moomin 10y ago
I know you can use the second diagram to prove the theorem, but it requires an algebraic argument (the other two squares aren't shown). Unless the text says something pretty interesting, this looks more like a proof just for a 3,4,5 triangle.
The first diagram I can't get my head round at all, or is it proving something different?
- greglindahl 10y agoThe top comment after the images of the two diagrams explains how the 1st diagram is another algebraic proof, similar to the 2nd diagram.
- jeffwass 10y agoThe first and second diagrams are similar, just using the 'outside' vs 'inside' deconstruction. If we label the sides a=3, b=4, and c=5 : The first diagram shows that the big outer square of length (a+b) equals the area of the 4 triangles plus the rotated square of side c. (a+b)^2 = 2ab + c^2 [I'm not sure why they drew an inner 3x3 square on its own]. The second diagram puts the same four triangles inside the rotated square of side c, which leaves an extra smaller square of side (b-a) inside. c^2 = 2ab + (b-a)^2
- moomin 10y agoYeah, the inner square is confusing.