4 ms·
Or, if you want a proof with fewer words, http://isomorphismes.tumblr.com/image/790452593 http://isomorphismes.tumblr.com/image/790452593
by justinpombrio 13y ago
Or, if you want a proof with fewer words,
http://isomorphismes.tumblr.com/image/790452593 http://isomorphismes.tumblr.com/image/790452593
- fryguy 13y agoThis is showing a^2 + b^2 + 2ab (left image) = c^2 + 2ab (right image), since they both have area (a + b)^2. This implies that a^2 + b^2 = c^2, since 2ab is constant across sides.
- csense 13y agoThis is probably the easiest, most intuitive proof of the Pythagorean Theorem. Euclid's proof, by contrast, is a bit of a slog.
- psykotic 13y agoEuclid has two proofs. The first is the one submitted here. The second one uses the complicated theory of proportion from Book V. However, it's very simple and intuitive when recast in modern terms. Take a right triangle ABC, drop an altitude onto the hypotenuse, note the two smaller right triangles are similar to ABC, calculate the area of ABC in two different ways using this decomposition, and compare the results.
- ryannevius 13y agoI always liked this one... http://25.media.tumblr.com/a7ac256b1db7bbb775f559bfa736b962/tumblr_mrsl3goCez1s6r1vho1_400.gif http://25.media.tumblr.com/a7ac256b1db7bbb775f559bfa736b962/...