Prove the Pythagorean theorem myself with no help. Do it from scratch geometrically.
Equal Areas: triangles d, e, f, g, h, i, j ≡ T since they are all 3 × 4.
Any other side sizes also work.
Equal Areas: squares ABCD and EFGH since they are both (3 + 4) × (3 + 4) = 7 × 7
But ABCD = a + b + d + e + f + g = a + b + 4T
and EFGH = c + f + h + i + j = c + 4T
So the areas of the three squares a, b and c are related by:
a + b = c
Sketch: xfig (http://www.xfig.org/)
document: latex (http://alum.mit.edu/www/toms/latex.html)
convert to html: tex4ht (http://tug.org/applications/tex4ht/mn.html)
pdf version: http://alum.mit.edu/www/toms/papers/pythagoras/pythagoras.pdf
Link to many proofs: http://www.cut-the-knot.org/pythagoras/index.shtml #24 has a picture of a diagram like mine without explanation.
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