Pythagorean Theorem Proof

Thomas D. Schneider *

version = 1.03 of pythagoras.tex 2012 Jun 14

*National Institutes of Health, Frederick National Laboratory for Cancer Research, Gene Regulation and Chromosome Biology Laboratory, P. O. Box B, Frederick, MD 21702-1201. (301) 846-5581, email: schneidt@mail.nih.gov http://alum.mit.edu/www/toms/

Prove the Pythagorean theorem myself with no help. Do it from scratch geometrically.

PIC

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

QED!!!
_________________________________________________________________________________________

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.
U.S. Department of Health and Human Services  |  National Institutes of Health  |  National Cancer Institute  |  USA.gov  | 
Policies  |  Viewing Files  |  Accessibility  |  FOIA