a visual
demonstration that for a right angled triangle,

the square of the hypotenuse is equal to the sum of the squares
of the other two sides, by Henry Bottomley.

The four blue triangles remain in the picture, so the red and
yellow areas are constant, so the area of the biggest red square
(on the hypotenuse) is equal to the sum of the other two red
squares (on the other two sides).

A proof of the
theorem based on the second diagram:

the area of the big square is (a+b)^2 , but it is also c^2 + 4.1/2.a.b,

so a^2 + 2.a.b + b^2 = c^2 + 2.a.b
, so a^2 + b^2 = c^2
.

return to top
Henry Bottomley's
home page Seven
formulae for the area of a triangle

An
optical illusion Medians
and area bisectors of triangles Chebyshev's
inequality

Alexander
Bogomolny's 29 proofs of Pythagoras's theorem

Oliver
Byrne's 19th century graphical translation of Euclid's
proposition I.47