Draw a square with sides of length A+B. Mark off the length B from each corner going around in a clockwise direction (say). Join up these marks to make a smaller, tilted square inside the larger square. Label the sides of the smaller, tilted square C.

Now the area of the larger square is (A+B)^{2}, as is obvious to see.

The area of each of the triangles is (A*B)/2, as can be seen in the triangle on the left.
So the total of all 4 triangles in the larger square is 4*(A*B)/2 = 2*(A*B).
The area of the tilted square is C^{2}, obviously.

Therefore (A+B)^{2} = 2*(A*B) + C^{2}.

Expanding the left side we get A^{2} + 2*(A*B) + B^{2}
= 2*(A*B) + C^{2}.

Cancelling 2*(A*B) from both sides, we get
A^{2} + B^{2} = C^{2}.

*Quod erat demonstrandum*.

Now go visit my blog please, or look at other interesting maths stuff :-)

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