Pythagoras (fl. 500 BCE)

The theorem of Pythagoras is one of the earliest and most important results in the history of mathematics. It has immense practical value and led to the discovery of irrational numbers - a right triangle with unit sides leads via Pythagoras to the square root of 2!

For further history: St. Andrews' history of Mathematics site

Theorem of Pythagoras

Given any right angle triangle, if one forms a square on each side of that triangle then the area of the largest square (that of the hypoteneuse) is equal to the sum of the areas of the two smaller squares (those which are formed on the sides about the right or 90 degree angle).

Proof of the theorem is demonstrated through the following Quicktime animation. Use the controls to animate the movie.

Note that the area of a given colour remains the same in the animation - no matter how the shape of the figure changes!

Notes on the demonstration:

Textual details of the proof are intentionally absent from the movie. This encourages the student to work through why this is in fact a proof and how they might produce a formal proof based on the demonstration.
Alternatively an instructor might like to fill in these details before/during/after the demonstration.
While the animation is paced so as to provide some time for thought on the steps in the proof, by using the video controls available, the student/instructor can proceed through the demonstration at their own pace.
Don't get it? Try moving the animation back and forth with the controls.
If you really are stuck (in spite of puzzling through the demo) then here's the key to the proof . Try working it out on your own first though.
The quantitative analysis environment called Quail was used to produce these dynamic graphics.

Author: R.W. Oldford June 13, 2001.