Pythagoras to lay

This exhibit is about another illustrative proof of the Pythagorean Theorem. The well-known theorem states that the side lengths a, b, and c of a right triangle satisfy the equation a^2+b^2=c^2 (where a and b are the two sides enclosing the right angle — the so-called cathetes — and c is the opposite side — the hypotenuse).

This time the proof is given in the form of a puzzle that the visitor has to solve himself in order to follow it: Above the catheti are two squares, each divided into four triangles. Each of these triangles is colored and the two opposite triangles in the square are congruent and colored the same.

If you now skillfully flip the total of eight triangles, they exactly fill the square above the hypotenuse (see Figure 1). This proves the Pythagorean theorem, because equality of content follows from equality of decomposition.

Figure 1: Arrangement of the exhibit

Further interesting facts about the Pythagorean theorem and another proof can be found here.


[1] Dewdney, A.K.: Reise in das Innere der Mathematik, Berlin, 2000.

[2] Fraedrich, A.M.: Die Satzgruppen des Pythagoras, Mannheim, 1995.

[3] Maor, E.: The Pythagorean Theorem: A 4,000-year History, Princeton, 2007.

[4] Schupp, H.: Elementargeometrie, Stuttgart, 1977.

[5] Singh, S.: Fermats letzter Satz, München, 2000.

[6] v. Wedemeyer, I.: Pythagoras, Weisheitslehrer des Abendlandes, Ahlerstedt, 1988.