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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, — called the cathetes — and c is the opposite side — the hypotenuse).

This time the proof is given in the form of a puzzle that the visitor must solve himself in order to comprehend it: Above the catheti are two squares, each divided into four triangles. Each of these triangles is coloured and the two opposite triangles in the square are each congruent (“congruent”) and coloured the same.

If you now cleverly lay the total of eight triangles around, they fill exactly 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

You can find more interesting facts about the Pythagorean theorem and another proof here.

Literature

[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.

Opening Hours and Ticket Prices

Tuesday – Friday: 9 am – 5 pm
Saturday, Sunday and holidays: 10 am – 6 pm

Entry: 5 Euro / discount. 4 Euro

Special prices apply for groups and families, for guided tours or for photo and video permission.

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Erlebnisland Mathematik
Technische Sammlungen Dresden
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