Pythagorean Theorem

It’s probably surprising for many people that the Pythagorean theorem was already known in ancient Mesopotamia more than four thousand years ago. Using a rope divided into 12 equal parts by 13 knots, they were able to form a right triangle.

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Are you sure about it?

If anyone was asked whether they knew the Pythagorean theorem, the answer would undoubtedly be, „Of course: a square plus b square equals c square.” But is this answer correct? We must disappoint everyone who answered „yes”. A formula by itself can never be a theorem. If you specify what the letters a, b and c in the formula stand for, the answer is more acceptable.

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IN ANY RIGHT TRIANGLE, THE SUM OF THE SQUARES OF THE TWO LEGS IS EQUAL TO THE SQUARE OF THE HYPOTENUSE

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Pythagorean Triples

The triple of positive integers that satisfies the equation a2+b2=c2, is called a Pythagorean triple. For example, the triples 3,4,5 or 6,8,10. This theorem was first proved by Pythagoras, although it had already been a known fact long before.

How Come?

Draw two squares with sides of length 10 units. Divide the squares into parts as shown in the figure. We can see that if we cut out the four congruent right triangles (with sides a, b, c) from both squares, in the figure above there remain two squares, one with side a and one with side b. The sum of the areas of these squares is equal to the area of the square with side c, which remains in the figure below.

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