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Pythagorean theorem

The Pythagorean theorem is

 

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Explanation

In the picture are 2 squares and 4 right triangles.

You can calculate the area of the large square as

(a + b)(a + b) = a² + 2ab + b²

and the area of the four triangles with

4 × ½ a b = 2ab

so that the area of the small square is equal to

(a² + 2ab + b²) − (2ab) = a² + b²

Froms this follows directly the Pythagorean theorem

a² + b² = c²

 

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Example 1

You can see that 3² + 4² = 5², as

3² + 4² = 25

 

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History The Indian mathematician Bhāskara II (1114 - 1185) is best known for his proof of the Pythagorean theorem.

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