Maeckes logo

<    1      2      3      4      5      6    >


Pythagorean theorem

The Pythagorean theorem is

 


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

 


Example 1

You can see that 32 + 42 = 52, as

32 + 42 = 25

 


History

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


Deutsch   Español   Français   Nederlands   中文