Pythagorean theorem

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry between the three sides of a right-angled triangle.

Related Topics:
Mathematics - Euclidean geometry - Right-angled triangle

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The theorem is as follows:

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In any right triangle, the area of the square whose side is the hypotenuse (the side of the triangle opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

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Where c is the length of the hypotenuse and a and b are the lengths of the other two sides, the theorem can be expressed as the following equation:

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: a^2 + b^2 = c^2. ,

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This means that knowing the lengths of two sides of a right triangle is enough to calculate the length of the third—something unique to right triangles.

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A paraphrase of the Pythagorean theorem is :

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: In the diagram, the sum of the areas of the blue and red squares is equal to the area of the purple square.

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This works for any right triangle laid out on a flat plane.

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