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The Pythagorean Theorem shows how to calculate the distance between any two points on a grid.
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It explains the relationship between the sides of a right triangle.
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Imagine drawing a square on each of the three sides.
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The Pythagorean theorem states that the area of the square opposite the right angle is equal to the sum of the other two areas.
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The lengths of the A and B sides are easy to measure on a grid. The Pythagorean theorem allows us to calculate the length of the C side accurately.
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The square of C is equal to the square of A plus the square of B.
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Or to write this another way, the length of the hypotenuse is the square root of the sum of the squares of the other two sides.
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For example, if the two sides next to the right angle are 3 and 4 centimeters long,
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We can find the length of the third side by squaring the other two lengths, adding them and calculating the square root.
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3 squared is 9, 4 squared is 16.
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Together they are 25.
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So the hypotenuse is 5 centimeters long.
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The theorem is named after Pythagoras, one of the most influential ancient Greek mathematicians.
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