The Pythagorean Theorem: Almost As Easy As ABC

One of the most useful and widely used rules in mathematics is the Pythagorean theorem. Your child's mastery of this theorem is critical to success in geometry. One helpful method for understanding and remembering a rule like the Pythagorean theorem is to fully explore its meaning and history.

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right triangle pythagorean theorem a squared plus b squared equals c squared

Understanding the Theorem

The Pythagorean theorem is used with right triangles. Imagine three squares that extend from each side of the triangle. The sides of the triangles form the bases of each of these squares. According to the Pythagorean theorem, the area of the largest square is equal to the sum of the areas of the two smaller squares. This theorem can be written as a^2 + b^2 = c^2.

Why Is It Useful?

The Pythagorean theorem helps us understand properties of right triangles. Since the area of a square is found by squaring the length of one of its sides, the Pythagorean theorem can be used to determine the length of the sides of a right triangle. The bases of the smaller triangles form the two sides of the triangle that are adjacent to the right angle. The sum of the square of these sides equals the square of the hypotenuse.

In the equation a^2 + b^2 = c^2, a and b are not only the sides of the two smaller squares, they're also the shorter sides of the triangle. Likewise, c is both the side of the largest square and the hypotenuse of the triangle.

Who Was Pythagoras?

Pythagoras was a Greek mathematician and philosopher who lived in the 500s BC. He founded a religious movement that fostered curiosity and controversy. His followers were known as Pythagoreans and they disseminated their leader's teachings. They valued simplicity and purity. They considered beans impure and didn't eat them. They also had long hair and simple clothing, including no footwear.

Pythagoras believed that mathematics, science and religion were unquestionably linked. One of his beliefs was in transmigration, which involved the soul being reincarnated into the body of a human, animal or plant time and again until it becomes immortal. Many considered Pythagoras to be something of a supernatural or divine figure. For example, some thought he could travel through space, a power he'd use to leave a message on the moon that could be read from Earth.

Many believe that Pythagoras wasn't the first to understand this property of right triangles for which he is credited. The Sumerians used the theorem thousands of years before the time of Pythagoras. It's also believed to have been known in India and China well before Pythagoras.

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