## Pythagorean theorem

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## Pythagorean Theorem

# Pythagorean Theorem

One of the most famous theorems in all mathematics, often attributed to Pythagoras of Samos (Greece) in the sixth century BC, states the sides a, b, and c of a right triangle satisfy the relation c^{2} = a^{2} + b^{2}, where c is the length of the hypotenuse of the triangle and a and b are the lengths of the other two sides.

This theorem was known earlier to the Babylonians, Chinese, and Egyptians. Pythagoras is said to have traveled to Babylon as a young man, where he could have learned the famous theorem. Nevertheless, Pythagoras (or some member of his school) is credited with the first proof of the theorem.

The converse of the Pythagorean theorem is also true. That is if a triangle with sides a, b, and c has a^{2} = b^{2} + c^{2}, we know that the triangle is a right triangle.

A special form of the theorem was used by the Egyptians for making square corners when they resurveyed land adjacent to the Nile river after the annual flood. They used a rope loop with 12 knots tied at equal intervals along the rope. Three of the knots were used as the vertices of a triangle. Since 3^{2} + 4^{2} = 5^{2} we know, by the converse of the Pythagorean theorem, that we have a right triangle.

## Pythagorean Theorem

# Pythagorean theorem

One of the most famous theorems of **geometry** , often attributed to Pythagoras of Samos (Greece) in the sixth century b.c., states the sides a, b, and c of a right triangle satisfy the **relation** c2 = a2 + b2 where c is the length of the hypotenuse of the triangle and a and b are the lengths of the other two sides.

This **theorem** was likely to have been known earlier to be the Babylonians, Pythagoras is said to have traveled to Babylon as a young man, where he could have learned the famous theorem. Nevertheless, Pythagoras (or some member of his school) is credited with the first **proof** of the theorem.

The converse of the Pythagorean theorem is also true. That is if a triangle with sides a, b, and c has a2 = b2 + c2, we know that the triangle is a right triangle.

A special form of the theorem was used by the Egyptians for making **square** corners when they re-surveyed the land adjacent to the Nile river after the annual flood. They used a rope loop with 12 knots tied at equal intervals along the rope. Three of the knots were used as the vertices of a triangle. Since 32 + 42 = 52 we know, by the converse of the Pythagorean theorem, that we have a right triangle.

## Pythagorean Theorem

# Pythagorean theorem

The Pythagorean theorem is one of the most famous theorems of geometry. It is often attributed to Pythagoras of Samos (Greece), who lived in the sixth century b.c. The theorem states that in any right triangle, the square of the hypotenuse of the triangle (the side opposite the right angle) is equal to the sum of the squares of the other two sides, or c^{2} = a^{2} + b^{2}.

This theorem was probably known long before the time of Pythagoras; it is thought to have been used by the ancient Egyptians and Babylonians. Nevertheless, Pythagoras (or some member of his school) is credited with the first proof of the theorem.

The converse of the Pythagorean theorem is also true. That is, if a triangle with sides a, b, and c has c^{2} = a^{2} + b^{2}, we know that the triangle is a right triangle.

## Pythagorean theorem

Py·thag·o·re·an the·o·rem / pəˌ[unvoicedth]agəˈrēən; pī-/ a theorem attributed to Pythagoras that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

#### NEARBY TERMS

**Pythagorean theorem**