The Pythagorean Theorem is a fundamental principle in geometry, specifically in the context of right-angled triangles. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed with the formula:

$$ c^2 = a^2 + b^2 $$

where:
- $ c $ is the length of the hypotenuse,
- $ a $ and $ b $ are the lengths of the other two sides.

This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery, although it was known to Babylonian mathematicians centuries earlier. The Pythagorean Theorem is not only a cornerstone of geometry but also has applications in various fields such as physics, engineering, computer science, and more. It is used to determine distances, analyze shapes, and solve problems involving right triangles. The theorem also serves as a basis for the distance formula in coordinate geometry, which calculates the distance between two points in a plane.

Question

The Pythagorean Theorem is a fundamental principle in geometry, specifically in the context of right-angled triangles. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed with the formula:

$$ c^2 = a^2 + b^2 $$

where:
- $ c $ is the length of the hypotenuse,
- $ a $ and $ b $ are the lengths of the other two sides.

This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery, although it was known to Babylonian mathematicians centuries earlier. The Pythagorean Theorem is not only a cornerstone of geometry but also has applications in various fields such as physics, engineering, computer science, and more. It is used to determine distances, analyze shapes, and solve problems involving right triangles. The theorem also serves as a basis for the distance formula in coordinate geometry, which calculates the distance between two points in a plane.

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The Pythagorean Theorem is a fundamental principle in geometry, specifically in the context of right-angled triangles. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed with the formula:

$$ c^2 = a^2 + b^2 $$

where:
- $ c $ is the length of the hypotenuse,
- $ a $ and $ b $ are the lengths of the other two sides.

This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery, although it was known to Babylonian mathematicians centuries earlier. The Pythagorean Theorem is not only a cornerstone of geometry but also has applications in various fields such as physics, engineering, computer science, and more. It is used to determine distances, analyze shapes, and solve problems involving right triangles. The theorem also serves as a basis for the distance formula in coordinate geometry, which calculates the distance between two points in a plane.

what is the pythagorean theorem

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what is the pythagorean theorem

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