- #1
Nano-Passion
- 1,291
- 0
I just learned the proof for the Pythagorean theorem.. my mind was blown! =D Simply amazing.
Nano-Passion said:
I liked this one particularly, the one in the post above is pretty awesome too.
DarthPickley said:Well, that one you mention isn't really a proof at all, it just sort of shows that it works for the case of a triangle with side lengths of 3, 4, and 5.
Nano-Passion said:Are you sure? It works for any right angle triangle. And the Pythagorean theorem works only for right angle triangles. So?
Nano-Passion said:Are you sure? It works for any right angle triangle. And the Pythagorean theorem works only for right angle triangles. So?
gb7nash said:I really like the geometric proof. The first time I saw it I stared at it for a long time.
The Pythagorean theorem is a fundamental principle in geometry that relates the three sides of a right triangle. It states that in a right 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 other two sides.
The Pythagorean theorem is named after the Greek mathematician Pythagoras, who lived around 500 BC. However, there is evidence that this theorem was known to earlier civilizations such as the Babylonians and the Egyptians.
The Pythagorean theorem has many practical applications in fields such as construction, engineering, and navigation. It can be used to calculate distances, heights, and angles in real-world scenarios, making it an essential tool for solving everyday problems.
A proof is a logical explanation that shows how a mathematical statement or theorem is true. In the case of the Pythagorean theorem, there are various proofs that use different methods, such as algebra, geometry, and trigonometry, to demonstrate its validity.
Yes, the Pythagorean theorem can be extended to other shapes in higher dimensions, such as squares in a 3D cube or rectangles in a 4D hypercube. This generalization is known as the Pythagorean theorem in n-dimensional space and is used in advanced mathematics and physics.