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thharrimw
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I have wondered about this for a while now and can anyone tell me the proof behind A^2+B^2=C^2?
robert Ihnot said:LukeD: I personally like the proof that uses the simple fact that if vectors u and v are orthagonal, then the dot product of u and v is 0. Pretty much gives the result immediately without needing any pretty pictures (as nice as those pretty pictures are)
I wonder how legitimate that is. Why not define a right angle such that the square of the sides equals the hypothesis?
The Pythagorean theorem is a fundamental concept in mathematics that explains the relationship between the 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. This theorem is important in various fields such as geometry, trigonometry, and physics, and is used to solve a wide range of real-life problems.
Pythagoras was a Greek mathematician, philosopher, and founder of the Pythagorean school in the 6th century BC. He is credited with discovering and proving the Pythagorean theorem, although there is evidence that the concept was known to other civilizations before him.
The exact process by which Pythagoras derived the Pythagorean theorem is unknown, as he did not leave behind any written records. However, it is believed that he and his followers used geometric proofs to arrive at the formula, based on their observations of the relationship between the sides of a right triangle.
The Pythagorean theorem is still widely used in mathematics today and has many applications in fields such as geometry, trigonometry, and calculus. It is also the basis for other important theorems, such as the law of cosines and the law of sines.
No, the Pythagorean theorem only applies to right triangles, where one of the angles measures 90 degrees. For non-right triangles, other trigonometric functions such as sine, cosine, and tangent must be used to find the relationship between the sides.