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In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
Since the diagonal of a rectangle is the hypotenuse of the right triangle formed by two adjacent sides, the statement is seen to be equivalent to the Pythagorean theorem. [8] Baudhāyana also provides a statement using a rope measure of the reduced form of the Pythagorean theorem for an isosceles right triangle:
Bhaskaracharya proof of the pythagorean Theorem. Some of Bhaskara's contributions to mathematics include the following: A proof of the Pythagorean theorem by calculating the same area in two different ways and then cancelling out terms to get a 2 + b 2 = c 2. [21] In Lilavati, solutions of quadratic, cubic and quartic indeterminate equations ...
The Pythagorean theorem was known and used by the Babylonians and Indians centuries before Pythagoras, [216] [214] [217] [218] but he may have been the first to introduce it to the Greeks. [219] [217] Some historians of mathematics have even suggested that he—or his students—may have constructed the first proof. [220]
Both constructions proceed by letting the largest of the squares be the square on the diagonal of a rectangle, and letting the two smaller squares be the squares on the sides of that rectangle. The assertion that each procedure produces a square of the desired area is equivalent to the statement of the Pythagorean theorem.
According to Iamblichus's The life of Pythagoras, [16] There were also two forms of philosophy, for the two genera of those that pursued it: the Acusmatici and the Mathematici. The latter are acknowledged to be Pythagoreans by the rest but the Mathematici do not admit that the Acusmatici derived their instructions from Pythagoras but from Hippasus.
The spiral is started with an isosceles right triangle, with each leg having unit length.Another right triangle (which is the only automedian right triangle) is formed, with one leg being the hypotenuse of the prior right triangle (with length the square root of 2) and the other leg having length of 1; the length of the hypotenuse of this second right triangle is the square root of 3.
This is a list of notable theorems.Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures