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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:
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.
[7] The interest in the question may suggest some knowledge of the Pythagorean theorem, though the papyrus only shows a straightforward solution to a single second degree equation in one unknown. In modern terms, the simultaneous equations x 2 + y 2 = 100 and x = (3/4) y reduce to the single equation in y : ((3/4) y ) 2 + y 2 = 100 , giving the ...
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 Bride's chair proof of the Pythagorean theorem, that is, the proof of the Pythagorean theorem based on the Bride's Chair diagram, is given below. The proof has been severely criticized by the German philosopher Arthur Schopenhauer as being unnecessarily complicated, with construction lines drawn here and there and a long line of deductive ...
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]
IM 67118, also known as Db 2-146, is an Old Babylonian clay tablet in the collection of the Iraq Museum that contains the solution to a problem in plane geometry concerning a rectangle with given area and diagonal.