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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.
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 ...
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. In the last part of the text, the solution is proved correct using the Pythagorean theorem. The steps of the solution are believed ...
Since squaring is a monotonic function of non-negative values, minimizing squared distance is equivalent to minimizing the Euclidean distance, so the optimization problem is equivalent in terms of either, but easier to solve using squared distance. [21]
When we recently wrote about the toughest math problems that have been solved, we mentioned one of the greatest achievements in 20th-century math: the solution to Fermat’s Last Theorem. Sir ...
The Berlin Papyrus contains two problems, the first stated as "the area of a square of 100 is equal to that of two smaller squares. The side of one is ½ + ¼ the side of the other." [ 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 ...
Noether's theorem (Lie groups, calculus of variations, differential invariants, physics) Noether's second theorem (calculus of variations, physics) Noether's theorem on rationality for surfaces (algebraic surfaces) Non-squeezing theorem (symplectic geometry) Norton's theorem (electrical networks) Novikov's compact leaf theorem
The exact value of the sofa constant is an open problem. The leading solution, by Joseph L. Gerver, has a value of approximately 2.2195. In November 2024, Jineon Baek posted an arXiv preprint claiming that Gerver's value is optimal, which if true, would solve the moving sofa problem. [2]