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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.
This principle, foundational for all mathematics, was first elaborated for geometry, and was systematized by Euclid around 300 BC in his book Elements. [ 21 ] [ 22 ] The resulting Euclidean geometry is the study of shapes and their arrangements constructed from lines, planes and circles in the Euclidean plane ( plane geometry ) and the three ...
He also wrote "The Teaching of Mathematics in High Schools", and "Original Investigation Or How to Attack an Exercise in Geometry". Possibly his best-known work however, is "The Pythagorean Proposition", in which he collected, classified, and discussed 344 proofs. The book is still a work of reference. [5]
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[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 ...
Hippasus, engraving by Girolamo Olgiati, 1580. Hippasus of Metapontum (/ ˈ h ɪ p ə s ə s /; Ancient Greek: Ἵππασος ὁ Μεταποντῖνος, Híppasos; c. 530 – c. 450 BC) [1] was a Greek philosopher and early follower of Pythagoras.
Garfield's proof of the Pythagorean theorem is an original proof the Pythagorean theorem discovered by James A. Garfield (November 19, 1831 – September 19, 1881), the 20th president of the United States. The proof appeared in print in the New-England Journal of Education (Vol. 3, No.14, April 1, 1876).
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.