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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 ...
The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c). Although Pythagoras is most famous today for his alleged mathematical discoveries, [132] [207] classical historians dispute whether he himself ever actually made any significant contributions to the field.
Pythagorean Method of Memorization (PYMOM), also known as Triangular Movement Cycle (TMC), is a game-based, educational methodology or associative-learning technique that primarily uses corresponding information, such as terms and definitions on opposing sides, displayed on cue cards, to exploit psychological retention of information for academic study and language acquisition.
[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.
2008-05-20T00:47:20Z Jokes Free4Me 500x540 (13967 Bytes) {{Information |Description=Illustration to Euclid's proof of the Pythagorean theorem, including less important labels and lines. |Source=[[:Image:Illustration to Euclid's proof of the Pythagorean theorem.svg]] |Date=May 20, 2; Uploaded with derivativeFX
The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula + =; thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with non-integer sides do not form Pythagorean triples.