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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 description of this diagram appears in verse 129 of Bijaganita of Bhaskara II. [4] There is a legend that Bhaskara's proof of the Pythagorean theorem consisted of only just one word, namely, "Behold!". However, using the notations of the diagram, the theorem follows from the following equation:
The diagram for Euclid's proof of the Pythagorean theorem: each smaller square has area equal to the rectangle of corresponding color. Main article: Pythagorean theorem The three sides of a right triangle are related by the Pythagorean theorem , which in modern algebraic notation can be written
Diagram to explain Garfield's proof of the Pythagorean theorem In the figure, A B C {\displaystyle ABC} is a right-angled triangle with right angle at C {\displaystyle C} . The side-lengths of the triangle are a , b , c {\displaystyle a,b,c} .
Diagram used to illustrate the proof of the rational trigonometry Pythagorean Theorem. Date: 21 April 2007 ... Description=Diagram used to illustrate the proof of the ...
Diagram describing a proof of the Pythagorean theorem; drawn with w:MetaPost and converted to w:SVG. See also Image:Pythagoras6.png for another diagram representing the same proof, with more details.
Liu provided a proof of a theorem identical to the Pythagorean theorem. [3] Liu called the figure of the drawn diagram for the theorem the "diagram giving the relations between the hypotenuse and the sum and difference of the other two sides whereby one can find the unknown from the known." [6]