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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.
Garfield in 1881. Garfield's proof of the Pythagorean theorem is an original proof the Pythagorean theorem invented 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). [1][2] At the time of ...
Bride's Chair. In geometry, a Bride's Chair is an illustration of the Pythagorean theorem. [1] The figure appears in Proposition 47 of Book I of Euclid's Elements. [2] It is also known by several other names, such as the Franciscan's cowl, peacock's tail, windmill, Pythagorean pants, Figure of the Bride, theorem of the married women, and chase ...
The Berlin Papyrus 6619 is an ancient Egyptian papyrus document from the Middle Kingdom, [3] second half of the 12th (c. 1990–1800 BC) or 13th Dynasty (c. 1800 BC – 1649 BC). [4] The two readable fragments were published by Hans Schack-Schackenburg in 1900 and 1902. [5][6]
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 ]
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2. [38] This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3.
Pythagorean expectation is a sports analytics formula devised by Bill James to estimate the percentage of games a baseball team "should" have won based on the number of runs they scored and allowed. Comparing a team's actual and Pythagorean winning percentage can be used to make predictions and evaluate which teams are over-performing and under ...
In geometry, the inverse Pythagorean theorem (also known as the reciprocal Pythagorean theorem[1] or the upside down Pythagorean theorem[2]) is as follows: [3] Let A, B be the endpoints of the hypotenuse of a right triangle ABC. Let D be the foot of a perpendicular dropped from C, the vertex of the right angle, to the hypotenuse.
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