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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.
Pythagorean trigonometric identity. The Pythagorean trigonometric identity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae, it is one of the basic relations between the sine and cosine functions. The identity is.
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 ...
Main article: Pythagorean trigonometric identity. Identity 1: The following two results follow from this and the ratio identities. To obtain the first, divide both sides of by ; for the second, divide by . Similarly. Identity 2: The following accounts for all three reciprocal functions. Proof 2: Refer to the triangle diagram above.
Definition of congruence in analytic geometry. In a Euclidean system, congruence is fundamental; it is the counterpart of equality for numbers. In analytic geometry, congruence may be defined intuitively thus: two mappings of figures onto one Cartesian coordinate system are congruent if and only if, for any two points in the first mapping, the ...
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 ...
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 Triangles is a book on right triangles, the Pythagorean theorem, and Pythagorean triples. It was originally written in the Polish language by Wacław Sierpiński (titled Trójkąty pitagorejskie), and published in Warsaw in 1954. [1][2] Indian mathematician Ambikeshwar Sharma translated it into English, with some added material from ...
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