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The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two legs. Mathematically, this can be written as a 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}} , where a is the length of one leg, b is the length of ...
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.
In mathematics, Pythagorean addition is a binary operation on the real numbers that computes the length of the hypotenuse of a right triangle, given its two sides.According to the Pythagorean theorem, for a triangle with sides and , this length can be calculated as = +, where denotes the Pythagorean addition operation.
The two squared formulas inside the square root give the areas of squares on the horizontal and vertical sides, and the outer square root converts the area of the square on the hypotenuse into the length of the hypotenuse. [3] It is also possible to compute the distance for points given by polar coordinates.
The formulas show how to transform any right triangle with integer legs into another right triangle with integer legs whose hypotenuse is the square of the first triangle's hypotenuse. A Pythagorean prime is a prime number of the form 4 n + 1 {\displaystyle 4n+1} .
A right triangle ABC with its right angle at C, hypotenuse c, and legs a and b,. A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle (1 ⁄ 4 turn or 90 degrees).
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To calculate a Pythagorean triple, take any term of this sequence and convert it to an improper fraction (for mixed number , the corresponding improper fraction is ). Then its numerator and denominator are the sides, b and a, of a right triangle, and the hypotenuse is b + 1. For example: