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  2. Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_theorem

    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.

  3. Pythagorean trigonometric identity - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_trigonometric...

    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.

  4. Inverse Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Inverse_Pythagorean_theorem

    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.

  5. Pythagorean means - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_means

    Pythagorean means. A geometric construction of the quadratic mean and the Pythagorean means (of two numbers a and b). Harmonic mean denoted by H, geometric by G, arithmetic by A and quadratic mean (also known as root mean square) denoted by Q. Comparison of the arithmetic, geometric and harmonic means of a pair of numbers.

  6. Bride's Chair - Wikipedia

    en.wikipedia.org/wiki/Bride's_Chair

    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 ...

  7. Pythagoras - Wikipedia

    en.wikipedia.org/wiki/Pythagoras

    Pythagoras. Pythagoras of Samos[a] (Ancient Greek: Πυθαγόρας; c. 570 – c. 495 BC) [b] was an ancient Ionian Greek philosopher, polymath and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, the West in ...

  8. Pythagorean prime - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_prime

    A Pythagorean prime is a prime number of the form . Pythagorean primes are exactly the odd prime numbers that are the sum of two squares; this characterization is Fermat's theorem on sums of two squares. Equivalently, by the Pythagorean theorem, they are the odd prime numbers for which is the length of the hypotenuse of a right triangle with ...

  9. Hypotenuse - Wikipedia

    en.wikipedia.org/wiki/Hypotenuse

    Hypotenuse. A right-angled triangle and its hypotenuse. In geometry, a hypotenuse is the side of a right triangle opposite the right angle. [1] It is the longest side of any such triangle; the two other shorter sides of such a triangle are called catheti or legs. The length of the hypotenuse can be found using the Pythagorean theorem, which ...

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