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  2. Formulas for generating Pythagorean triples - Wikipedia

    en.wikipedia.org/wiki/Formulas_for_generating...

    With a the shorter and b the longer legs of a triangle and c its hypotenuse, the Pythagoras family of triplets is defined by c − b = 1, the Plato family by c − b = 2, and the Fermat family by | a − b | = 1. The Stifel sequence produces all primitive triplets of the Pythagoras family, and the Ozanam sequence produces all primitive triples ...

  3. Tree of primitive Pythagorean triples - Wikipedia

    en.wikipedia.org/wiki/Tree_of_primitive...

    If any of the above matrices, say A, is applied to a triple (a, b, c) T having the Pythagorean property a 2 + b 2 = c 2 to obtain a new triple (d, e, f) T = A(a, b, c) T, this new triple is also Pythagorean.

  4. Pythagorean triple - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_triple

    If a is replaced with the fraction m/n in the sequence, the result is equal to the 'standard' triple generator (2mn, m 2 − n 2, m 2 + n 2) after rescaling. It follows that every triple has a corresponding rational a value which can be used to generate a similar triangle (one with the same three angles and with sides in the same proportions as ...

  5. Pell number - Wikipedia

    en.wikipedia.org/wiki/Pell_number

    If a right triangle has integer side lengths a, b, c (necessarily satisfying the Pythagorean theorem a 2 + b 2 = c 2), then (a,b,c) is known as a Pythagorean triple. As Martin (1875) describes, the Pell numbers can be used to form Pythagorean triples in which a and b are one unit apart, corresponding to right triangles that are nearly isosceles ...

  6. Pythagorean Triangles - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_Triangles

    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.

  7. 25 to watch in 2025 - AOL

    www.aol.com/25-watch-2025-181318561.html

    In the final days of the 2024 calendar, there's a lot to look forward to in the sports world in 2025. Field Level Media surveyed writers and editors in its network to come up with 25 to watch in ...