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Home > Art, Film & Photography > Arithmetic Problems of Plane Geometry: Pythagorean Triple, Mrs. Miniver's Problem, Heronian Triangle, Congruent Number, Pythagorean Quadruple
Arithmetic Problems of Plane Geometry: Pythagorean Triple, Mrs. Miniver's Problem, Heronian Triangle, Congruent Number, Pythagorean Quadruple

Arithmetic Problems of Plane Geometry: Pythagorean Triple, Mrs. Miniver's Problem, Heronian Triangle, Congruent Number, Pythagorean Quadruple


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About the Book

Chapters: Pythagorean Triple, Mrs. Miniver's Problem, Heronian Triangle, Congruent Number, Pythagorean Quadruple. Source: Wikipedia. Pages: 34. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: A Pythagorean triple consists of three positive integers a, b, and c, such that . Such a triple is commonly written, and a well-known example is . If is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime. The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula; thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with non-integer sides do not form Pythagorean triples. For instance, the triangle with sides and c = 2 is right, but (1, 1, 2) is not a Pythagorean triple because 2 is not an integer. Moreover, 1 and 2 do not have an integer common multiple because 2 is irrational. There are 16 primitive Pythagorean triples with: A scatter plot of the legs (a, b) of the Pythagorean triples with c less than 6000. Negative values are included to illustrate the parabolic patterns in the plot more clearly. A plot of triples generated by Euclid's formula map out part of the z = x + y cone. A constant m or n trace out part of a parabola on the cone.Euclid's formula is a fundamental formula for generating Pythagorean triples given an arbitrary pair of positive integers m and n with . The formula states that the integers form a Pythagorean triple. The triple generated by Euclid's formula is primitive if and only if m and n are coprime and exactly one of them is even. If both n and m are odd, then a, b, and c will be even, and so the triple will not be primitive. Every primitive triple (possibly afte...More: http: //booksllc.net/?id=24172


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Product Details
  • ISBN-13: 9781156328873
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: Pythagorean Triple, Mrs. Miniver's Problem, Heronian Triangle, Congruent Number, Pythagorean Quadruple
  • Width: 229 mm
  • ISBN-10: 115632887X
  • Publisher Date: 15 Sep 2010
  • Binding: Paperback
  • Spine Width: 2 mm
  • Weight: 68 gr


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