Pythagorean Triples
Many algebraic methods exist for generating Pythagorean triples. In this book you will find various methods and the geometry behind these formulas.
Table of Contents
- Formulas for generating Pythagorean Triples
- Rath's (1873 -1874) construction of Pythagorean Triples
- Dickson 1894 rule for generating Pythagorean triples
- Cattaneo's method for generating Pythagorean Triples(1908)
- L E Dickson's (1920) method for generating Pythagorean triples
- Tabulating all Pythagorean triples - Klostergaard (1978)
- Generating Pythagorean Triples (Bredenkamp 2013)
- Pythagorean Triples and the Unit Circle
- Fibonacci Box method for generating Pythagorean triples
- Fibonacci Box Method using Bredenkamp's (i,j)-generators
- Odd and even series of Pythagorean triples
Rath's (1873 -1874) construction of Pythagorean Triples
It is well known that all Pythagorean triples can be generated from two positive integers m and n. Iff n<m, m and n relatively prime and not both odd, the three numbers a=m²-n², b=2mn, and c=m²+n² form a primitive Pythagorean triple. Rath (1873-1874) has taken the difference between m and n to be equal to d. Use the sliders to change the values of n and d. Note that the product of n and d is equal to the radius of the incircle (r=nd).
Rath H, Die rationalen Dreiecke, Archiv der Mathematik und Physik. v.55-56.1873-1874