Abstract
Given a leg of a right-angled triangle a, this formula gives the other leg b and the hypotenuse c by the usage of a pattern observed in Pythagorean triples. This is different as compared to Euclids method since Euclids method takes two arbitrary numbers as the input while this uses the side of the right-angled triangle as the input.
Highlights
1.1 The Current ProblemThe Euclid’s formula is the most commonly used formula for generating Pythagorean triples given an arbitrary pair of integers m and n with m > n > 0
Given a leg of a right-angled triangle a, this formula gives the other leg b and the hypotenuse c by the usage of a pattern observed in Pythagorean triples
This is different as compared to Euclids method since Euclids method takes two arbitrary numbers as the input while this uses the side of the right-angled triangle as the input
Summary
The Euclid’s formula is the most commonly used formula for generating Pythagorean triples given an arbitrary pair of integers m and n with m > n > 0. The limitation in this formula is that we have no control over the values of the sides of the triangle. If we want to find a Pythagorean triple with side length of 156, this is quite a challenge with Euclid’s method. The basis of the method presented in this paper has complete control over the side length
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