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Pythagorean triples using the relativistic velocity addition formula

Published online by Cambridge University Press:  23 August 2024

Howard Sporn
Howard Sporn*
Affiliation:
Department of Mathematics and Computer Science, Queensborough Community College, 3 Bayside, NY, USA 11364 e-mail: hsporn@qcc.cuny.edu
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Extract

In the special theory of relativity, there is an unusual formula for addition of velocities. We will use this formula to generate Pythagorean triples. We define a Pythagorean triple in the usual manner as a triple of positive integers (a, b, c) such that a2 + b2 = c2. The numbers a and b are called legs, and c is called the hypotenuse. Later, we will allow b to take on the value of any integer. A primitive Pythagorean triple is a Pythagorean triple for which a, b and c are relatively prime.

Type
Articles
Information
The Mathematical Gazette , Volume 108 , Issue 572 , July 2024 , pp. 219 - 224
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Copyright
© The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association

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References

‘Pythagorean triple’, Wikipedia, accessed September 2022.Google Scholar
Di Lorenzo, A., A relation between pythagorean triples and the special theory of relativity, accessed September 2022 at https://www.academia.edu/37574176/A_relation_between_pythagorean_triples_and_the_special_theory_of_relativity Google Scholar