Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-27T22:18:48.905Z Has data issue: false hasContentIssue false
  • English
  • Français

A group of Pythagorean triples using the inradius

Published online by Cambridge University Press:  21 June 2021

Howard Sporn
Howard Sporn*
Affiliation:
Department of Mathematics and Computer Science, Queensborough Community College, Bayside, NY11364, USA e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

Pythagorean triples are triples of integers (a, b, c) satisfying the equation a2 + b2 = c2. For the purpose of this paper, we will take a, b and c to be positive, unless otherwise stated. Then, of course, it follows that a triple represents the lengths of sides of a right triangle. Also, for the purpose of this paper, we will consider the triples (a, b, c) and (b, a, c) to be distinct, even though they represent the same right triangle. A primitive Pythagorean triple is one for which a, b and c are relatively prime.

Type
Articles
Information
The Mathematical Gazette , Volume 105 , Issue 563 , July 2021 , pp. 209 - 215
Check for updates
Copyright
© Mathematical Association 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Eckert, E. J., The group of primitive pythagorean triples, Mathematics Magazine 57 (1984) pp. 22–27.CrossRefGoogle Scholar
Tan, L., The group of rational points on the unit circle, Mathematics Magazine 69 (1996) pp. 163–171.CrossRefGoogle Scholar
Beauregard, R. A. and Suryanarayan, E. R., Pythagorean triples: The hyperbolic view, College Mathematics Journal 27 (1996) pp. 170–181.CrossRefGoogle Scholar
Sporn, H., Pythagorean triples, complex numbers, and perplex numbers, College Mathematics Journal 48 (2017) pp. 115–122.CrossRefGoogle Scholar
Akhtar, M. S., Inscribed circles of Pythagorean triangles, Math. Gaz. 86 (July 2002) pp. 302–303.CrossRefGoogle Scholar
Clarke, R. J., Incircles of right-angled triangles, Math. Gaz. 89 (March 2005) pp. 82–86.CrossRefGoogle Scholar
O’Loughlin, M., Half angles and the inradius of a Pythagorean triangle, Math. Gaz. 94 (March 2010) pp. 144–146.CrossRefGoogle Scholar
Tong, J.-C., Conjugates of Pythagorean triples, Math. Gaz. 87 (November 2003) pp. 496–499.CrossRefGoogle Scholar
Bernhart, F. R. and Price, H. L., Pythagoras’ garden, revisited, Australian Senior Mathematics Journal 26 (2012) pp. 29–40.Google Scholar
Gomes, L. T., Pythagoras triples explained via central squares, Australian Senior Mathematics Journal 29 (2015) pp. 7–15.Google Scholar