Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-13T12:00:00.395Z Has data issue: false hasContentIssue false
  • English
  • Français

A group structure on the golden triples

Published online by Cambridge University Press:  17 February 2021

Howard Sporn
Howard Sporn*
Affiliation:
Dept. of Mathematics and Computer Science, Queensborough Community College, Bayside, NY, USA 11364 e-mail: hsporn@qcc.cuny.edu
Get access Rights & Permissions [Opens in a new window]

Extract

Some favourite topics of both mathematics teachers and mathematics students are the golden ratio, Fibonacci numbers, groups, and Pythagorean triples. The material of this paper involves the first three, and there are some analogies with the fourth.

Type
Articles
Information
The Mathematical Gazette , Volume 105 , Issue 562 , March 2021 , pp. 87 - 97
Check for updates
Copyright
© The 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

Cuoco, A. A., Meta-problems in mathematics, College Mathematics Journal 31 (2000) pp. 373–378.CrossRefGoogle Scholar
Read, E., On integer-sided triangles containing angles of 120° or 60°, Math. Gaz. 90 (July 2006) pp. 299–305.CrossRefGoogle Scholar
Fässler, A., Multiple Pythagorean number triples, American Mathematical Monthly 98 (1991) pp. 505–517.CrossRefGoogle Scholar
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. 163–171.10.1080/0025570X.1996.11996421CrossRefGoogle Scholar
Lehrer, G. I. and Taylor, D. E., Unitary reflection groups, Cambridge University Press (2009).Google Scholar
Rokhsar, D. S., Mermin, N. D., and Wright, D. C., Rudimentary quasicrystallography: the icosahedral and decagonal reciprocal lattices, Physical Review B: Condensed Matter 35 (1987) pp. 5487–5495.CrossRefGoogle ScholarPubMed
Janot, C., Quasicrystals: A Primer, Clarendon Press, Oxford (1994).Google Scholar
Ling, S. and Solé, P., Type II Codes over F 4 + uF 4, Europ. J. Combinatorics 22 (2001) pp. 983–997.10.1006/eujc.2001.0509CrossRefGoogle Scholar
Koshy, T., Fibonacci and Lucas numbers with applications, John Wiley, New York (2001).CrossRefGoogle Scholar
Dickson, L. E., History of the Theory of Numbers, Volume 1, Chelsea Publishing Company, New York (1952).Google Scholar
Vajda, S., Fibonacci and Lucas Numbers and the Golden Section, Dover, Mineola, NY (1989).Google Scholar