Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-09T07:50:34.006Z Has data issue: false hasContentIssue false
  • English
  • Français

Pythagorean ratios in arithmetic progression, part i. three Pythagorean ratios

Published online by Cambridge University Press:  18 May 2009

John Leech
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let {a, b} designate the Pythagorean ratio (a2 - b2)/2ab between the sides of a rational right angled triangle. This paper studies the circumstances in which Pythagorean ratios can occupy consecutive places in an arithmetic progression. Part I deals with sets of three such ratios, while Part II discusses sets of four ratios.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 3 , September 1993 , pp. 395 - 407
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

REFERENCES

1.Cohn, J. H. E., Squares in arithmetical progressions. Math. Scand. 52 (1983), 5–19.CrossRefGoogle Scholar
2.Dickson, L. E., History of the Theory of Numbers, vol. 2, Diophantine analysis (Carnegie Institute, Washington 1920) 172–174.Google Scholar
3.Guy, R. K., Unsolved Problems in Number Theory (Springer Verlag, New York and Berlin, 1981).CrossRefGoogle Scholar
4.Lagrange, J. and Leech, J., Two triads of squares. Maths. Comp. 46 (1986), 751–758.CrossRefGoogle Scholar
5.Leech, J., The rational cuboid revisited. Amer. Math. Monthly 84 (1977), 518–533.CrossRefGoogle Scholar