Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-25T02:40:00.118Z Has data issue: false hasContentIssue false
  • English
  • Français

Perfect pyramids

Published online by Cambridge University Press:  17 April 2009

Ralph Heiner Buchholz
Ralph Heiner Buchholz
Affiliation:
Department of MathematicsUniversity of Newcastle New South Wales2308, Australia
Rights & Permissions [Opens in a new window]

Abstract

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.

This paper discusses rational edged tetrahedra, in 3, 4 and n dimensions, with rational volume. The main results are (i) a proof of the existence of infinitely many tetrahedra with rational edge-lengths, face-areas and volume and (ii) a proof that there exist dimensions for which all regular hypertetrahedra with rational edge-lengths have rational hypervolume.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 3 , June 1992 , pp. 353 - 368
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Carmichael, R.D., The theory of numbers and diophantine analysis (Dover, 1952).Google Scholar
[2]Dickson, L.E., History of the theory of numbers 2 (Chelsea, 1952).Google Scholar
[3]Guy, R.K., Unsolved problems in number theory (Springer-Verlag, Berlin, Heidelberg, New York, 1981).CrossRefGoogle Scholar
[4]Guy, R.K., private communication.Google Scholar
[5]Silverman, J.H., The arithmetric of elliptic curves (Springer-Verlag, Berlin, Heidelberg, New York, 1986).CrossRefGoogle Scholar