Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-16T22:23:28.676Z Has data issue: false hasContentIssue false
  • English
  • Français

Note on the generalized Wallace theorem and related topics

Published online by Cambridge University Press:  24 October 2008

D. W. Babbage
D. W. Babbage
Affiliation:
Magdalene College, Cambridge
Get access Rights & Permissions [Opens in a new window]

Extract

1. Wallace's theorem, that the circumcircles of the four triangles formed by the sets of three from four coplanar lines meet in a point, has a generalization to Euclidean affine space of any even dimension n: namely, if we have n + 2 general primes (or hyperplanes) in such a space, the n + 2 circumhyperspheres of the simplexes formed by the sets of n + 1 of the primes meet in a point.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 2 , March 1975 , pp. 289 - 292
Copyright
Copyright © Cambridge Philosophical Society 1975

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

REFERENCES

(1)Grace, J. H.Circles, spheres and linear complexes. Proc. Cambridge Philos. Soc. 16 (1898), 153–190.Google Scholar
(2)Baker, H. F.Principles of geometry, vol. 4 (1927) (Cambridge University Press, 60–62.)Google Scholar
(3)White, F. P.An extension of Wallace–s, Miquel–s and Clifford's theorems on circles. Proc. Cambridge Philos. Soc. 22 (1925), 684–687.CrossRefGoogle Scholar
(4)Hirchfeld, J. W. P. A projective configuration. Computational problems in abstract algebra, ed. Leech, J., pp. 321–323 (Oxford Pergamon Press, 1970).Google Scholar
(5)Longuet-Higgins, M. S.A numerical disproof of a conjecture in projective geometry. Proc. Roy. Soc. Ser. A 323 (1971), 443–453.Google Scholar
(6)Longuet-Higgins, M. S.On a conjectured analogue to Clifford's chain in [4]. Proc. Cambridge Philos. Soc. 73 (1973), 37–43.CrossRefGoogle Scholar