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A Pappus Type Theorem in the Affine Group

Published online by Cambridge University Press:  20 November 2018

R. Paré
R. Paré*
Affiliation:
McGill University
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Extract

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In [3] H. Schwerdtfeger embedded the one-dimensional affine group over the real numbers in the projective plane. The relationship between group-theoretical properties and geometrical concepts was studied.

In this paper the methods of [3] are used to prove Pappus' theorem. In the final section we give a similar theorem for (4n+2)-gons.

This paper is a generalization of part of my master's thesis, written under the direction of Professor H. Schwerdtfeger.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 4 , October 1968 , pp. 547 - 554
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Heyting, A., Axiomatic projective geometry (Amsterdam).Google Scholar
2. Kurosh, A. G., The theory of groups (New York).Google Scholar
3. Schwerdtfeger, H., Projective geometry in the one-dimensional affine group. Canad. J. Math. 16 (1964) 683-700.Google Scholar
4. Veblen, O. and Young, J. W., Projective geometry, Vol. 1 (Boston 1910).Google Scholar