A Pappus Type Theorem in the Affine Group
Canadian mathematical bulletin, Tome 11 (1968) no. 4, pp. 547-554
Voir la notice de l'article provenant de la source Cambridge University Press
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.
Paré, R. A Pappus Type Theorem in the Affine Group. Canadian mathematical bulletin, Tome 11 (1968) no. 4, pp. 547-554. doi: 10.4153/CMB-1968-065-5
@article{10_4153_CMB_1968_065_5,
author = {Par\'e, R.},
title = {A {Pappus} {Type} {Theorem} in the {Affine} {Group}},
journal = {Canadian mathematical bulletin},
pages = {547--554},
year = {1968},
volume = {11},
number = {4},
doi = {10.4153/CMB-1968-065-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-065-5/}
}
[1] 1. Heyting, A., Axiomatic projective geometry (Amsterdam). Google Scholar
[2] 2. Kurosh, A. G., The theory of groups (New York). Google Scholar
[3] 3. Schwerdtfeger, H., Projective geometry in the one-dimensional affine group. Canad. J. Math. 16 (1964) 683-700. Google Scholar
[4] 4. Veblen, O. and Young, J. W., Projective geometry, Vol. 1 (Boston 1910). Google Scholar
Cité par Sources :