Open Access Repository

A cross ratio in continuous geometry

Downloads

Downloads per month over past year

Jones, BD (1962) A cross ratio in continuous geometry. Unspecified thesis, University of Tasmania.

[img]
Preview
PDF (Whole thesis)
whole_JonesBarr...pdf | Download (2MB)
Available under University of Tasmania Standard License.

| Preview

Abstract

A. Fuhrmann generalizes Sperner's definition of the cross ratio of four collinear points with coordinates in a division ring to apply to four linear varieties over a division ring. The form of, his cross ratio is still very classical. In Part 2 of this a cross ratio is defined for a configuration of subspaces of a continuous or discrete geometry. Although this cross ratio couldn’t be further removed in appearance from the classical form we give a simple proof (Section 4) to show that, for the case of four points on a line, it does in fact agree with the usual cross ratio. Moreover, it will follow from the results of Sections 5,6 that for the case of finite dimensional (i.e discrete) geometries, Fuhrmann's cross ratio is essentially the same as the one introduced here. The cross ratio has the desired property of invariance under collineations ( Theorem 3).

Item Type: Thesis (Unspecified)
Keywords: Geometry, Projective
Copyright Holders: The Author
Copyright Information:

Copyright 1961 the Author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s).

Additional Information:

Thesis (M.Sc.) - University of Tasmania, 1962. Includes bibliography

Date Deposited: 19 Dec 2014 02:26
Last Modified: 05 Apr 2017 05:04
Item Statistics: View statistics for this item

Actions (login required)

Item Control Page Item Control Page
TOP