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Shadows of RealityThe Fourth Dimension in Relativity, Cubism, and Modern Thought$
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Tony Robbin

Print publication date: 2006

Print ISBN-13: 9780300110395

Published to Yale Scholarship Online: October 2013

DOI: 10.12987/yale/9780300110395.001.0001

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PRINTED FROM YALE SCHOLARSHIP ONLINE (www.yale.universitypressscholarship.com). (c) Copyright Yale University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in YSO for personal use.date: 19 September 2021

A Very Short Course in Projective Geometry

A Very Short Course in Projective Geometry

Chapter:
(p.53) 5 A Very Short Course in Projective Geometry
Source:
Shadows of Reality
Author(s):

Tony Robbin

Publisher:
Yale University Press
DOI:10.12987/yale/9780300110395.003.0005

This chapter serves as a brief lesson on projective geometry. It starts by discussing two basic theorems of projective geometry, which are concerned with perspectives from a point and perspectives from a line. The discussion then looks at projectivities and perspectivities, which result from several perspectivities and relate a range, respectively. This is followed by the study of analytic projective geometry and the connection between projective and projection. The chapter concludes with a discussion on the complex projective line, the projective three-space, and Felix Klein's thoughts on the presence of non-Euclidean geometries in projective geometry, specifically the topology of the projective plane.

Keywords:   projective geometry, projectivities, perspectivities, analytic projective geometry, projective line, three-space, Felix Klein, non-Euclidean geometries, projective plane

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