Introduction: The Projective Plane and Central Collineations

Christopher Baltus ()
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Christopher Baltus: State University of New York at Oswego, Department of Mathematics

Chapter Chapter 1 in Collineations and Conic Sections, 2020, pp 1-13 from Springer

Abstract: Abstract This book grew from the idea that much of projective geometry is the elaboration of a simple concept, the central collineation. A central collineationCentral collineation is a construction, carried out with just a straightedge and a device to construct parallel lines, following the simplest rules, that transforms one diagram into another. We call it a collineation because a line is always transformed to a line. We’ll soon explain the meaning of central. And how is a circle transformed? That is the marvelous part, for a circle becomes a parabola or ellipse or hyperbola—a conic section. And all conic sections can be formed this way.

Date: 2020
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DOI: 10.1007/978-3-030-46287-1_1

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