On the Projective Methods for Investigating the Singularities at Infinity of Curves: Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Arts in Mathematics in the - Hardcover

Merlin Grant Smith

9780265542996: On the Projective Methods for Investigating the Singularities at Infinity of Curves: Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Arts in Mathematics in the

Hardcover

ISBN 10: 0265542995 ISBN 13: 9780265542996

Publisher: Forgotten Books, 2018

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Explore the geometry of infinity through projective methods

Discover how curved and straight lines behave when points at infinity are brought into the finite plane, transforming our view of curves and their singularities.

This classic thesis presents practical approaches to studying the singularities that appear at infinity on plane curves. It explains several methods to project infinite points to the finite plane while preserving the curve’s character, and it walks through two main analytic frameworks: perspective transformations and homogeneous coordinates. Along the way, it ties the ideas to historical developments in geometry and outlines concrete steps for analyzing a curve’s behavior near infinity.

How perspective and projection relate to the finite description of curves at infinity
Two methods for transforming infinite points and preserving curve characteristics
Techniques for finding asymptotes, cusps, inflection points, and double points at infinity

Ideal for readers of advanced geometry, algebraic curves, and the history of mathematical methods who want a hands-on look at how infinity is treated in projective geometry.

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