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.