Interactive Methods for Visualizable Geometry

Andrew J. Hanson(Indiana University),
Tamara Munzner (The Geometry Center),
George Francis (University of Illinois at Urbana-Champaign)

Title Page Abstract

Interactive computer graphics methods provide new insights into the world of pure geometry.

• Introduction
• Pictures and Mathematics
  • Goals and Methods of Mathematical Visualization
  • Creating mental models.
• Problems in Visualizable Geometry
  • Manifolds
    • What is a manifold?
    • Surfaces in 4D
    • Knotted Surfaces in 4D
    • 3-manifolds
    • Viewing with 4D Light-
    • Non-Euclidean Geometry
  • Minimal Surfaces
    • Software Systems.
  • Homotopies and the Sphere Eversion Problem
• Design Philosophies for Geometry Visualization
  • Mathematical Virtual Reality.
• Prospects for the Future
• Acknowledgments
• References
• Glossary
• Background for Further Reading
• Mathematical Videos
• Author Information
• Figures
• About this document ...