Geometry: The Line and the Circle

ISBN-13: 9781470448431 / Angielski / Twarda / 2019 / 480 str.

Maureen T. Carroll;Elyn Rykken

Spis treści

• The line and the circle
• Euclid's Elements: Definitions and axioms
• Book I of Euclid's Elements: Neutral geometry
• Spherical geometry
• Taxicab geometry
• Hilbert and Godel
• Book I: Non-Neutral geometry
• Book II: Geometric algebra
• Book VI: Similarity
• Book III: Circles
• Book IV: Circles & polygons
• Models for the hyperbolic plane
• Axiomatic hyperbolic geometry
• Finite geometries
• Isometries
• Constructibility
• Appendix A: Euclid's definitions and axioms
• Appendix B: Euclid's propositions
• Appendix C: Visual guide to Euclid's propositions
• Appendix D: Euclid's proofs
• Hilbert's axioms for plane Euclidean geometry
• Credits, permissions and acknowledgments
• Bibliography
• Notation index
• Index.