Geometry: Euclid and Beyond

1. Corrected Auflage 2000. Corr. 3rd printing 2005
ISBN: 978-0-387-98650-0
Verlag: Springer

Buch, Englisch, 528 Seiten, Format (B × H): 183 mm x 260 mm, Gewicht: 1332 g

Reihe: Undergraduate Texts in Mathematics

This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Hartshorne, Robin

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Mathematik | Informatik Mathematik Geometrie Euklidische Geometrie

Inhaltsverzeichnis

1. Euclid’s Geometry.- 2. Hilbert’s Axioms.- 3. Geometry over Fields.- 4. Segment Arithmetic.- 5. Area.- 6. Construction Problems and Field Extensions.- 7. Non-Euclidean Geometry.- 8. Polyhedra.- Appendix: Brief Euclid.- Notes.- References.- List of Axioms.- Index of Euclid’s Propositions.