Geometry: Euclid and Beyond

1. Auflage 2000. Corr. 4th printing. Softcover version of original hardcover Auflage 2000
ISBN: 978-1-4419-3145-0
Verlag: Springer

Buch, Englisch, 528 Seiten, Previously published in hardcover, Format (B × H): 178 mm x 254 mm, Gewicht: 1011 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 Euklidische Geometrie
• Mathematik | Informatik Mathematik Geometrie Nicht-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.