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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. Also included are complete proofs, introduction of coordinates, the theory of area, geometrical constructions and finite field extensions, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra. The text is intended for junior-senior level mathematics majors. Robin…mehr

Produktbeschreibung
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. Also included are complete proofs, introduction of coordinates, the theory of area, geometrical constructions and finite field extensions, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra. The text is intended for junior-senior level mathematics majors. Robin Hartshorne is a professor of mathematics at the University of California, Berkeley, and is the author of "Foundations of Projective Geometry" (Benjamin, 1967) and "Algebraic Geometry" (Springer, 1977).
  • Produktdetails
  • Undergraduate Texts in Mathematics
  • Verlag: Springer / Springer New York / Springer, Berlin
  • 1st Corrected ed. 2000. Corr. 3rd printing 2005
  • Seitenzahl: 544
  • Erscheinungstermin: 28. September 2005
  • Englisch
  • Abmessung: 260mm x 183mm x 38mm
  • Gewicht: 1277g
  • ISBN-13: 9780387986500
  • ISBN-10: 0387986502
  • Artikelnr.: 08773668
Autorenporträt
Robin Hartshorne is a professor of mathematics at the University of California, Berkeley and is the author of Foundations of Projective Geometry (Benjamin, 1967) and Algebraic Geometry (Springer, 1977).
Inhaltsangabe
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.