SØG - mellem flere end 8 millioner bøger:
Viser: Geometry - Euclid and Beyond
Geometry
Euclid and Beyond
Robin Hartshorne
(2005)
Sprog: Engelsk
Springer New York
571,00 kr.
ikke på lager, Bestil nu og få den leveret
om ca. 10 hverdage
om ca. 10 hverdage
Detaljer om varen
- 1. Udgave
- Hardback
- Udgiver: Springer New York (September 2005)
- ISBN: 9780387986500
In recent years, I have been teaching a junior-senior-level course on the classi- cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa- rately. The remainder of the book is an exploration of questions that arise natu- rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And in the last chapter we provide what is missing from Euclid's treatment of the five Platonic solids in Book XIII of the Elements. For a one-semester course such as I teach, Chapters 1 and 2 form the core material, which takes six to eight weeks.
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.
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.
De oplyste priser er inkl. moms
Butikker og åbningstid
Handler du som firma
Forretningsbetingelser
Porto og forsendelse
Data & cookiepolitik
Handler du som firma
Forretningsbetingelser
Porto og forsendelse
Data & cookiepolitik
Polyteknisk Boghandel og Forlag A/S - Anker Engelundsvej 1 - 2800 Lyngby
Tlf 77 42 43 44 - email poly@polyteknisk.dk - CVR 34072655 - Sydbank Reg: 6748 Konto 0001107927
Tlf 77 42 43 44 - email poly@polyteknisk.dk - CVR 34072655 - Sydbank Reg: 6748 Konto 0001107927