Cantitate/Preț
Produs

Geometry: Euclid and Beyond

Autor Robin Hartshorne
en Limba Engleză Hardback – 8 iun 2000
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.
Citește tot Restrânge

Toate formatele și edițiile

Toate formatele și edițiile Preț Express
Paperback (1) 42527 lei  6-8 săpt.
  Springer – 15 dec 2010 42527 lei  6-8 săpt.
Hardback (1) 46711 lei  6-8 săpt.
  Springer – 8 iun 2000 46711 lei  6-8 săpt.

Preț: 46711 lei

Nou

Puncte Express: 701

Preț estimativ în valută:
8264 9687$ 7266£

Carte tipărită la comandă

Livrare economică 29 ianuarie-12 februarie 26

Preluare comenzi: 021 569.72.76

Specificații

ISBN-13: 9780387986500
ISBN-10: 0387986502
Pagini: 544
Ilustrații: XII, 528 p.
Dimensiuni: 183 x 260 x 38 mm
Greutate: 1.16 kg
Ediția:2000
Editura: Springer
Locul publicării:New York, NY, United States

Public țintă

Lower undergraduate

Cuprins

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.