Isbn: 9780387255309 - the four pillars of geometry (undergraduate texts in mathematics) (4 Ergebnisse)

Hardcover. Zustand: Very Good.

8vo, pp. xi, [1], 227, [3]; diagrams in text; yellow paper covered boards; pen annotations in text, top edge damp stained, good. Part of the Undergraduate texts in Mathematics series.

Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - Many people think there is only one 'right' way to teach geometry. For two millennia, the 'right' way was Euclid's way, and it is still good in many respects. But in the 1950s the cry 'Down with triangles!' was heard in France and new geometry books appeared, packed with linear algebra but with no diagrams. Was this the new 'right' way, or was the 'right' way something else again, perhaps transformation groups In this book, I wish to show that geometry can be developed in four fundamentally different ways, and that all should be used if the subject is to be shown in all its splendor. Euclid-style construction and axiomatics seem the best way to start, but linear algebra smooths the later stages by replacing some tortuous arguments by simple calculations. And how can one avoid projective geometry It not only explains why objects look the way they do; it also explains why geometry is entangled with algebra. Finally, one needs to know that there is not one geometry, but many, and transformation groups are the best way to distinguish between them. Two chapters are devoted to each approach: The rst is concrete and introductory, whereas the second is more abstract. Thus, the rst chapter on Euclid is about straightedge and compass constructions; the second is about axioms and theorems. The rst chapter on linear algebra is about coordinates; the second is about vector spaces and the inner product.…

Hardcover. Zustand: Brand New. 1st edition. 227 pages. 9.25x6.25x0.75 inches. In Stock.