A Long Way from Euclid

Front Cover
Courier Corporation, 2004 - Mathematics - 292 pages
1 Review

Mathematics has come a long way indeed in the last 2,000 years, and this guide to modern mathematics traces the fascinating path from Euclid's Elements to contemporary concepts. No background beyond elementary algebra and plane geometry is necessary to understand and appreciate author Constance Reid's simple, direct explanations of the arithmetic of the infinite, the paradoxes of point sets, the "knotty" problems of topology, and "truth tables" of symbolic logic. Reid illustrates the ways in which the quandaries that arose from unsolvable problems promoted new ideas. Numerical concepts expanded to accommodate such concepts as zero, irrational numbers, negative numbers, imaginary numbers, and infinite numbers.
Geometry advanced into the widening territories of projective geometry, non-Euclidean geometries, the geometry of n-dimensions, and topology or "rubber sheet" geometry. More than 80 drawings, integrated with the text, assist in cultivating a grasp of the abstract foundations of modern mathematics, the search for truly consistent assumptions, the recognition that absolute consistency is unattainable, and the realization that some problems can never be solved.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

VII
1
XI
16
XII
30
XV
60
XVI
78
XIX
97
XX
115
XXI
133
XXVI
174
XXVIII
188
XXX
204
XXXII
226
XXXIV
245
XXXVI
258
XXXVII
271
XXXVIII
283

XXIII
148
XXV
163

Other editions - View all

Common terms and phrases

References to this book

All Book Search results »

Bibliographic information