A Long Way From Euclid

( 3 )

Overview

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 ...
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A Long Way from Euclid

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Overview

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.
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Product Details

  • ISBN-13: 9781113809018
  • Publisher: BiblioBazaar
  • Publication date: 9/1/2009
  • Pages: 306
  • Product dimensions: 0.75 (w) x 10.00 (h) x 7.00 (d)

Table of Contents

1 The Golden Knot in the Golden Thread 1
2 Nothing, Intricately Drawn Nowhere 16
3 The Inexhaustible Storehouse 30
4 A Number for Every Point on the Line 46
5 Journey That Begins at O 60
6 How Big? How Steep? How Fast? 78
7 How Many Numbers Are Enough? 97
8 Enchanted Realm, Where Thought Is Double 115
9 The Possibility of Impossibility 133
10 Euclid Not Alone 148
11 Worlds We Make 163
12 Where Is In and Where Is Out? 174
13 What a Geometry IS 188
14 Counting the Infinite 204
15 A Most Ingenious Paradox 226
16 The New Euclid 245
17 Of Truth Tables and Truths 258
18 Mathematics, the Inexhaustible 271
Index 283
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Customer Reviews

Average Rating 3.5
( 3 )
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Sort by: Showing all of 3 Customer Reviews
  • Posted January 23, 2011

    A well-written survey of Mathematics from Euclid to present times

    I really enjoyed this book. Just the right combination of survey level and detail, highlighting key theorems and directions in the primary branches of mathematics since Euclid.

    This eBook version can be a little tough to read in spots since it was converted using OCR. Some diagrams are scanned images, but many equations are OCR'ed which makes them unintelligible. That's a shame. But, still, it's a great book.

    3 out of 3 people found this review helpful.

    Was this review helpful? Yes  No   Report this review
  • Anonymous

    Posted October 15, 2013

    Excellent

    As a lover ofmathematics *and* history I can say this is a great book! Thank you.

    1 out of 1 people found this review helpful.

    Was this review helpful? Yes  No   Report this review
  • Anonymous

    Posted February 5, 2011

    No text was provided for this review.

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