Negative Math: How Mathematical Rules Can Be Positively Bent

Negative Math: How Mathematical Rules Can Be Positively Bent

by Alberto A. Martinez
     
 

ISBN-10: 0691123098

ISBN-13: 9780691123097

Pub. Date: 11/07/2005

Publisher: Princeton University Press

A student in class asks the math teacher: "Shouldn't minus times minus make minus?" Teachers soon convince most students that it does not. Yet the innocent question brings with it a germ of mathematical creativity. What happens if we encourage that thought, odd and ungrounded though it may seem?

Few books in the field of mathematics encourage such creative

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Overview

A student in class asks the math teacher: "Shouldn't minus times minus make minus?" Teachers soon convince most students that it does not. Yet the innocent question brings with it a germ of mathematical creativity. What happens if we encourage that thought, odd and ungrounded though it may seem?

Few books in the field of mathematics encourage such creative thinking. Fewer still are engagingly written and fun to read. This book succeeds on both counts. Alberto Martinez shows us how many of the mathematical concepts that we take for granted were once considered contrived, imaginary, absurd, or just plain wrong. Even today, he writes, not all parts of math correspond to things, relations, or operations that we can actually observe or carry out in everyday life.

Negative Math ponders such issues by exploring controversies in the history of numbers, especially the so-called negative and "impossible" numbers. It uses history, puzzles, and lively debates to demonstrate how it is still possible to devise new artificial systems of mathematical rules. In fact, the book contends, departures from traditional rules can even be the basis for new applications. For example, by using an algebra in which minus times minus makes minus, mathematicians can describe curves or trajectories that are not represented by traditional coordinate geometry.

Clear and accessible, Negative Math expects from its readers only a passing acquaintance with basic high school algebra. It will prove pleasurable reading not only for those who enjoy popular math, but also for historians, philosophers, and educators.

Key Features:

  • Uses history, puzzles, and lively debates to devise new mathematical systems
  • Shows how departures from rules can underlie new practical applications
  • Clear and accessible
  • Requires a background only in basic high school algebra


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Product Details

ISBN-13:
9780691123097
Publisher:
Princeton University Press
Publication date:
11/07/2005
Edition description:
New Edition
Pages:
280
Sales rank:
1,420,226
Product dimensions:
6.64(w) x 9.64(h) x 0.95(d)

Table of Contents

Ch. 1Introduction1
Ch. 2The problem10
Ch. 3History : much ado about less than nothing18
Ch. 4History : meaningful and meaningless expressions43
Ch. 5History : making radically new mathematics80
Ch. 6Math is rather flexible110
Ch. 7Making a meaningful math174

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