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

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

Product Details

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

Table of Contents

Figures ix
Chapter 1: Introduction 1
Chapter 2: The Problem 10
Chapter 3: History: Much Ado About Less than Nothing 18
The Search for Evident Meaning 36
Chapter 4: History: Meaningful and Meaningless Expressions 43
Impossible Numbers? 66
Chapter 5: History: Making Radically New Mathematics 80
From Hindsight to Creativity 104
Chapter 6: Math Is Rather Flexible 110
Sometimes -1 Is Greater than Zero 112
Traditional Complications 115
Can Minus Times Minus Be Minus? 131
Unity in Mathematics 166
Chapter 7: Making a Meaningful Math 174
Finding Meaning 175
Designing Numbers and Operations 186
Physical Mathematics? 220
Notes 235
Further Reading 249
Acknowledgments 259
Index 261

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