Negative Math

How Mathematical Rules Can Be Positively Bent

Alberto A. Martinez

268 pages, parution le 12/01/2006

Ajouter à une liste

Indisponible

Résumé

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

L'auteur - Alberto A. Martinez

Alberto A. Martinez teaches history of science and mathematics at the University of Texas, Austin. He studies history to better understand scientific creativity and to clarify ambiguities in the elements of physics and algebra.

Sommaire

Figures
Introduction
The Problem
History: Much Ado About Less than Nothing
History: Meaningful and Meaningless Expressions
History: Making Radically New Mathematics
Math Is Rather Flexible
Making a Meaningful Math
Notes
Further Reading
Acknowledgments
Index

Voir tout

Replier

Caractéristiques techniques

	PAPIER
Éditeur(s)	Princeton University Press
Auteur(s)	Alberto A. Martinez
Parution	12/01/2006
Nb. de pages	268
Format	16 x 24
Couverture	Relié
Poids	530g
Intérieur	Noir et Blanc
EAN13	9780691123097
ISBN13	978-0-691-12309-7