Negative Math: How Mathematical Rules Can Be Positively Bent

Couverture
Princeton University Press, 5 janv. 2014 - 288 pages

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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Negative math: how mathematical rules can be positively bent

Avis d'utilisateur  - Not Available - Book Verdict

It's a rare person who describes negative numbers (or any numbers) as "unassuming but fun," and he is likely the same person who would notice that negative numbers "stand as just about the only kind ... Consulter l'avis complet

Table des matières

A number line
11
Much Ado About
18
Meaningful and Meaningless
43
The sum of a positive number and an imaginary number represented as a line
45
The geometric sum of two straight lines
63
The complex number 4 + 5i represented as a diagonal line
75
A rectangular triangle
76
Making Radically
80
A diagram of the Pythagorean theorem
144
A triangle constructed on a plane of positive and imaginary numbers
146
A representation of numbers as units on perpendicular lines
148
Lines determined by the same two numbers but in different order
150
Lines rotated 90 from one another without imaginary numbers
151
Making chapter 7 a Meaningful Math
174
notes
235
further reading
249

Math Is Rather Flexible
110
A number line
114
acknowledgments
259
Droits d'auteur

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À propos de l'auteur (2014)

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.

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