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Negative Math : How Mathematical Rules Can Be Positively Bent

Author: Alberto A Martínez
Publisher: Princeton, NJ : Princeton University Press, [2018] ©2005
Edition/Format:   eBook : Document : Government publication : EnglishView all editions and formats
Summary:
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 more...
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Details

Genre/Form: Electronic books
Material Type: Document, Government publication, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Alberto A Martínez
ISBN: 9780691187822 0691187827
OCLC Number: 1076409492
Language Note: In English.
Description: 1 online resource
Contents: Frontmatter --
Contents --
Figures --
Chapter 1: Introduction --
Chapter 2: The Problem --
Chapter 3: History: Much Ado About Less than Nothing --
Chapter 4: History: Meaningful and Meaningless Expressions --
Chapter 5: History: Making Radically New Mathematics --
Chapter 6: Math Is Rather Flexible --
Chapter 7: Making a Meaningful Math --
Notes --
Further reading --
Acknowledgments --
Index
Responsibility: Alberto A. Martínez.
More information:

Abstract:

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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