Measurement by Paul Lockhart, ISBN-13: 978-0674284388
[PDF eBook eTextbook]
- Publisher: Belknap Press: An Imprint of Harvard University Press; Reprint edition (May 12, 2014)
- Language: English
- 416 pages
- ISBN-10: 0674284380
- ISBN-13: 978-0674284388
For seven years, Paul Lockhart’s A Mathematician’s Lament enjoyed a samizdat-style popularity in the mathematics underground, before demand prompted its 2009 publication to even wider applause and debate. An impassioned critique of K–12 mathematics education, it outlined how we shortchange students by introducing them to math the wrong way. Here Lockhart offers the positive side of the math education story by showing us how math should be done. Measurement offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living.
In conversational prose that conveys his passion for the subject, Lockhart makes mathematics accessible without oversimplifying. He makes no more attempt to hide the challenge of mathematics than he does to shield us from its beautiful intensity. Favoring plain English and pictures over jargon and formulas, he succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable. His elegant discussion of mathematical reasoning and themes in classical geometry offers proof of his conviction that mathematics illuminates art as much as science.
Lockhart leads us into a universe where beautiful designs and patterns float through our minds and do surprising, miraculous things. As we turn our thoughts to symmetry, circles, cylinders, and cones, we begin to see that almost anyone can “do the math” in a way that brings emotional and aesthetic rewards. Measurement is an invitation to summon curiosity, courage, and creativity in order to experience firsthand the playful excitement of mathematical work.
Table of Contents:
Reality and Imagination 1
On Problems 5
Part One: Size and Shape 21
In which we begin our investigation of abstract geometrical figures.
Symmetrical tiling and angle measurement. Scaling and proportion.
Length, area, and volume. The method of exhaustion and its
consequences. Polygons and trigonometry. Conic sections and projective
geometry. Mechanical curves.
Part Two: Time and Space 199
Containing some thoughts on mathematical motion. Coordinate systems
and dimension. Motion as a numerical relationship. Vector representation
and mechanical relativity. The measurement of velocity. The differential
calculus and its myriad uses. Some final words of encouragement to the
reader.
Acknowledgments 399
Index 401
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