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Measurement

Measurement

23692891
2423 руб.
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Описание
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. Content: Reality and Imagination On Problems Part One: Size and Shape 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 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 Index

"This invitation to tackle mathematical questions is infused with the joys of the rarefied reality of maths. Paul Lockhart largely avoids complex formulae and the wilder shores of jargon, opting instead for simple geometric drawings, lucid instructions and honest warnings about the hurdles. Covering size, shape, space and time, Lockhart, a maths teacher, gets through scores of problems, from showing that a cone in a hemisphere occupies half the volume to determining the size of the largest circle that can sit at the bottom of a parabola. Elegant, amusing and challenging" – Nature "Lockhart presents math as an art and argues that just as there is no systematic way to create beautiful and meaningful art, there is also no method for producing beautiful and meaningful mathematical arguments. Doing mathematics, according to Lockhart, is to make a discovery (by, say, physical objects like string or rubber bands) and then to explain it in the simplest and most elegant way possible. Using illustrations of various shapes and mathematical formulas, he leads readers through several problems step by step, encouraging them to collaborate with others in working through the problem. Measuring, for example, is relative because it involves comparing the object being measured to another object. Measurement is only one of the many rivers in the 'vast, ever-expanding jungle' of mathematics, which for Lockhart satisfies our need to find patterns as well as our curiosity... His playful and ingenious approach not only takes the fear out of math but also elegantly illustrates that universe and the joy he finds in it" – Publishers Weekly "Lockhart is famous in the math world for a 2002 essay about the state of mathematics teaching. He described it as akin to teaching music by forcing children to transcribe notation without ever touching an instrument or singing. 'Measurement' is his attempt to change the equation: a conversational book about mathematics as an art that invites the reader to join in the fun. Sounding every bit the teacher whose love for his subject is infectious, he guides us through exercises in geometry and calculus – giving information and hints along the way while always encouraging us to ask, and answer, 'Why?' Lockhart does not try to make math seem easy; instead he wants his readers to understand that the difficulty brings rewards" – Evelyn Lamb, Scientific American "The book is a love song and a philosophical manifesto about the pleasures and frustrations, but mainly the pleasures, of doing math" – Steven Strogatz, New York Times contributor and author of "The Joy of X: A Guided Tour of Math, from One to Infinity" "No matter wh