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Measurement
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Review
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 (forthcoming))No matter what mathematical education you had, or didn't have, you will be delighted by this enticing book if you take up Paul Lockhart's invitation to engage in the mathematical sensibility that radiates from its pages, and try your own hand―not only at answering, but even more fruitfully, at formulating questions as you explore the world of mathematics. (Barry Mazur, author of Imagining Numbers (Particularly the Square Root of Minus Fifteen))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 2012-06-15)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 2012-09-01)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 2012-09-20)Prospective readers should rest assured that while aimed at the nonexpert, Lockhart's writing is sophisticated and mathematically modern...In place of the usual boxed and high-lighted formulas and tricks, Measurement offers questions to be pondered. Lockhart invites readers to trade tutorial fake problems about actual objects, which lead students to abhor school mathematics, for real problems about fantastical objects, which lead mathematicians to love math. (Brie Finegold Science 2012-11-09)This book forced me to use mental muscles I haven't exercised in a long time, but it felt fantastic! Paul Lockhart is a mathematics evangelist; his passion for his subject is evident on every page, in every line. Looking at the subject of Measurement, he takes the reader on a journey that covers geometry, algebra, trigonometry, and on through differential calculus. He has a conversational tone and self-deprecating humor that sets the reader at ease. He understands that many people have been turned off of mathematics. His attitude is playful and joyous...Math is usually taught in such a compartmentalized way that it loses any meaning or coherence, and certainly any sense of wonder or beauty, but Measurement restores the connection. Paul Lockhart feels that math is the most beautiful, abstract and pure art form, and that it is actually fun! By the end of the book, you come to agree with him. (Gretchen Wagner Sacramento Book Review 2012-12-07)There are many books available these days on what mathematicians do, and this is one of the best...Lockhart's approach is fresh and effective. (C. A. Gorini Choice 2013-02-01)
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About the Author
Paul Lockhart teaches mathematics at Saint Ann’s School in Brooklyn, New York.
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Product details
Hardcover: 416 pages
Publisher: Belknap Press; 8/26/12 edition (September 25, 2012)
Language: English
ISBN-10: 0674057554
ISBN-13: 978-0674057555
Product Dimensions:
6 x 1.5 x 8.5 inches
Shipping Weight: 1.3 pounds
Average Customer Review:
4.3 out of 5 stars
49 customer reviews
Amazon Best Sellers Rank:
#681,269 in Books (See Top 100 in Books)
This is a great math book even for people who don't think they are good at math. When I watched the video of this guy talking about the subject I thought I would give it a try. The book is great because the author breaks down the subject into simple concepts that even I could understand. So far I have only read the first chapter. The book discusses the deep philosophical thoughts in math, for example what is a proof?. The first chapter discusses geometry. I recommend this book to any one who want to develop an love for the subject.
Mr. Lockhart has previously written (A Mathematician's Lament) about the joyless methods that were used to teach most of us mathematics. Fortunately I was one who found the joy behind both the practical significance of arithmetic (yes the bank needs to know the exact balance of your account even if you don't care to figure it out) and the memorization of tables; now called math facts (yes, even musicians need to practice scales and train their fingers if they wish to make music, not just appreciate it).If you already know how joyful and remarkable mathematics can be, Mr. Lockhart writes in a way that is easy to read and offers many examples of familiar problems and solves them in a way that emphasizes the elegance and beauty of both the problem and its solution.If you wonder WHY some of us KNOW that mathematics is elegant and beautiful and wish to share that joy, give the book a whirl. You don't need to know more about mathematics than basic arithmetic. As long as you know that algebra and geometry exist; expertise is not required, you will do fine. However as easy as it is to read, be warned that sometimes the mathematics and logic will appear so clearly as if by magic and other times your brain will be challenged and you may struggle mentally as mightily as a women struggles physically (and mentally) to give birth. Whether the struggle is worth it is entirely up to you and fortunately for you, unlike the woman who cannot undo her pregnancy if she finds the struggle to give birth too difficult, you can just give up and read on to the next problem and hope it is easier. There are many, many problems to solve in the book.
I only read the first couple chapters. This book is for when you have time/mental space to devote to study, as a student of the subject. You can do it in small amounts, recreationally, but for the average layperson like myself, this book involves intense mathematical reasoning. I mean, it welcomes everyone! With the same elegance, simplicity and conversational writing that we loved in A Mathematician's Lament. From the first page, you are captivated and wanting more. This is a must-buy for the bookshelf, to have on hand when the mood strikes.
There's a map of how the universe works, and mathematics is the engine that scientists have chosen to generate that map. Lockhart never gets too far from that map, though his examples are often abstract in appearance - at first. I'm going to see that my grand-daughters (who are struggling with math and wondering what it will do for them in a Common Core age) will be exposed (by me, naturally...) to Lockhart's way of explaining how mathematicians do their thing - or at least the ones he claims to know.
The art of mathematics is the real subject of this book--and its treasure. Paul Lockhart reveals that with geometric forms and the numerical relationships to be unlocked in them. He caused me to see the beauty and complexity of the mathematic possibilities--and the perplexity and difficulty he delightfully endures discovering methods and formulas to calculate those relationships. The brain wrenching puzzles he delights in solving are the penchant of a mathematician, and far beyond the simple arithmetic I learned as a teen. But reading about his art now gave me a view of mathematics that I needed then, but was hidden to me, when as a teenager I turned away those subjects intimidated. Had I known about the art of it, I might have ventured into Paul's world of numerical wonders.
A wonderful book! It shows clearly the beauty of mathematics at a quite elementary level. The author goes to great lengths to show what is interesting about Mathematics. It is not the complicated formulae, or the algebra, but great, simple, utterly convincing ideas. If the reader is willing to think hard while reading, he/she will be rewarded by many stunning results presented in a completely straightforward manner. The first part, probably the one that best achieves its stated purpose, deals only with geometry. Since the basics objects of geometry (straight lines, circles, angles...) are familiar to anybody, it is really possible to prove beautiful results without using any of the apparatus, such as algebra and calculus, which many people find difficult. The second part is an attempt to introduce algebra and calculus in a very simple and well motivated way. Since I already know the material quite well, I cannot really say whether the attempt actually succeeds, but I certainly found the presentation very striking and quite engrossing.
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