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Measurement [Hardcover]

by Paul Lockhart
4.5 out of 5 stars  See all reviews (26 customer reviews)

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Book Description

October 25, 2012 0674057554 978-0674057555

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.

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Measurement + A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form + The Joy of x: A Guided Tour of Math, from One to Infinity
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Editorial Reviews


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)

About the Author

Paul Lockhart teaches mathematics at Saint Ann’s School in Brooklyn, New York.

Product Details

  • Hardcover: 416 pages
  • Publisher: Belknap Press (October 25, 2012)
  • Language: English
  • ISBN-10: 0674057554
  • ISBN-13: 978-0674057555
  • Product Dimensions: 8.7 x 5.7 x 1.3 inches
  • Shipping Weight: 1.3 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (26 customer reviews)
  • Amazon Best Sellers Rank: #65,958 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
47 of 50 people found the following review helpful
5.0 out of 5 stars An existence proof that math is art. September 14, 2012
Format:Hardcover|Verified Purchase
Lockhart's enthusiasm and humor shows through on every page of this book, as he makes cheerful battle with fundamental ideas. Too often we teach dead & dry facts, and leave creativity as an exercise for the reader, if we mention it at all. Measurement's primary subject is that intuition and creativity, spelling out tricks and tools that creative mathematicians use to cope, and the joy in it that keeps them going:

Keep asking questions! They are more important than answers.

Prove something more than one way. Can you generalize?

Pay attention to symmetry, wherever you find it.

Guess. Then guess again. Get used to being stuck.
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21 of 21 people found the following review helpful
5.0 out of 5 stars Measurement and Then Some October 23, 2012
Format:Hardcover|Verified Purchase
I am now half way through this book and it is one of the best books explaining the process of mathematical thinking that I have ever read. It explains in plain English lots of interesting and basic mathematical theorems, many of them geometrical, without obscuring them in a blizzard of algebra. Even though the author decries depending on diagrams as proofs, there are lots of very clear and helpful hand drawn diagrams which make various concepts clear. Yes, there are algebraic formulas but they are germane to the subjects being discussed and are not inserted just to make the author look good.
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11 of 11 people found the following review helpful
By Garrett
Format:Hardcover|Verified Purchase
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.
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10 of 11 people found the following review helpful
5.0 out of 5 stars The best math book you will ever read! November 28, 2012
By Lhianna
Format:Hardcover|Verified Purchase
If you only ever read one book on mathematics in your life, read this. Paul Lockhart writes so clearly and passionately. (Yes, I used "passion" and "math" together!) He is a brilliant mathematician AND a great writer! This is a very rare combination. He presents math in an intuitive and conceptual way that shows you the beauty of discovery and patterns and symmetry but requires very little calculation or knowledge of the mathematical language. For non-math people this presentation is very accessible and easy to read. He is talking about concepts that are universal. For math-people to presentation style is a reinforcement of why you love math, do math, and a demonstration of how you really think when you are solving a problem. I highly, highly recommend this book!
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30 of 40 people found the following review helpful
2.0 out of 5 stars This book is not meant for beginners. January 3, 2013
Format:Hardcover|Verified Purchase
Paul Lockhart uses a different approach to teaching mathematics. He introduces axioms, then asks questions about possible extrapolations, but does not guide, and does not provide answers which would allow the reader/student to verify their ideas.

E.g., page 29 shows two star-like figures. He asks if I can work out the angles of a regular n-sided polygon. I had some ideas but could not balance them against a solution provided, and thus work out where I went right/wrong. This happened in an even more discouraging manner on page 31, where he asks, again without guidance, What are all symmetrical polyhedra? That's when I stopped reading because I felt inadequate.

Without having been able to remember some of the terms from school, I would not even have been able to know what the latter part of the first topic was about.

This is not meant as a criticism. Students of mathematics may very well appreciate his teaching methodology. I just would like to say that this book was not meant for the likes of me: a person who would like to learn about mathematics from the beginning.
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4 of 4 people found the following review helpful
5.0 out of 5 stars pencil and paper January 12, 2013
Format:Hardcover|Verified Purchase
Read this with a pencil and paper beside you so you can do the problems and draw diagrams for yourself. The book isnt easy. It gives a non-mathematican an insight into how the math guy thinks and its fascinating. How many degrees are there in a pentagon? I loved the book, I'm reading it for the second time.
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3 of 3 people found the following review helpful
Format:Hardcover|Verified Purchase
I will only say this: if I had this book and this teacher in my High School curriculum, I would have majored in math.

I cried tears of awe reading this book. The man is writing poetry with mathematics. Don't think it can be done? Read this book and lament on the fact that you were deprived of this art-form.

If you are a parent, consider providing inspiration for all the hard work in your kids math classes with this book as a guide.

Start reading and enjoy the journey into the jungle where odd creatures behave in all kind of interesting patterns for us to explore!
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2 of 2 people found the following review helpful
Format:Kindle Edition|Verified Purchase
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.
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Most Recent Customer Reviews
5.0 out of 5 stars Measurements
The book arrived early. The text is very interesting. I found it very informative. I found reading this book along side other books with similar topics helpful.
Published 3 months ago by L. Chance
5.0 out of 5 stars Mathematics is beautiful and fun!
This book forced me to use mental muscles I haven't exercised in a long time, but it felt fantastic! Read more
Published 4 months ago by G. Wagner
5.0 out of 5 stars Wonderful, if you're up for the challenge
If you already like math (like me), you'll love this book. I am curious about the reactions of people who are less comfortable with the subject. Read more
Published 4 months ago by Voracious Reader
2.0 out of 5 stars Waste of money.
Lockhart is an arrogant bore. He never misses a chance to tell you what a dunce you are if you are not interested in his subject. Read more
Published 5 months ago by Robert B. Miller
4.0 out of 5 stars Don't be afraid of math
Math is fun and everyone can do it, it just needs as much practice as any other thing that you want to be good at. Read more
Published 7 months ago by Oleg
5.0 out of 5 stars Yup yup yup
If you like Lockhart's "A Mathematician's Lament", you won't be disappointed by this book. It's that simple. Read more
Published 7 months ago by Eric Stucky
3.0 out of 5 stars Too much work.
I have gone through only about a third of the book and have put it aside out of fatigue, though I expect to pick it back up in a month or so. Read more
Published 10 months ago by Robert Pelini
5.0 out of 5 stars A Must Read For All Levels
While I enjoy almost every book about math that I read, Measurement is 1000 steps above the rest. Never before have I had such an intuitive understanding about what math really is. Read more
Published 12 months ago by Devin F
5.0 out of 5 stars A great read. Interesting for everyone!
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. Read more
Published 12 months ago by Francois Leyvraz
5.0 out of 5 stars A new way of seeing
Loved the fresh way of envisioning what doing math really means. Even the math phobic will catch some of the enthusiasm and the beauty.
Published 12 months ago by Foilman
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