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on September 14, 2012
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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on October 23, 2012
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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on November 13, 2012
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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on February 25, 2013
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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on November 28, 2012
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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on January 12, 2013
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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on July 24, 2013
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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on January 3, 2013
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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on July 12, 2016
All numbers _ all shapes and sizes _ time and space _ all are connected. Such relationships are everywhere at all times. Thus, patterns are created; some tangible; some not so much. Deciphering these connections, determining the general pattern, becomes the task of the mathematician. I discovered this concept when, some sixty plus years ago, my 6th grad teacher spent an entire morning detailing how common shapes (squares, rectangles, triangles, trapezoids, etc) were derived from one another by deriving their area formulas from a single equation. They were, in this way, shown to be all one and the same but simply stretched out into this or that shape or, geometrically, as viewed from various perspectives. This revelation came as a major eye-opener for me and changed my entire direction in life's pursuits. (Now that they 'teach to the test,' such revelations are generally and sadly absent from today's classrooms). Measurement as discussed in this wonderful book is not measurement in the classic sense of the word. In other words, one will not find a ruler with the sq rt of 2 on it. In this case, measurement represents a systematic assignment of a value to some subset of a system such that comparisons can be made between the elements of the system and between systems and (consequently) mathematical links between seemingly unrelated areas of the mathematical universe. The book is divided into two main sections. The first concerns what we used to refer to as "Synthetic" geometry. That is: to build up knowledge based on first principles. Numbers as such are conspicuously absent. Only pure reason is utilized much as it was in "ancient" times. In this manner, the author puts us directly into the mind of the mathematician; solving the riddle with nothing more the the one or two elements at hand. The ancient Greeks did this not so much because they lacked the so-called "brilliance" of the modern day Human but by choice, neglecting the more analytical approach. As such synthesis was more in keeping with their predominantly aesthetic view of nature. The second section adds the coordinate system (ala Descartes), thereby providing an Analytical approach and somewhat greater precision to the solutions (and consequently providing some deeper insights into the connections at large!). This is not a How-To book. It is an argument that is detailed and punctuated with an excellent choice of problems to challenge one's perspective. If the reader has no mathematical background, this book will pose a major challenge for sure. Additionally, if the reader lacks a fair background in both Trig. and The Calculus, this too will make forward motion along the line of comprehension rather tedious. That is not to say that one cannot follow the argument but it will be, at minimum, tough going, especially when the author reveals such links as between the Hyperbolic Integral area (dA = dw/w) and the Natural Log (ln). Calculus is, of course, simply a short cut to solving an infinite series of calculations in a few steps. It's use was initially implemented during the so-called "Kerala" Period in Southern India several centuries before Newton or Leibniz, both of whom systemized the science. It's rules are few but rather messy and often difficult (if not impossible) to apply without extensive practice and a good visual sense. Trig is stymied by its extensive use of the ever so transcendental Sin and Cos, etc. and also requires some fairly able visuals. The ability to convert from the geometric to algebraic represents a major breakthrough in extending Mathematics into further realms of exploration and therefore lends a helping hand to those less able to follow the visual signs so to speak. Again, 'measurement' represents only one area of the whole of Mathematics but this book will give anyone who wishes to tread through the mesmerizing tangle of Mathematical mystery an excellent sense of the Mathematical mind.
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on September 9, 2013
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. These seem to be Lockhart's main messages and the book wraps them into more than 50 comprehensive sections. The sections combine explanations and plenty of illustrations with questions (or homework) for the reader, so the reader should expect some time away from the book thinking about the problems and maybe discover their own questions and answers.

There is a lot of fun and entertainment in these some 300 pages, but there are also (maybe naturally) many things that could have been improved. Lockhart is a mathematician and he repeatedly points out that this profession is completely unconnected from the physical world. To make this even clearer, all the sketches in the book are what looks like hand-copied versions of computer printouts - imperfect representations of the ideal object one has in mind.

Almost from the very first page, though, any units are removed from the discussion so we deal with numbers only. But instead of simply referring to meters , inches, degrees or whatever unit you want to use, in the following we are constantly reminded of arbitrary "units of length" and others. In the same way, the book moves from measurement to motion by introducing time - which is then again simply replaced by (or reduced to) an arbitrary dimension similar to length. All that would have been a little easier to swallow if the title of the book had been "geometry" instead of "measurement." Maybe the better approach is to not try to force the reader to decouple the sketches (i.e. the real world) from the objects in mind.

Also it is not quite clear who this book is aiming at. Although it starts out with very simple ideas, it is probably not intended as a replacement for a basic course in geometry. While the topics pick up speed pretty soon, the style almost moves in the opposite direction. And I would rather let the reader discover the beauty of the subject herself instead of repeatedly interrupting the text with joyous exclamations by the author.

To sum it up, this is still a fun book with an almost honorable purpose. While there were things that I really didn't like, they probably won't interrupt other people's enjoyment of the book. So give it a try.
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