# Measurement

Paul Lockhart
Pages: 416
https://www.jstor.org/stable/j.ctt2jbt0k

1. Front Matter
(pp. [i]-[vi])
(pp. [vii]-[viii])
3. REALITY AND IMAGINATION
(pp. 1-4)

There are many realities out there. There is, of course, the physical reality we find ourselves in. Then there are those imaginary universes that resemble physical reality very closely, such as the one where everything is exactly the same except I didn’t pee in my pants in fifth grade, or the one where that beautiful dark-haired girl on the bus turned to me and we started talking and ended up falling in love. There are plenty of those kinds of imaginary realities, believe me. But that’s neither here nor there.

I want to talk about a different sort of place....

4. ON PROBLEMS
(pp. 5-20)

What is a math problem? To a mathematician, a problem is a probe—a test of mathematical reality to see how it behaves. It is our way of “poking it with a stick” and seeing what happens. We have a piece of mathematical reality, which may be a configuration of shapes, a number pattern, or what have you, and we want to understand what makes it tick: What does it do and why does it do it? So we poke it—only not with our hands and not with a stick. We have to poke it with our minds.

As...

5. PART ONE SIZE AND SHAPE
(pp. 21-198)

Here is a nice pattern.

Let me tell you why I find this kind of thing so attractive. First of all, it involves some of my favorite shapes.

I like these shapes because they are simple and symmetrical. Shapes like these that are made of straight lines are called polygons (Greek for “many corners”). A polygon with all its sides the same length and all its angles equal is called regular. So I guess what I’m saying is, I like regular polygons.

Another reason why the design is appealing is that the pieces fit together so nicely. There are no...

6. PART TWO TIME AND SPACE
(pp. 199-398)

What is motion? What exactly do we mean when we say that something is moving? We mean that as time goes by its position changes. When something moves, where it is depends on when it is, and the precise way that where depends on when is what makes the motion what it is. In other words, motion is a relationship between time and space.

In order to describe and measure motions, then, we’ll need to be able to tell where something is—to record the position of an object and to know at what time that position occurred.

Needless to...

7. ACKNOWLEDGMENTS
(pp. 399-400)
8. INDEX
(pp. 401-407)