Measurement by Paul Lockhart - A review
A few weeks ago I discovered somewhat serendipitously the book “Measurement” by Paul Lockhart. Even though I haven’t finished it yet I want to share some of my thoughts on this excellent book.
The Joy of Mathematics
If you’ve ever taken a maths class (high school or undergrad level), the way it’s usually thought is “Here is this theorem, here is the proof on why it’s true. Here you have some exercises to apply this new theorem”.
This approach can be fine, and you might have ended up liking mathematics despite it. But it’s missing a sense of wonder, of organic growth. Why did someone decide to prove that particular theorem? What problems was he trying to solve? How did he come up with that, and how did he work on writing a proof? We usually study the start, and the end, but nothing in the middle, or what brought us to that start in the first place.
That’s what Paul Lockhart is trying to convey in his book.
For example, on the first few pages we see the following idea. Draw some triangles. Join each vertex with the midpoint of the oposite side. It seems that those three segments always meet at one point, for every triangle. Is that the case? Why? What’s the distance from vertex to intersection point, and from intersection point to side?
You probably recall from your elementary math classes that this point is called barycenter, and you might also recall that the distance AP is 2/3 of AA’, and PA’ is 1/3 of AA’. The thing is, I was taught this as a fact. I was never impressed by why these lines always intersect at one point (instead of three), or thought too much about it.
Paul Lockhart tries to share this sense of wonder with you, and in doing so he doesn’t provide any answers, only questions. And it’s on you to work on them.
I’m slowly advancing through the book. Reading some pages, thinking about the problems, coming up with new questions, advancing…You are not going to learn complex calculus from this book, but soo far it’s been a very fun journey for me. I recommend it.