I have a huge bone to pick with Kuipers.

“We shall distinguish between two perspectives on rotations in the plane, and shall determine the effect which each has on coordinates of points in the plane. The first is rotation of the coordinate frame with respect to fixed points (vectors) in the plane; the second is rotation of points (vectors) with respect to a fixed coordinate frame.”

His writing suffers from the typical things that make an engineer’s / mathematicians writing harder to understand.

Can’t “we” just be clear?

There are two different types of planar rotation that we shall now discuss.

1. A rotation of the actual coordinate frame with respect to fixed points in the plane.
2. A rotation of the points with respect to a fixed coordinate frame.

The way I have written it is at least twice as fast to read, by my estimation. My criticisms are as follows:

– We know points are vectors, no need to slow us down with the parenthesis
– Use paragraphs more wisely. There was a need for a paragraph break as I have demonstrated.
– Removed the entire sentence “We shall determine the effect that each type of rotation has on the coordinates of points in the plane.” because the reader doesn’t care what you’re going to do with them yet. He’ll find out soon enough. Unless he sleeps. Let them have some degree of suspense, Kuipers.

Reading Kuipers’ writing is like trudging through a park with leaden shoes. The things he has to show you are very nice, but its the stifling formality of his writing that holds one back from enjoying the experience.