The author makes the point that turns allow for exact representation of many commonly used angles, but with binary floating point, many common angles (1/6 of a turn, for example) are inexact.

This could be addressed by using a whole number other than 1 to represent a turn ... one that is a multiple of 3 (or 3x3) and 5, and while we're at it, 2 (or 2x2x2), so most commonly-used angles are whole numbers! That gives us 360 as the value representing a whole turn.