simple double pendulum and four equilibrium configurations

Question

I have difficulty in understanding the notion of "configuration space" and "toroidal spaces" in the following explanation:

The configuration space of any double pendulum can be represented as the points on the toroidal surface.

Answer 1

To describe the current position (“configuration”) of a double pendulum, it is necessary and sufficient to give two angles (say the angle that each arm makes with the vertical).

The set of such pairs of angles $(\alpha,\beta)$ is called the “configuration space” of the double pendulum.

On the other hand, to describe the location of a point on a Torus, it is also necessary and sufficient to give two angles. So one may say that the configuration space of a double pendulum is the same thing as a torus.