[fizzynut]

Maybe this article is way over my head, but is it not really simple?

If my function to generate a circle is a simple for loop 0 to 2 PI.

Then the inverse of that maps each point on the circle back to a line with points between 0 and 2 PI.

[smoyer]

You're thinking of the inverse of the function. There's also a lot hidden in your function as generating a circle from an angle requires sin and cos functions. These are repeating functions so asin and acos don't result necessarily represent a single angle (e.g. if 1.5pi is returned, does it mean 1.5pi, 3.5pi or 5.5pi). Similarly, if you invert the formula for the unit circle, taking the square-root of the terms results in both positive and negative values.

This article is instead talking about the inverse per the identity a * 1/a = 1.