Stereographic projection from North Pole
Let there be a point N on a sphere that can be called North Pole. Let’s consider the projection (called stereographic) that maps to each point P of the sphere that is distinct to N, the intersection Q of the line NP with the tangent plane to the sphere in the South Pole (diametrically opposed to N).
We note that after such a transformation (which is the restriction of an inversion), the image of a circle is transformed into a circle.
The original figure was made by Luigi Tomasi.