During last year Advent of Code, I ended up discovering a beautiful relation between bounded integer compositions and the generalized Fibonacci sequence. Probably it is an already known relation, but the fact that it popped up in a totally unrelated problem is a remarkable example on how number theory properties may pop up in the most unexpected places.

Because I started a small series about astronomical algorithms and the magic of math in space, I think we need to cover an important prerequisite. In the series, I will talk a lot about ellipses (duh), I will move from the semi-axis majors, to the periapsis, to eccentricity, to ellipse’s center and ellipse’s foci. I am concerned that things can get more complicated than expected if the readers does not know many of the geometric properties of the ellipse. For this reason, I put here this vade mecum on the ellipse geometry. A summary with all the basic points and lengths. A place that I can link everywhere I need to refresh a definition.