Ciro Santilli @cirosantilli 35

We map each point and a small enough neighbourhood of it to ${\mathbb{R}}^n$, so we can talk about the manifold points in terms of coordinates.

Does not require any further structure besides a consistent topological map. Notably, does not require metric nor an addition operation to make a vector space.

Manifolds are cool. Especially differentiable manifolds which we can do calculus on.

A notable example of a Non-Euclidean geometry manifold is the space of generalized coordinates of a Lagrangian. For example, in a problem such as the double pendulum, some of those generalized coordinates could be angles, which wrap around and thus are not euclidean.

When debugging complex software, make sure to keep notes of every interesting find you make in a note file, as you extract it from the integrated development environment or debugger.

Especially if your memory sucks like Ciro's.

This is incredibly helpful in fully understanding and then solving complex bugs.

The length of its cycle.

Bibliography:

There are no stable isotopes.

It is exactly what you'd expect from the name, Waring was watching Netflix with Goldbach, when they suddenly came up with this.