After a line, a circle is the simplest example of a topological manifold. Topology ignores bending, so a small piece of a circle is treated the same as a small piece of a line. Considering, for instance, the top part of the unit circle, … See more

Informally, a manifold is a space that is "modeled on" Euclidean space.
There are many different kinds of manifolds. In geometry and topology, all manifolds are topological manifolds, possibly wit… See more

The spherical Earth is navigated using flat maps or charts, collected in an atlas. Similarly, a manifold can be described using mathematical maps, called coordinate charts, collected in a mathematical atlas. It is not gene… See more