Shape of Space

Frank Sottile

In mathematics and science, we often need to think about 
high (3 or more) dimensional objects, called spaces, which 
are hard or impossible to visualize. Besides the question 
of what such objects are or could be, is the problem of 
how can we make sense of such spaces.

The goal of this discussion is to give you an idea of how 
mathematicians manage to make sense of higher-dimensional 
spaces.  We will do this by exploring the simplest spaces, 
and through our explorations, we will begin to see how we 
may tell different spaces apart.  Along the way, we will 
dissect donuts.