November 4, 2017 – Frank Sottile – “The Shape of Space”
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 activity is to give you an idea of how mathematicians manage to make sense of higher-dimensional spaces, and relate this to the recent proof of the Poincar ́e conjecture that won the Millenium Prize of the Clay Institute. 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.
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