SC 2015 Semilab: Introduction to Topology: How to drink coffee from a donut, and why life in 2 dimensions can't exist.

by Tatiana Portnaya

Topology is a very important branch of mathematics, and is the "nemesis" of geometry. In geometry, shapes are defined by the lengths, angles, etc. In contrast, for a "Topologist", triangles, trapezoids and circles are the same object...but a "figure 8" different. At this semilab, we will strip all distractions from everyday objects, and focus on just a few properties such as the number of holes, "inside" and "outside", clockwise/counterclockwise. This will allow us to discover many applications of topology through continuous deformations, and figure out things about objects quickly that for a "Geometrist" would be very difficult.

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