In Topology, When Are Two Shapes the Same?
As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent. The post In Topology, When Are Two Shapes the Same? first appeared on Quanta Magazine
Sorting a collection of shapes is child’s play. Circles here, squares there, triangles in their own pile. But if you take the task seriously, there’s a lot more to it. In fact, one of the largest subdisciplines in mathematics — topology — is devoted exactly to this kind of endeavor, and after centuries of concerted effort, mathematicians aren’t even close to finishing.
Originally published in Quanta Abstractions.
