How can a doughnut be equivalent to a mug?

CHAPTERS:
00:00 - Turning a Mug into a Doughnut
01:30 - Geometry vs. Topology
02:05 - Review on Polyhedra
02:58 - Euler Characteristic of a Sphere
04:07 - Euler Characteristic of a Torus
04:51 - Euler Characteristic Formula given no. of Holes
05:10 - A Homeomorphism Puzzle
05:42 - Puzzle Solution
06:54 - Topology Complexity Iceberg
07:07 - Closing

Previous Video on Möbius Strip and Klein Bottle:    • Paradox of the Möbius Strip and Klein...  

Patreon:   / andrewscampfire  

Visit https://brilliant.org/AndrewsCampfire/ to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription.

#SoME2
This video is sponsored by Brilliant.