Geometry // Domain_04
TOPOLOGY
Rubber Sheet Geometry. Deformation & Connectivity.
Homeomorphism
In Topology, two shapes are the same if you can stretch, squeeze, and bend one into the other without tearing or gluing.
A Donut is the same as a Coffee Cup because they both have exactly one hole.
Stretching Allowed
No Tearing
Continuous Deformation
Surface Classification
0
Sphere
Genus 0
No holes. Includes cubes, tetrahedrons, and plates. If you inflate them, they all become balls.
1
Torus
Genus 1
One hole. Donuts, coffee cups, and wedding rings. You cannot shrink a loop around the hole to a point.
2
Double Torus
Genus 2
Two holes. Like a figure-8 pretzel. The complexity of possible loops increases exponentially.
Non-Orientable
The Möbius Strip
A surface with only one side and one edge. If you walk along it, you will eventually return to your starting point, but upside down.
Trace the Path
Klein Bottle →