Step 1 — What is “topology”?
Topology studies properties that stay the same under continuous deformation (stretching/bending, but no cutting or gluing).
You’ll later connect this to graphs drawn on surfaces.
Step 2 — Orientable Surfaces
Orientable examples: Sphere, Torus.
Cylinder – Orientability Demo
Move the yellow arrow along the cylinder’s center circle.
turns = 0.000
Step 3 — Non-Orientable Surfaces
Non-Orientable examples: Möbius strip, Klein bottle.
Möbius strip – Non-Orientability Demo
Move the yellow arrow along the möbius strip.
turns = 0.000
Step 4 — Homeomorphism + genus
Two shapes are “the same topologically” if there is a homeomorphism between them. Genus counts “handles” (roughly) for orientable surfaces.
Later you’ll use genus ideas to understand embeddings of graphs beyond the plane.