# topology
Topology studies the properties of shapes that survive stretching and bending, but not cutting or gluing — a coffee cup and a donut are "the same" because both have exactly one hole. This tag gathers the sims built around that idea: Möbius Strip and Klein Bottle show one-sided and non-orientable surfaces, Torus & Surface Genus and Torus & Genus both explore how genus (hole count) defines a surface's topology, Knot Theory works through invariants and Reidemeister moves for tangled loops, and Brouwer Fixed Point Theorem covers a foundational result about continuous mappings. Parametric Surfaces, Self-Organising Map and Neural Gas round it out with surface generation and topology-preserving neural mapping.
Found: 10 simulations · 0 articles
🧪 Simulations (10)
Facts about this collection
- 10 simulations carry the topology tag; no articles yet.
- Two pairs of sims cover overlapping ground: Torus & Surface Genus with Torus & Genus, and Topology Surfaces with Parametric Surfaces.
- Möbius Strip and Klein Bottle are the two non-orientable surfaces in the set — surfaces with no distinct "inside" or "outside".
- Self-Organising Map and Neural Gas apply topology-preserving mapping to neural-network algorithms rather than pure geometric surfaces.
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