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Sphere vs Torus Topology

Sphere vs Torus Topology
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2020-03-05 16:31
Solid GeometryGeometric Construction
This example demonstrates a visual comparison between the basic topological spaces of a sphere and a torus. It involves core mathematical concepts such as fundamental forms in topology, homeomorphism, and genus. The construction uses GeoGebra commands like Cartesian curves, points, and surfaces to build and display these geometric shapes, making it suitable for high school students and math enthusiasts studying basic topology and geometric visualization.

GeoGebra Commands & Parameters

  1. CurveCartesian(((((r + d) * cos((q * t))) + (R * (d - 1))) * cos((p * t))), ((((r + d) * cos((q * t))) + (R * (d - 1))) * sin((p * t))), ((-(r + d)) * sin((q * t))), t, 0, α) → c
  2. Point(c) → A
  3. Surface((((R * (d - 1)) + ((r + d) * cos(u))) * cos(v)), (((R * (d - 1)) + ((r + d) * cos(u))) * sin(v)), ((r + d) * sin(u)), u, 0, 6.28319, v, 0, 6.28319) → e