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Torus Knot

Torus Knot
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2018-04-30 18:33
Coordinate GeometryParametric EquationGeometric Construction
This example demonstrates the construction of a torus knot. A torus knot is a special kind of knot that lies on a torus. Key mathematical concepts include coordinate geometry and parametric equations. Using commands like CurveCartesian, GCD, and Surface, a torus knot can be constructed. Suitable for high school mathematics education and research.

GeoGebra Commands & Parameters

  1. CurveCartesian(((2 + cos((a * t))) * cos((b * t))), ((2 + cos((a * t))) * sin((b * t))), sin((a * t)), t, 0, (2 * π)) → knoten
  2. GCD(a, b) → g
  3. Surface(((2 + cos(u)) * cos(v)), ((2 + cos(u)) * sin(v)), sin(u), u, 0, (2 * π), v, (-π), π) → Torus

AI Drawing Prompt Reference

Draw a torus knot, which lies on a torus surface. Use parametric equations to draw a specific type of knot where a and b are parameters. First, draw a torus surface, then draw a specific knot path on the surface. Ensure the path covers the torus once and forms a complex closed curve on the surface.
The prompt above was compiled from the original drawing commands and is for reference only.