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Finite Torus Circle Network

Finite Torus Circle Network
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2018-04-30 00:19
CircleSequenceGeometric Construction
This example demonstrates the construction of a finite torus circle network. Key mathematical concepts include circles, sequences, and geometric construction. Using GeoGebra commands such as Sequence, Circle, and Intersect, the dynamic generation of the network can be shown. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sequence(Circle[((R * cos(σ + ((k / n * 2) * π))), (R * sin(σ + ((k / n * 2) * π))), 0), r, Vector[(sin(σ + ((k / n * 2) * π)), (-cos(σ + ((k / n * 2) * π))), 0)]], k, 0, n - 1) → QKreise
  2. Circle(Mσ, R, vcNormaleσ) → vcKreis1
  3. Surface(((R + (r * cos(v))) * cos(u)), ((R + (r * cos(v))) * sin(u)), (r * sin(v)), u, 0, (2 * π), v, 0, (2 * π)) → a
  4. Intersect(zAxis, yAxis) → A
  5. Point(zAxis) → B
  6. Line(A, B) → f
  7. Line(A, C) → g
  8. OrthogonalLine(Mσ, vcEbeneσ) → vcNormaleσ_2
  9. Circle(A, Pr, xOyPlane) → t
  10. Point(t) → K
  11. Line(A, K) → m
  12. Zip(Intersect[vcKreis1, kr], kr, QKreise) → L_2
  13. Zip(Circle[f, pkt], pkt, L_2) → LKreise
  14. Circle((-Mσ), R, vcNormaleσ) → vcKreis2
  15. Sequence(Circle[((r * cos(σ + ((k / n * 2) * π))), (r * sin(σ + ((k / n * 2) * π))), 0), R, Vector[((r / R * sin(σ + ((k / n * 2) * π))), (((-r)) / R * cos(σ + ((k / n * 2) * π))), sqrt(R^(2) - r^(2)) / R)]], k, 0, n - 1) → VCNetz1
  16. Sequence(Circle[(((-r) * cos(σ + ((k / n * 2) * π))), ((-r) * sin(σ + ((k / n * 2) * π))), 0), R, Vector[((r / R * sin(σ + ((k / n * 2) * π))), (((-r)) / R * cos(σ + ((k / n * 2) * π))), sqrt(R^(2) - r^(2)) / R)]], k, 0, n - 1) → VCNetz2

AI Drawing Prompt Reference

Draw a finite torus circle network, including a central circle surrounded by concentric circles forming a torus structure. First, draw a central circle, then draw a series of concentric circles around it. Next, draw a line and a circle passing through the center point. Finally, generate a series of circles that intersect with the previous concentric circles, forming a network structure.
The prompt above was compiled from the original drawing commands and is for reference only.