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Simulation of Minimal Surface of Soap in a Cube

Simulation of Minimal Surface of Soap in a Cube
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2015-09-04 16:49
VectorSolid GeometryGeometric Construction
This example simulates the minimal surface of soap in a cube. Key mathematical concepts include surface, vector, and geometric construction. Using GeoGebra commands such as Segment and Polygon, a geometric model of the cube and its surface is constructed. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Segment(A_0, A_1) → a_0
  2. Segment(A_2, A_1) → a_1
  3. Segment(A_2, A_3) → a_2
  4. Segment(A_0, A_3) → a_3
  5. Segment(A_7, A_3) → a_4
  6. Segment(A_2, A_6) → a_5
  7. Segment(A_5, A_1) → a_6
  8. Segment(A_0, A_4) → a_7
  9. Segment(A_7, A_4) → a_8
  10. Segment(A_7, A_6) → a_9
  11. Segment(A_5, A_6) → a_a
  12. Segment(A_5, A_4) → a_b
  13. Polygon(S_1, S_2, S_3, S_4) → poly1, s_1, s_2, s_3, s_4
  14. Polygon(A_2, A_3, S_2) → poly2, s_5, a_{10}, a_{11}
  15. Polygon(A_0, A_1, S_1) → poly3, s_6, a_{12}, a_{13}
  16. Polygon(A_6, A_7, S_3) → poly4, s_7, a_{14}, a_{15}
  17. Polygon(A_5, A_4, S_4) → poly5, s_9, a_{18}, a_{19}
  18. Polygon(S_1, S_2, A_2, A_1) → polya, b, c, d, e
  19. Polygon(A_0, A_3, S_2, S_1) → polyb, a_{16}, a_{17}, s_8, s_{10}
  20. Polygon(A_5, A_6, S_3, S_4) → polyc, a_{20}, a_{21}, s_{11}, s_{12}
  21. Polygon(A_4, A_7, S_3, S_4) → polyd, a_{22}, a_{23}, s_{13}, s_{14}
  22. Polygon(A_2, A_6, S_3, S_2) → polye, a_{24}, a_{25}, s_{15}, s_{16}
  23. Polygon(A_3, A_7, S_3, S_2) → polyf, a_{26}, a_{27}, s_{17}, s_{18}
  24. Polygon(A_0, A_4, S_4, S_1) → polyg, a_{28}, a_{29}, s_{19}, s_{20}
  25. Polygon(A_1, A_5, S_4, S_1) → polyh, a_{30}, a_{31}, s_{21}, s_{22}

AI Drawing Prompt Reference

Draw a cube with its eight vertices forming a 3D wireframe. Inside the cube, choose four points on four edges to form an inscribed quadrilateral. Using this quadrilateral as the top face, connect its vertices to the cube's vertices to create multiple triangular and quadrilateral facets, simulating a soap film minimal surface. Construction order: first draw the cube's twelve edges, then define the four interior points, then connect these points to the cube's vertices to form six side faces and the top face, resulting in a polyhedral approximation of the minimal surface.
The prompt above was compiled from the original drawing commands and is for reference only.