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The Rabbit's Surface: 3D Geometry and Random Experiments

The Rabbit's Surface: 3D Geometry and Random Experiments
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2020-11-06 17:36
PolygonSolid GeometryProbability & StatisticsTransformationGeometric Construction
① This GeoGebra example constructs a 3D solid called 'The Rabbit's Surface', combining random experiments with geometric transformations to display a complex polyhedron. ② Core mathematical concepts include solid geometry (polyhedra), transformations (rotation, reflection), and probability/statistics (confidence intervals as tagged), along with basic elements like rhombi, cones, and quadrilaterals. ③ Construction highlights: uses GeoGebra commands such as Surface, Point, Mirror, Line, Circle, Sequence, Polygon, Prism, Rotate, and Midpoint; creates multiple objects (points A, B, C, faces face1-face6, etc.) to form a symmetric structure via rotation and mirroring. ④ Suitable for high school and above, useful for exploring 3D geometric modeling, transformations, and stochastic simulations, and as a teaching resource for math labs or demonstrations.

GeoGebra Commands & Parameters

  1. Surface(x(O) + (1.2 * f(u, v)), y(O) + g(u, v), z(O) - (c * h(u, v)), u, 0, (2 * π), v, 0, (2 * π)) → b
  2. Point(zAxis) → A
  3. Mirror(B, zAxis) → B'
  4. Mirror(C, zAxis) → C'
  5. Line(B, B' + (1, 0, -1)) → i
  6. Line(C' + (-1, 0, -1), C) → j
  7. Circle(C, 0.5, j) → e
  8. Mirror(D, zAxis) → D'
  9. Line(D, D') → k
  10. Circle(D, 0.7, k) → p
  11. Point(p) → E
  12. Sequence(Rotate[E, i, k], i, 0, (2 * π), (2 * π / n)) → l1
  13. Polygon(l1) → t1
  14. Prism(t1, 1) → l, F, face5, face2, face6, faceFGHIJ, arête1, arête2, arête3, arête4, arête5, arête6, G, arêteFG, arêteGH, arêteHI, arêteIJ, arêteFJ, arête7, H, I, J, K, face1, face3, face4
  15. Circle(B, 0.5, i) → d
  16. Point(d) → L
  17. Point(e) → M
  18. Rotate(L, m, i) → L'
  19. Midpoint(B, L') → N
  20. Line(N, i) → q
  21. Circle(N, 0.25, d) → r
  22. Rotate(M, (-m), j) → M'
  23. Midpoint(M', C) → P
  24. Line(P, j) → s
  25. Circle(P, 0.25, e) → t
  26. Circle(C, 0.5, j) → c_1
  27. Circle(B, 0.5, i) → o

AI Drawing Prompt Reference

Create a 3D solid called 'The Rabbit's Surface' by combining random experiments and geometric transformations. Start by drawing a surface, then use rotation and mirroring to create multiple faces and edges, forming a symmetric structure. Next, draw several circles and points, and use rotation and mirroring to generate more faces and edges, ultimately creating a complex polyhedron.
The prompt above was compiled from the original drawing commands and is for reference only.