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N-Dimensional Spiky Ball Projection Model

N-Dimensional Spiky Ball Projection Model
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2019-02-02 11:41
VectorTrigonometryCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the projection of an N-dimensional sphere onto a 2D plane, resulting in a spiky geometric shape. Key math concepts include vectors, solid geometry, symmetry, logarithmic functions, and stochastic processes. Construction highlights involve GeoGebra commands such as Intersect, Point, Segment, OrthogonalLine, Circle, Midpoint, and Dilate. Suitable for high school and advanced learners exploring high-dimensional geometry and projection transformations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Segment(A, B) → f
  4. Segment(B, D) → g
  5. Segment(D, C) → h
  6. Segment(C, A) → i
  7. Segment(B, C) → j
  8. Segment(D, A) → k
  9. Intersect(j, k) → E
  10. Intersect(j, l) → F
  11. Intersect(j, m) → G
  12. Intersect(k, l) → H
  13. Intersect(k, m) → I
  14. OrthogonalLine(H, g) → n_1
  15. OrthogonalLine(F, g) → p
  16. Intersect(p, g) → J
  17. Intersect(n_1, g) → K
  18. Intersect(n_1, i) → L
  19. Intersect(p, i) → M
  20. Circle(H, K) → c
  21. Circle(G, L) → d
  22. Circle(I, M) → e
  23. Circle(F, J) → q
  24. Intersect(l, f) → O
  25. Intersect(m, f) → P
  26. Intersect(m, h) → Q
  27. Intersect(l, h) → R
  28. Segment(O, R) → s
  29. Segment(Q, P) → t
  30. Midpoint(A, C) → N
  31. Midpoint(B, A) → S
  32. Dilate(H, 1 - 1 / sqrt(n), E) → H'
  33. Circle(E, H') → r
  34. Segment(B, O) → a
  35. Segment(O, S) → b
  36. Segment(S, P) → f_1
  37. Segment(P, A) → g_1
  38. Midpoint(D, C) → U
  39. Segment(S, U) → h_1