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Animation 165: Geometric Transformations and Continuity Demo

Animation 165: Geometric Transformations and Continuity Demo
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2017-01-18 06:04
TrigonometrySolid GeometryProbability & StatisticsTransformationGeometric Construction
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This example demonstrates the relationship between geometric transformations of a cuboid and the normal distribution through animation. Core math concepts include continuity, cuboid, geometric transformations, normal distribution, and median value. It uses commands like Circle, Segment, Point, Intersect, Polygon, Dilate, Angle, Rotate in GeoGebra for construction, suitable for high school students and math enthusiasts learning geometric transformations and probability statistics.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Segment(A, B) → f
  3. Circle(B, f) → d
  4. Point(d) → C
  5. Circle(C, f) → e
  6. Segment(B, C) → g
  7. Point(e) → D
  8. Segment(C, D) → h
  9. Circle(D, f) → k
  10. Intersect(c, k, 1) → E
  11. Polygon(A, B, C, D, E) → poly1, a, b, c_1, d_1, e_1
  12. Segment(A, B) → i
  13. Segment(B, C) → j
  14. Segment(C, D) → l
  15. Segment(D, E) → m
  16. Segment(E, A) → n
  17. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], A) → A'
  18. Segment(B, A') → p
  19. Angle(B, A, E) → α
  20. Angle(A, E, D) → β
  21. Angle(E, D, C) → γ
  22. Angle(D, C, B) → δ
  23. Rotate(B, If[1 < o ≤ 2, ((o - 1) * α), α], A) → B'
  24. Rotate(A', If[1 < o ≤ 2, ((o - 1) * α), α], A) → A''
  25. Segment(B', A'') → p'
  26. Rotate(B', If[2 < o ≤ 3, ((o - 2) * β), β], E) → B''
  27. Rotate(A'', If[2 < o ≤ 3, ((o - 2) * β), β], E) → A'''
  28. Segment(B'', A''') → p''
  29. Rotate(B'', If[3 < o ≤ 4, ((o - 3) * γ), γ], D) → B'''
  30. Rotate(A''', If[3 < o ≤ 4, ((o - 3) * γ), γ], D) → F
  31. Segment(B''', F) → p'''
  32. Rotate(B''', If[4 < o ≤ 5, ((o - 4) * δ), δ], C) → G
  33. Rotate(F, If[4 < o ≤ 5, ((o - 4) * δ), δ], C) → F'
  34. Segment(G, F') → q