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Animation Demonstrating Median, Logarithmic Functions, and Fractal Geometry

Animation Demonstrating Median, Logarithmic Functions, and Fractal Geometry
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2017-01-19 03:39
In collections Area, Surface Area, Volume, Cross Section, 3D
This example visually demonstrates the median in data distribution, integrates logarithmic function graphs with fractal geometry, and illustrates the geometric application of mathematical concepts. Core concepts include median, logarithmic function properties, fractal iteration, parametric curve generation, and frequency distribution visualization. GeoGebra commands like Dilate, Segment, Cylinder, Circle, Vector, Translate, and Rotate, along with objects r, h, e, A, B, C, D, j, B', l, a, c, d, b, E, E', f, F, G, G', F', g, i, H, A', A'_1, I, k, A'_2, m, p, q, n, A'_3, s, J, A'_4, u, m', o are used to construct the visualization. Suitable for high school and above mathematics education, covering parametric equations, geometric transformations, and data visualization.

GeoGebra Commands & Parameters

  1. Dilate(B, If[0 < j ≤ 1, 1 - j, 0], A) → B'
  2. Segment(B, B') → l
  3. Cylinder(B, B', r) → a, c, d, b
  4. Dilate(E, If[2 < j ≤ 3, 3 - j, 0], C) → E'
  5. Segment(E, E') → f
  6. Dilate(G, If[1 < j ≤ 2, 2 - j, 0], C) → G'
  7. Dilate(F, If[1 < j ≤ 2, 2 - j, 0], E) → F'
  8. Segment(G, G') → g
  9. Segment(F, F') → i
  10. Dilate(A, If[3 < j ≤ 4, 4 - j, 0], H) → A'
  11. Dilate(A, If[3 < j ≤ 4, 4 - j, 0], D) → A'_1
  12. Circle(A', A'_1, I) → k
  13. Dilate(A, If[4 < j ≤ 5, 5 - j, 0], B) → A'_2
  14. Cylinder(A, A'_2, e) → m, p, q, n
  15. Dilate(G, If[1 < j ≤ 2, 2 - j, 0], A) → A'_3
  16. Segment(G, A'_3) → s
  17. Dilate(A, If[6 < j ≤ 7, 7 - j, 0], B) → A'_4
  18. Vector(A, A'_4) → u
  19. Translate(m, u) → m'
  20. Cylinder(A, A'_4, e) → o, t, c_1, v
  21. Dilate(B, If[7 < j ≤ 8, 8 - j, 0], J) → B'_1
  22. Vector(B, B'_1) → w
  23. Translate(m', w) → m''
  24. Dilate(J, If[8 < j ≤ 9, 9 - j, 0], K) → J'
  25. Segment(J, J') → f_1
  26. Dilate(C, If[9 < j ≤ 10, 10 - j, 0], L) → C'
  27. Vector(C, C') → u_1
  28. Translate(E, u_1) → E'_1
  29. Translate(E', u_1) → E''
  30. Segment(E'_1, E'') → f'
  31. Translate(G, u_1) → G'_1
  32. Translate(G', u_1) → G''
  33. Segment(G'_1, G'') → g'
  34. Translate(F, u_1) → F'_1
  35. Translate(F', u_1) → F''
  36. Segment(F'_1, F'') → i'
  37. Dilate(K, If[9 < j ≤ 10, 10 - j, 0], M) → K'
  38. Dilate(O, If[9 < j ≤ 10, 10 - j, 0], N) → O'
  39. Segment(K, K') → g_1
  40. Segment(O, O') → h_1
  41. Rotate(J, π, Line[(0, 0, 0), (0, 0, 1)]) → J'_1
  42. Rotate(J', π, Line[(0, 0, 0), (0, 0, 1)]) → J''
  43. Segment(J'_1, J'') → i_1
  44. Rotate(G, π, Line[(0, 0, 0), (0, 0, 1)]) → G'_2
  45. Rotate(A'_3, π, Line[(0, 0, 0), (0, 0, 1)]) → P
  46. Segment(G'_2, P) → s'