MathPlotAI Logo MathPlotAI

Bicycle Geometry Model

Bicycle Geometry Model
Loading the math board and drawing, please wait…
2015-11-18 08:14
VectorFunctionCoordinate GeometryGeometric Construction
In collections Algebra 1|3: Linear Equations
This example dynamically demonstrates geometric relationships related to a bicycle, revealing the intrinsic connection between geometric mean, parabola, scatter plot, and curve sketching. Core concepts include geometric mean, parabola, scatter plot, curve sketching, and median value. The construction utilizes commands and objects such as Segment, Circle, Point, Rotate, Angle, Intersect, Vector, Translate, Line, and Mirror in GeoGebra. Suitable for high school and above learners to understand complex geometric relationships and function graphing.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, A) → c
  4. Segment(A, D) → d
  5. Segment(B, D) → e
  6. Circle(E, 1) → h
  7. Point(h) → G
  8. Rotate(G, 45°, E) → G'
  9. Angle(G, E, G') → α
  10. Rotate(G', 45°, E) → G''
  11. Angle(G', E, G'') → β
  12. Rotate(G'', 45°, E) → G'''
  13. Angle(G'', E, G''') → γ
  14. Rotate(G''', 45°, E) → H
  15. Angle(G''', E, H) → δ
  16. Rotate(H, 45°, E) → H'
  17. Angle(H, E, H') → ε
  18. Rotate(H', 45°, E) → H''
  19. Angle(H', E, H'') → ζ
  20. Rotate(H'', 45°, E) → H'''
  21. Angle(H'', E, H''') → η
  22. Segment(G', H') → g
  23. Segment(G'', H'') → i
  24. Segment(G''', H''') → j
  25. Segment(H, G) → k
  26. Intersect(xAxis, yAxis) → F
  27. Point(xAxis) → I
  28. Vector(F, I) → u
  29. Translate(h, u) → h'
  30. Translate(G'', u) → G'''_1
  31. Translate(H'', u) → H'''_1
  32. Segment(G'''_1, H'''_1) → i'
  33. Translate(G', u) → G''_1
  34. Translate(H', u) → H''_1
  35. Segment(G''_1, H''_1) → g'
  36. Translate(H, u) → H'_1
  37. Translate(G, u) → G'_1
  38. Segment(H'_1, G'_1) → k'
  39. Translate(G''', u) → J
  40. Translate(H''', u) → K
  41. Segment(J, K) → j'
  42. Segment(D, L) → l
  43. Segment(L, M) → m
  44. Point(d) → N
  45. Segment(N, O) → n
  46. Segment(P, Q) → p
  47. Intersect(g, i) → R
  48. Intersect(d, e) → S
  49. Segment(R, S) → q
  50. Point(f) → T
  51. Line(U, V) → r
  52. Mirror(R, r) → R'
  53. Mirror(S, r) → S'
  54. Segment(R', S') → q'
  55. Mirror(C, r) → C'
  56. Mirror(A, r) → A'
  57. Segment(C', A') → c'
  58. Mirror(A, r) → A'_1
  59. Mirror(B, r) → B'
  60. Segment(A'_1, B') → a'
  61. Mirror(B, r) → B'_1
  62. Mirror(C, r) → C'_1
  63. Segment(B'_1, C'_1) → b'
  64. Mirror(A, r) → A'_2
  65. Mirror(B, r) → B'_2
  66. Segment(A'_2, B'_2) → a'_1
  67. Mirror(B, r) → B'_3
  68. Mirror(D, r) → D'
  69. Segment(B'_3, D') → e'
  70. Mirror(D, r) → D'_1
  71. Mirror(L, r) → L'
  72. Segment(D'_1, L') → l'
  73. Mirror(L, r) → L'_1
  74. Mirror(M, r) → M'
  75. Segment(L'_1, M') → m'
  76. Mirror(N, r) → N'
  77. Mirror(O, r) → O'
  78. Segment(N', O') → n'
  79. Mirror(P, r) → P'
  80. Mirror(Q, r) → Q'
  81. Segment(P', Q') → p'
  82. Mirror(A, r) → A'_3
  83. Mirror(D, r) → D'_2
  84. Segment(A'_3, D'_2) → d'
  85. Intersect(a', b') → W
  86. Circle(W, 0.25) → s
  87. Point(s) → Z
  88. Line(Z, b') → t
  89. Point(t) → A_1
  90. Point(t) → B_1
  91. Segment(A_1, B_1) → a_1
  92. Segment(W, Z) → b_1