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Ferriswheel: Imagine

Ferriswheel: Imagine
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2021-06-05 15:21
CircleTrigonometryGeometric Construction
This example demonstrates the motion trajectory of a Ferris wheel. It involves the geometric properties of circles and trigonometric functions. Using commands such as Circle, Point, Line, Intersect, Segment, OrthogonalLine, Polygon, Angle, CircleSector, Mirror, and Vector, a dynamic model of the Ferris wheel can be constructed. Suitable for high school mathematics education, particularly in coordinate geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Circle(A, 5) → c
  2. Point(c) → B
  3. Line(A, B) → f
  4. Intersect(c, f, 2) → E
  5. Segment(B, E) → i
  6. Line(T_1, i) → j_1
  7. OrthogonalLine(A, f) → g
  8. Intersect(c, g, 2) → C
  9. Intersect(c, g, 1) → D
  10. Segment(C, D) → h
  11. Point(c) → H
  12. Segment(H, A) → j
  13. Point(Circle[H, 1]) → I
  14. Segment(H, I) → k
  15. Point(Circle[I, 0.5]) → J
  16. Segment(I, J) → l
  17. Point(Circle[I, 0.5]) → K
  18. Segment(I, K) → m
  19. Polygon(K, J, 4) → poly1, n, p, q, r, L, M
  20. Polygon(M, L, 3) → poly2, s, t, a, N
  21. Angle(D, A, H) → α
  22. CircleSector(A, D, H) → d
  23. Point(j) → S
  24. Point(h) → T
  25. Mirror(A, h) → A'
  26. Mirror(U, h) → U'
  27. Mirror(V, h) → V'
  28. Vector(W, Z) → w
  29. Intersect(c, h, 2) → A_1
  30. Segment(A, A_1) → b
  31. Mirror(pic4, h) → pic4'
  32. Line(F_1, i) → f_1
  33. Segment(G_1, F_1) → g_1
  34. Point(f_1) → I_1
  35. Segment(H_1, I_1) → h_1
  36. Point(f_1) → K_1
  37. Segment(J_1, K_1) → i_1
  38. Point(f_1) → L_1
  39. Point(j_1) → N_1
  40. Point(f_1) → O_1
  41. Point(j_1) → M_1
  42. Polygon(L_1, M_1, N_1, O_1) → q1, l_1, m_1, n_1, o_1
  43. Mirror(L_1, h) → P_1
  44. Mirror(M_1, h) → Q_1
  45. Mirror(N_1, h) → R_1
  46. Mirror(O_1, h) → S_1
  47. Polygon(P_1, Q_1, R_1, S_1) → q1', p_1, q_1, r_1, s_1
  48. OrthogonalLine(M_1, j_1) → k_1
  49. OrthogonalLine(N_1, j_1) → t_1
  50. Intersect(f_1, r_1) → U_1
  51. Intersect(f_1, n_1) → V_1
  52. Segment(U_1, V_1) → b_1
  53. Point(j_1) → W_1
  54. OrthogonalLine(W_1, j_1) → a_1
  55. Point(j_1) → Z_1
  56. Polygon(W_1, Z_1, 3) → poly3, c_1, d_1, e_1, A_2
  57. Mirror(poly3, h) → poly3'
  58. Point(c) → B_2
  59. Segment(A, B_2) → e
  60. Point(e) → C_2
  61. Point(j) → D_2
  62. Point(e) → E_2
  63. CircleSector(E_2, C_2, D_2) → c_2

AI Drawing Prompt Reference

Draw a Ferris wheel model: start with a large circle as the wheel, centered at a fixed point. Place a point on the circle to represent a cabin attachment, and draw a radius from the center to this point. Construct a vertical diameter through the center, perpendicular to the initial radius, dividing the circle into upper and lower halves. Add another point on the circle, connect it to the center to form a second radius, and mark the angle between this radius and the vertical diameter. At the cabin attachment point, draw a small circle to represent the cabin, and inside it construct a polygon and a triangle to simulate the cabin structure. Mirror some of these shapes across the vertical diameter to create symmetric cabins. Finally, add a horizontal line below the wheel and draw a polygon to represent the ground support structure, giving the overall appearance of a rotating Ferris wheel.
The prompt above was compiled from the original drawing commands and is for reference only.