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4D Frame Catapult

4D Frame Catapult
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2016-08-24 06:16
CircleVectorSolid GeometryProbability & StatisticsMatrix
This example demonstrates a mathematical model of a 4D frame catapult, showcasing spatial geometric transformations through dynamic interactions. It involves core concepts like circles, stochastic processes, matrix operations, special points, and derivatives. Construction utilizes GeoGebra commands and objects such as points, segments, orthogonal planes, lines, circles, intersections, vectors, translations, rotations, etc. Suitable for high school and above learners to understand the integration of spatial geometry and linear algebra.

GeoGebra Commands & Parameters

  1. Point(zAxis) → A
  2. Segment(O_1, PointIn[Sphere[O_1, 6]]) → b_5
  3. OrthogonalPlane(A, zAxis) → a_1
  4. OrthogonalLine(O_1, b_5, a_1) → c_5
  5. OrthogonalLine(O_1, a_1) → e_5
  6. Circle(A, (4 * a), e_5) → p_1
  7. Intersect(c_5, p_1) → U, V
  8. Point(Circle[A, (5 * a), a_1]) → P
  9. Segment(A, P) → k_1
  10. Circle(A, (3 * a), k_1) → e_1
  11. Intersect(e_5, e_1) → S, T
  12. Circle(A, (10 * a), a_1) → d_1
  13. Intersect(c_5, d_1) → Q, R
  14. OrthogonalPlane(B, zAxis) → b
  15. OrthogonalLine(N_1, b_5, a_1) → d_5
  16. Segment(P_1, O_1) → f_6
  17. OrthogonalLine(P_1, c_5, a_1) → g_6
  18. Intersect(d_5, g_6) → R_1
  19. Segment(R_1, P_1) → h_6
  20. Segment(R_1, N_1) → i_6
  21. OrthogonalLine(Q_1, c_5, a_1) → j_6
  22. Intersect(d_5, j_6) → S_1
  23. Intersect(e_5, b) → T_1
  24. Vector(O_1, T_1) → u_1
  25. Translate(R_1, u_1) → U_1
  26. Translate(N_1, u_1) → W_1
  27. Translate(P_1, u_1) → V_1
  28. Segment(W_1, T_1) → i_1
  29. Segment(U_1, W_1) → k_6
  30. Segment(U_1, V_1) → l_6
  31. Segment(V_1, T_1) → m_6
  32. Segment(V_1, P_1) → n_6
  33. Segment(U_1, R_1) → p_6
  34. Segment(O_1, Q_1) → q_6
  35. Segment(N_1, S_1) → r_6
  36. Segment(S_1, Q_1) → s_6
  37. Segment(T_1, Q_1) → h_2
  38. Segment(W_1, S_1) → l_2
  39. Circle(T_1, m_6, i_1) → e
  40. Intersect(e_5, e) → D, E
  41. Segment(V_1, D) → n
  42. Line(U_1, n) → p
  43. Line(D, l_6) → q
  44. Intersect(p, q) → K
  45. Segment(K, D) → r
  46. Segment(U_1, K) → s
  47. Segment(B, A) → t
  48. Midpoint(i_1) → L
  49. Segment(D, B) → f_1
  50. Segment(K, W_1) → g_1
  51. Segment(W_1, N_1) → f
  52. Circle(L, f_1, i_1) → c
  53. Circle(L, (3 * a), i_1) → d
  54. Midpoint(m_6) → F
  55. Circle(l_6, F) → h
  56. Intersect(n, h) → G,
  57. Line(G, l_6) → i
  58. Intersect(i, s) → H
  59. Segment(H, G) → j
  60. Midpoint(j) → I
  61. Segment(I, L) → k
  62. Rotate(I, (-(135°)), L, c) → I'
  63. Angle(I', L, I, c) → α
  64. Segment(L, I') → l
  65. Intersect(l, d, 1) → C
  66. Line(L, f_1) → g
  67. Intersect(g, d, 2) → J
  68. Rotate(J, (-(135°)), L, d) → J'
  69. Angle(J', L, J, d) → β
  70. CircleArc(L, J', C, d) → c_1
  71. Point(c_1) → M
  72. Segment(M, L) → m
  73. Rotate(M, 135°, L, d) → M'
  74. Angle(M, L, M', d) → γ
  75. Ray(L, M') → h_1
  76. Intersect(h_1, c) → N, O
  77. Segment(N, L) → j_1
  78. Line(N, j) → l_1
  79. Plane(h_1, l_1) → o
  80. Circle(N, (5 * a), o) → q_1
  81. Intersect(h_1, q_1) → Z, A_1
  82. OrthogonalLine(Z, o) → n_1
  83. Sphere(Z, (sqrt(2) * a / 2)) → u
  84. Intersect(n_1, u) → W, B_1
  85. Plane(B_1, o) → v
  86. Line(B_1, l_1) → m_1
  87. Line(B_1, h_1) → r_1
  88. Circle(B_1, (1.5 * a), v) → s_1
  89. Circle(B_1, (2.5 * a), v) → t_1
  90. Intersect(m_1, t_1) → C_1, D_1
  91. Intersect(r_1, s_1) → E_1, F_1
  92. Line(E_1, m_1) → b_1
  93. Line(F_1, m_1) → f_2
  94. Line(D_1, r_1) → g_2
  95. Line(C_1, r_1) → i_2
  96. Intersect(b_1, g_2) → H_1
  97. Intersect(b_1, i_2) → I_1
  98. Intersect(f_2, g_2) → J_1
  99. Intersect(i_2, f_2) → K_1
  100. Segment(H_1, I_1) → j_2
  101. Segment(I_1, K_1) → k_2
  102. Segment(K_1, J_1) → m_2
  103. Segment(J_1, H_1) → n_2
  104. Segment(H_1, Z) → p_2
  105. Segment(Z, K_1) → q_2
  106. Segment(Z, J_1) → r_2
  107. Segment(Z, I_1) → s_2
  108. Segment(J_1, N) → t_2
  109. Segment(Z, N) → a_2
  110. Segment(K_1, N) → b_2

AI Drawing Prompt Reference

Draw a 4D frame catapult model, including a central point O1, and construct a series of circles and lines around it, generating complex geometric structures through rotations and translations. Start by creating a plane A perpendicular to the Z-axis, then build a series of circles and lines on this plane, using intersections and rotations to generate more geometric elements, ultimately forming a complex 4D frame structure.
The prompt above was compiled from the original drawing commands and is for reference only.