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Rotating Ballerina Music Box

Rotating Ballerina Music Box
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2022-06-30 23:35
Solid GeometryTransformationGeometric Construction
This example demonstrates a rotating ballerina music box. It involves core mathematical concepts such as rotation and solid geometry. Using commands like Polygon, Prism, Mirror, Line, Rotate, Centroid, OrthogonalLine, Point, Cylinder, Intersect, Cone, Sphere, Midpoint, Ray, Segment, a dynamic rotating ballerina model can be constructed. Suitable for high school or university solid geometry and geometric transformations courses.

GeoGebra Commands & Parameters

  1. Polygon(C, G, H, B) → q1, c, g, h, b
  2. Polygon(C, G, F, D) → q2, c_1, g_1, f, d
  3. Polygon(D, F, E, A) → q3, d_1, f_1, e, a
  4. Polygon(E, A, B, H) → q4, e_1, a_1, b_1, h_1
  5. Prism(q2, -2) → j, Q, edgeCQ, edgeGR, edgeFS, edgeDT, edgeQR, edgeRS, edgeST, edgeQT, R, S, T, faceCGRQ, faceFGRS, faceDFST, faceCDTQ, faceQRST
  6. Prism(q1, 2) → k, U, edgeCU, edgeGV, edgeHW, edgeBZ, edgeUV, edgeVW, edgeWZ, edgeUZ, V, W, Z, faceCGVU, faceGHWV, faceBHWZ, faceBCUZ, faceUVWZ
  7. Prism(q4, 2) → l, A_1, edge3, edge1, edge2, edge4, edge5, edge7, edge8, edge6, B_1, C_1, D_1, face2, face1, face3, face4, face5
  8. Prism(q3, -2) → m, E_1, edge10, edge12, edge11, edge9, edge13, edge15, edge16, edge14, F_1, G_1, H_1, face8, face9, face7, face6, face10
  9. Polygon(F, G, H, E) → q5, f_2, g_2, h_2, e_2
  10. Polygon(D, L, I, A) → q6, d_2, l_1, i, a_2
  11. Polygon(A, I, J, B) → q7, a_3, i_1, j_1, b_2
  12. Polygon(B, J, K, C) → q8, b_3, j_2, k_1, c_2
  13. Polygon(K, L, D, C) → q9, k_2, l_2, d_3, c_3
  14. Polygon(K, J, I, L) → q10, k_3, j_3, i_2, l_3
  15. Mirror(J, p) → J'
  16. Mirror(I, p) → I'
  17. Mirror(L, p) → L'
  18. Mirror(D, p) → D'
  19. Mirror(K, p) → K'
  20. Mirror(C, p) → C'
  21. Mirror(B, p) → B'
  22. Mirror(A, p) → A'
  23. Line(H_1, C_1) → n
  24. Rotate(D', ang, n) → D''
  25. Rotate(L', ang, n) → L''
  26. Rotate(C', ang, n) → C''
  27. Rotate(K', ang, n) → K''
  28. Rotate(A', ang, n) → A''
  29. Rotate(I', ang, n) → I''
  30. Rotate(B', ang, n) → B''
  31. Rotate(J', ang, n) → J''
  32. Polygon(K'', L'', I'', J'') → q11, k'', l'', i'', j''
  33. Polygon(L'', D'', A'', I'') → q12, q, d'', a'', r
  34. Polygon(K'', C'', D'', L'') → q13, s, c'', t, m_1
  35. Polygon(J'', B'', C'', K'') → q14, n_1, b'', p_1, q_1
  36. Polygon(I'', A'', B'', J'') → q15, r_1, s_1, t_1, m_2
  37. Rotate(E_1, ang, n) → M
  38. Rotate(U, ang, n) → U'
  39. Mirror(G, p) → G'
  40. Mirror(F, p) → F'
  41. Mirror(H, p) → H'
  42. Mirror(E, p) → E'
  43. Rotate(H', ang, n) → H''
  44. Rotate(E', ang, n) → E''
  45. Rotate(G', ang, n) → G''
  46. Rotate(F', ang, n) → F''
  47. Polygon(C'', G'', H'', B'') → q16, n_2, g'', h'', p_2
  48. Prism(q16, -2) → u, J_1, edge20, edge23, edge22, edge21, edge24, edge26, edge27, edge25, K_1, L_1, M_1, face15, face17, face16, face14, face18
  49. Polygon(B'', H'', E'', A'') → q17, q_2, r_2, e'', s_2
  50. Polygon(F'', E'', A'', D'') → q18, f'', t_2, f_3, g_3
  51. Polygon(G'', F'', D'', C'') → q19, h_3, i_3, m_3, n_3
  52. Prism(q18, 2) → w, R_1, edge39, edge38, edge37, edge36, edge40, edge42, edge43, edge41, S_1, T_1, U_1, face27, face26, face24, face25, face28
  53. Prism(q17, -2) → o_1, V_1, edge45, edge46, edge47, edge44, edge48, edge50, edge51, edge49, W_1, Z_1, A_2, face31, face32, face30, face29, face33
  54. Polygon(B, J, K, C) → q20, b_4, j_4, k_4, c_4
  55. Polygon(C, K, L, D) → q21, c_5, k_5, l_4, d_4
  56. Polygon(D, L, I, A) → q22, d_5, l_5, i_4, a_4
  57. Polygon(A, I, J, B) → q23, a_5, i_5, j_5, b_5
  58. Polygon(L'', D'', A'', I'') → q24, p_3, q_3, r_3, s_3
  59. Polygon(I'', A'', B'', J'') → q25, t_3, e_3, f_4, g_4
  60. Polygon(J'', B'', C'', K'') → q26, h_4, m_4, n_4, p_4
  61. Polygon(L'', D'', C'', K'') → q27, q_4, r_4, s_4, t_4
  62. Centroid(q5) → N
  63. OrthogonalLine(N, q5) → e_4
  64. Point(e_4) → O
  65. Cylinder(N, O, 1) → o, e_5, f_5, u_1
  66. Point(e_4) → P
  67. Intersect(e_4, f_5) → I_1,
  68. Point(e_4) → B_2
  69. Cylinder(B_2, P, 0.06) → v_1, g_5, h_5, w_1
  70. Point(e_4) → C_2
  71. Cone(P, C_2, 0.5) → o_2, p_5, u_2
  72. Point(e_4) → D_2
  73. Point(e_4) → E_2
  74. OrthogonalLine(E_2, faceGHWV) → m_5
  75. OrthogonalLine(D_2, faceGHWV) → n_5
  76. OrthogonalLine(E_2, face4) → q_5
  77. OrthogonalLine(D_2, face4) → r_5
  78. Point(m_5) → F_2
  79. Mirror(F_2, E_2) → G_2
  80. OrthogonalLine(F_2, q5) → s_5
  81. OrthogonalLine(G_2, q5) → t_5
  82. Intersect(n_5, s_5) → H_2
  83. Intersect(n_5, t_5) → I_2
  84. Polygon(F_2, H_2, I_2, G_2) → q28, f_6, g_6, h_6, i_6
  85. Prism(q28, 0.16308498706014124) → w_2, N_2, edge57, edge59, edge60, edge58, edge61, edge63, edge64, edge62, O_2, P_2, Q_2, face37, face39, face38, face36, face40
  86. Prism(q28, -0.12477514781668185) → o_3, R_2, edge65, edge67, edge68, edge66, edge69, edge71, edge72, edge70, S_2, T_2, U_2, face42, face44, face43, face41, face45
  87. Point(e_4) → J_2
  88. Cylinder(J_2, E_2, 0.05) → v_2, c_6, d_6, u_3
  89. Sphere(J_2, 0.15) → v_3
  90. Midpoint(P, B_2) → K_2
  91. OrthogonalLine(P, h_5) → j_6
  92. Midpoint(P, K_2) → L_2
  93. Midpoint(L_2, B_2) → M_2
  94. OrthogonalLine(L_2, face9) → k_6
  95. Point(k_6) → V_2
  96. Cylinder(P, V_2, 0.06) → w_3, e_6, p_6, o_4
  97. Cylinder(M_2, V_2, 0.06) → u_4, q_6, r_6, v_4
  98. Point(j_6) → W_2
  99. Ray(W_2, G_2) → l_6
  100. Ray(W_2, F_2) → m_6
  101. Point(t_5) → Z_2
  102. Point(l_6) → A_3
  103. Segment(A_3, Z_2) → n_6
  104. Segment(A_3, G_2) → s_6
  105. Rotate(R_2, (-rtt), zAxis) → B_3
  106. Rotate(U_2, (-rtt), zAxis) → C_3
  107. Rotate(U_2, (-rtt), zAxis) → D_3
  108. Rotate(Q_2, (-rtt), zAxis) → E_3
  109. Rotate(Q_2, (-rtt), zAxis) → F_3
  110. Rotate(N_2, (-rtt), zAxis) → G_3
  111. Rotate(S_2, (-rtt), zAxis) → H_3
  112. Rotate(S_2, (-rtt), zAxis) → I_3
  113. Rotate(T_2, (-rtt), zAxis) → J_3
  114. Rotate(T_2, (-rtt), zAxis) → K_3
  115. Rotate(P_2, (-rtt), zAxis) → L_3
  116. Rotate(O_2, (-rtt), zAxis) → M_3
  117. Rotate(A_3, (-rtt), zAxis) → N_3
  118. Rotate(G_2, (-rtt), zAxis) → O_3
  119. Segment(N_3, O_3) → a_6
  120. Rotate(A_3, (-rtt), zAxis) → P_3
  121. Rotate(A_3, (-rtt), zAxis) → Q_3
  122. Rotate(Z_2, (-rtt), zAxis) → R_3
  123. Segment(Q_3, R_3) → b_6
  124. Rotate(o_4, (-rtt), zAxis) → o_5
  125. Rotate(V_2, (-rtt), zAxis) → S_3
  126. Rotate(v_4, (-rtt), zAxis) → w_4
  127. Polygon(L_3, J_3, I_3, M_3) → q29, f_7, g_7, h_7, i_7
  128. Prism(q29, 0.61) → v_5, Z_3, edge75, edge74, edge73, edge76, edge77, edge79, edge80, edge78, A_4, B_4, C_4, face48, face46, face47, face49, face50
  129. Rotate(N_3, 180°, zAxis) → T_3
  130. Rotate(O_3, 180°, zAxis) → U_3
  131. Segment(T_3, U_3) → j_7
  132. Rotate(Q_3, 180°, zAxis) → V_3
  133. Rotate(Q_3, 180°, zAxis) → W_3
  134. Rotate(R_3, 180°, zAxis) → D_4
  135. Segment(W_3, D_4) → k_7
  136. Polygon(C'', J_1, U_1, D'') → q30, l_7, m_7, n_7, p_7
  137. Prism(q19, 2) → u_5, F_4, edge35, edge52, edge33, edge34, edge53, edge55, edge56, edge54, G_4, H_4, I_4, face34, face22, face21, face23, face35

AI Drawing Prompt Reference

Create a rotating ballerina music box. Start by drawing four rectangles and combining them into two prisms. Then draw four triangles to form another prism. Use mirror and rotate commands to create the rotating effect. Finally, apply mirroring and rotating to generate the rotating ballerina figure.
The prompt above was compiled from the original drawing commands and is for reference only.