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球壳剥除：体积

球壳剥除：体积
几何画板及绘图内容加载中，请稍等……
2015-12-29 04:36
立体几何变换
所属专题 Geometry: Surface Area & Volume Geometry: Surface Area & Volume Geometry: Surface Area & Volume GA Chapter 11: Surface Area and Volume Surface Area & Volume Surface Area & Volume
这个范例演示了球壳剥除的过程，涉及球体体积的概念。通过使用Dilate、Translate、Mirror和Rotate等GeoGebra命令，可以动态展示球壳的剥除过程。该范例适合高中数学教学，特别是立体几何和体积计算的教学。

GeoGebra 命令及参数

  1. If(2 < a < 3, Translate[h, (((0.9 * π) * (a - 2)), 0)]) → e_2
  2. Center(e_2) → Q_1
  3. Dilate(D, If[0 < a < 1, 1 - a, 1], B) → D'
  4. Intersect(c, yAxis, 2) → E
  5. Point(yAxis) → F
  6. Translate(c, If[0 < a < 1, ((π * a), 0)]) → c'
  7. Center(c') → G
  8. Mirror(D, f) → D'_1
  9. Mirror(D', f) → D''
  10. Intersect(g, f, 2) → J
  11. Mirror(K, f) → K'
  12. Mirror(L, f) → L'
  13. Mirror(N, f) → N'
  14. Mirror(P, f) → P'
  15. Mirror(Q, f) → Q'
  16. Mirror(R, f) → R'
  17. Mirror(S, f) → S'
  18. Mirror(T, f) → T'
  19. Mirror(U, f) → U'
  20. Mirror(V, f) → V'
  21. Mirror(W, f) → W'
  22. Mirror(Z, f) → Z'
  23. Mirror(A_1, f) → M
  24. Mirror(B_1, f) → O
  25. Mirror(C_1, f) → H_1
  26. Mirror(D_1, f) → I_1
  27. Mirror(E_1, f) → J_1
  28. Mirror(F_1, f) → K_1
  29. Mirror(G_1, f) → L_1
  30. Dilate(J, If[1 < a < 2, 2 - a, 1], K) → J'
  31. If(1 < a < 2, Translate[g, (((0.95 * π) * (a - 1)), 0)]) → t_1
  32. Center(t_1) → N_1
  33. Mirror(J', f) → J''_1
  34. Mirror(J, f) → J'_1
  35. Mirror(J', f) → J''_2
  36. Intersect(g, f, 1) → I
  37. Intersect(h, f) → M_1, O_1
  38. Intersect(k, f) → P_1, R_1
  39. Intersect(p, f) → S_1, T_1
  40. If(1 < a < 2, Translate[I, (((0.95 * π) * (a - 1)), 0)]) → U_1
  41. Rotate(U_1, (((1 - a) * 180))°, N_1) → V_1
  42. CircleArc(N_1, J', V_1) → c_2
  43. Mirror(c_2, f) → d_2
  44. If(2 < a < 3, Translate[M_1, (((0.9 * π) * (a - 2)), 0)]) → W_1
  45. Dilate(O_1, If[2 < a < 3, 3 - a, 1], L) → Z_1
  46. Rotate(W_1, (((2 - a) * 180))°, Q_1) → A_2
  47. CircleArc(Q_1, Z_1, A_2) → f_2
  48. Mirror(f_2, f) → g_2
  49. Mirror(O_1, f) → B_2
  50. Mirror(Z_1, f) → C_2
  51. Intersect(k, f, 1) → D_2
  52. Dilate(R_1, If[3 < a < 4, 4 - a, 1], N) → E_2
  53. If(3 < a < 4, Translate[k, (((0.85 * π) * (a - 3)), 0)]) → h_2
  54. Center(h_2) → F_2
  55. If(3 < a < 4, Translate[D_2, (((0.85 * π) * (a - 3)), 0)]) → G_2
  56. Rotate(G_2, (((3 - a) * 180))°, F_2) → H_2
  57. CircleArc(F_2, E_2, H_2) → k_2
  58. Mirror(R_1, f) → I_2
  59. Mirror(E_2, f) → J_2
  60. Intersect(f, yAxis) → K_2
  61. Intersect(f, yAxis) → L_2
  62. Intersect(f, yAxis) → M_2
  63. Intersect(c, f) → N_2, O_2
  64. If(0 < a < 1, Translate[N_2, ((a * π), 0)]) → P_2
  65. Rotate(P_2, If[0 < a < 1, (((-a) * 180))°], C) → H
  66. CircleArc(C, D', H) → e
  67. Mirror(e, f) → e'
  68. Intersect(q, f) → Q_2, R_2
  69. Intersect(f, yAxis) → S_2
  70. Intersect(f, yAxis) → T_2
  71. Intersect(f, yAxis) → U_2
  72. Intersect(f, yAxis) → V_2
  73. Intersect(f, yAxis) → W_2
  74. Intersect(f, yAxis) → Z_2
  75. Intersect(f, yAxis) → A_3
  76. Intersect(r, s) → B_3, , ,
  77. Intersect(f, yAxis) → C_3
  78. Intersect(r, f, 1) → D_3
  79. Intersect(s, f, 1) → E_3
  80. Intersect(t, f, 1) → F_3
  81. Intersect(c_1, f, 1) → G_3
  82. Intersect(d_1, f, 1) → H_3
  83. Intersect(e_1, f, 1) → I_3
  84. Intersect(f_1, f, 1) → J_3
  85. Intersect(g_1, f, 1) → K_3
  86. Intersect(h_1, f, 1) → L_3
  87. Intersect(k_1, f, 1) → M_3
  88. Intersect(p_1, f, 1) → N_3
  89. Intersect(q_1, f, 1) → O_3
  90. Intersect(r_1, f, 1) → P_3
  91. Intersect(s_1, f, 1) → Q_3
  92. Intersect(s_1, f, 2) → R_3
  93. Intersect(r_1, f, 2) → S_3
  94. Intersect(q_1, f, 2) → T_3
  95. Intersect(f, yAxis) → U_3
  96. Intersect(p_1, f, 2) → V_3
  97. Intersect(k_1, f, 2) → W_3
  98. Intersect(h_1, f, 2) → Z_3
  99. Intersect(g_1, f, 2) → A_4
  100. Intersect(f_1, f, 2) → B_4
  101. Intersect(e_1, f, 2) → C_4
  102. Intersect(d_1, f, 2) → D_4
  103. Intersect(c_1, f, 2) → E_4
  104. Intersect(t, f, 2) → F_4
  105. Intersect(s, f, 2) → G_4
  106. Intersect(r, f, 2) → H_4
  107. Dilate(T_1, If[4 < a < 5, 5 - a, 1], P) → I_4
  108. Dilate(R_2, If[5 < a < 6, 6 - a, 1], Q) → J_4
  109. Mirror(T_1, f) → K_4
  110. Mirror(I_4, f) → L_4
  111. Dilate(H_4, If[6 < a < 7, 7 - a, 1], R) → M_4
  112. Dilate(G_4, If[7 < a < 8, 8 - a, 1], S) → N_4
  113. Dilate(F_4, If[8 < a < 9, 9 - a, 1], T) → O_4
  114. Dilate(E_4, If[9 < a < 10, 10 - a, 1], U) → P_4
  115. Dilate(D_4, If[10 < a < 11, 11 - a, 1], V) → Q_4
  116. Dilate(C_4, If[11 < a < 12, 12 - a, 1], W) → R_4
  117. Dilate(B_4, If[12 < a < 13, 13 - a, 1], Z) → S_4
  118. Dilate(A_4, If[13 < a < 14, 14 - a, 1], A_1) → T_4
  119. Dilate(Z_3, If[14 < a < 15, 15 - a, 1], B_1) → U_4
  120. Dilate(W_3, If[15 < a < 16, 16 - a, 1], C_1) → V_4
  121. Dilate(V_3, If[16 < a < 17, 17 - a, 1], D_1) → W_4
  122. Dilate(T_3, If[17 < a < 18, 18 - a, 1], E_1) → Z_4
  123. Dilate(S_3, If[18 < a < 19, 19 - a, 1], F_1) → A_5
  124. Dilate(R_3, If[19 < a < 20, 20 - a, 1], G_1) → B_5
  125. If(4 < a < 5, Translate[p, (((0.8 * π) * (a - 4)), 0)]) → d_4
  126. If(4 < a < 5, Translate[S_1, (((0.8 * π) * (a - 4)), 0)]) → C_5
  127. Center(d_4) → D_5
  128. Rotate(C_5, (((4 - a) * 180))°, D_5) → E_5
  129. CircleArc(D_5, I_4, E_5) → e_4
  130. If(5 < a < 6, Translate[q, (((0.75 * π) * (a - 5)), 0)]) → f_4
  131. If(5 < a < 6, Translate[Q_2, (((0.75 * π) * (a - 5)), 0)]) → F_5
  132. Center(f_4) → G_5
  133. Rotate(F_5, (((5 - a) * 180))°, G_5) → H_5
  134. CircleArc(G_5, J_4, H_5) → g_4
  135. If(6 < a < 7, Translate[r, (((0.7 * π) * (a - 6)), 0)]) → h_4
  136. If(6 < a < 7, Translate[D_3, (((0.7 * π) * (a - 6)), 0)]) → I_5
  137. Center(h_4) → J_5
  138. Rotate(I_5, (((6 - a) * 180))°, J_5) → K_5
  139. CircleArc(J_5, M_4, K_5) → k_4
  140. If(7 < a < 8, Translate[s, (((0.65 * π) * (a - 7)), 0)]) → p_4
  141. If(7 < a < 8, Translate[E_3, (((0.65 * π) * (a - 7)), 0)]) → L_5
  142. Center(p_4) → M_5
  143. Rotate(L_5, (((7 - a) * 180))°, M_5) → N_5
  144. CircleArc(M_5, N_4, N_5) → q_4
  145. If(8 < a < 9, Translate[t, (((0.6 * π) * (a - 8)), 0)]) → r_4
  146. If(8 < a < 9, Translate[F_3, (((0.6 * π) * (a - 8)), 0)]) → O_5
  147. Center(r_4) → P_5
  148. Rotate(O_5, (((8 - a) * 180))°, P_5) → Q_5
  149. CircleArc(P_5, O_4, Q_5) → s_4
  150. If(9 < a < 10, Translate[c_1, (((0.55 * π) * (a - 9)), 0)]) → t_4
  151. If(9 < a < 10, Translate[G_3, (((0.55 * π) * (a - 9)), 0)]) → R_5
  152. Center(t_4) → S_5
  153. Rotate(R_5, (((9 - a) * 180))°, S_5) → T_5
  154. CircleArc(S_5, P_4, T_5) → c_5
  155. If(10 < a < 11, Translate[d_1, (((0.5 * π) * (a - 10)), 0)]) → d_5
  156. If(10 < a < 11, Translate[H_3, (((0.5 * π) * (a - 10)), 0)]) → U_5
  157. Center(d_5) → V_5
  158. Rotate(U_5, (((10 - a) * 180))°, V_5) → W_5
  159. CircleArc(V_5, Q_4, W_5) → e_5
  160. If(11 < a < 12, Translate[e_1, (((0.45 * π) * (a - 11)), 0)]) → f_5
  161. If(11 < a < 12, Translate[I_3, (((0.45 * π) * (a - 11)), 0)]) → Z_5
  162. Center(f_5) → A_6
  163. Rotate(Z_5, (((11 - a) * 180))°, A_6) → B_6
  164. CircleArc(A_6, R_4, B_6) → g_5
  165. If(12 < a < 13, Translate[f_1, (((0.4 * π) * (a - 12)), 0)]) → h_5
  166. If(12 < a < 13, Translate[J_3, (((0.4 * π) * (a - 12)), 0)]) → C_6
  167. Center(h_5) → D_6
  168. Rotate(C_6, (((12 - a) * 180))°, D_6) → E_6
  169. CircleArc(D_6, S_4, E_6) → k_5
  170. If(13 < a < 14, Translate[g_1, (((0.35 * π) * (a - 13)), 0)]) → p_5
  171. If(13 < a < 14, Translate[K_3, (((0.35 * π) * (a - 13)), 0)]) → F_6
  172. Center(p_5) → G_6
  173. Rotate(F_6, (((13 - a) * 180))°, G_6) → H_6
  174. CircleArc(G_6, T_4, H_6) → q_5
  175. If(14 < a < 15, Translate[h_1, (((0.3 * π) * (a - 14)), 0)]) → r_5
  176. If(14 < a < 15, Translate[L_3, (((0.3 * π) * (a - 14)), 0)]) → I_6
  177. Center(r_5) → J_6
  178. Rotate(I_6, (((14 - a) * 180))°, J_6) → K_6
  179. CircleArc(J_6, U_4, K_6) → s_5
  180. If(15 < a < 16, Translate[k_1, (((0.25 * π) * (a - 15)), 0)]) → t_5
  181. If(15 < a < 16, Translate[M_3, (((0.25 * π) * (a - 15)), 0)]) → L_6
  182. Center(t_5) → M_6
  183. Rotate(L_6, (((15 - a) * 180))°, M_6) → N_6
  184. CircleArc(M_6, V_4, N_6) → c_6
  185. If(16 < a < 17, Translate[p_1, (((0.2 * π) * (a - 16)), 0)]) → d_6
  186. If(16 < a < 17, Translate[N_3, (((0.2 * π) * (a - 16)), 0)]) → O_6
  187. Center(d_6) → P_6
  188. Rotate(O_6, (((16 - a) * 180))°, P_6) → Q_6
  189. CircleArc(P_6, W_4, Q_6) → e_6
  190. If(17 < a < 18, Translate[q_1, (((0.15 * π) * (a - 17)), 0)]) → f_6
  191. If(17 < a < 18, Translate[O_3, (((0.15 * π) * (a - 17)), 0)]) → R_6
  192. Center(f_6) → S_6
  193. Rotate(R_6, (((17 - a) * 180))°, S_6) → T_6
  194. CircleArc(S_6, Z_4, T_6) → g_6
  195. If(18 < a < 19, Translate[r_1, (((0.1 * π) * (a - 18)), 0)]) → h_6
  196. If(18 < a < 19, Translate[P_3, (((0.1 * π) * (a - 18)), 0)]) → U_6
  197. Center(h_6) → V_6
  198. Rotate(U_6, (((18 - a) * 180))°, V_6) → W_6
  199. CircleArc(V_6, A_5, W_6) → k_6
  200. If(19 < a < 20, Translate[s_1, (((0.05 * π) * (a - 19)), 0)]) → p_6
  201. If(19 < a < 20, Translate[Q_3, (((0.05 * π) * (a - 19)), 0)]) → Z_6
  202. Center(p_6) → A_7
  203. Rotate(Z_6, (((19 - a) * 180))°, A_7) → B_7
  204. CircleArc(A_7, B_5, B_7) → q_6
  205. Mirror(R_2, f) → C_7
  206. Mirror(J_4, f) → D_7
  207. Mirror(H_4, f) → E_7
  208. Mirror(M_4, f) → F_7
  209. Mirror(G_4, f) → G_7
  210. Mirror(N_4, f) → H_7
  211. Mirror(F_4, f) → I_7
  212. Mirror(O_4, f) → J_7
  213. Mirror(E_4, f) → K_7
  214. Mirror(P_4, f) → L_7
  215. Mirror(D_4, f) → M_7
  216. Mirror(Q_4, f) → N_7
  217. Mirror(C_4, f) → O_7
  218. Mirror(R_4, f) → P_7
  219. Mirror(B_4, f) → Q_7
  220. Mirror(S_4, f) → R_7
  221. Mirror(A_4, f) → S_7
  222. Mirror(T_4, f) → T_7
  223. Mirror(Z_3, f) → U_7
  224. Mirror(U_4, f) → V_7
  225. Mirror(W_3, f) → W_7
  226. Mirror(V_4, f) → Z_7
  227. Mirror(V_3, f) → A_8
  228. Mirror(W_4, f) → B_8
  229. Mirror(T_3, f) → C_8
  230. Mirror(Z_4, f) → D_8
  231. Mirror(S_3, f) → E_8
  232. Mirror(A_5, f) → F_8
  233. Mirror(R_3, f) → G_8
  234. Mirror(B_5, f) → H_8
  235. Sequence(Cylinder[(0, k, 0), (0, k + 0.05, 0), ((1 - k) * π)], k, 0, 0.95, 0.05) → baselist
  236. Element(baselist, 1) → cyl1
  237. Line((0, 0, 0), (0, 1, 0)) → m_6
  238. Sequence(Rotate[e, α, m_6], α, 1*°, 359*°, 1*°) → arc_1
  239. Cylinder((0, 0, 0), (0, 0.05, 0), (a * π)) → cyl1_a, d_8, e_8, o
  240. Sequence(If[a ≤ 0, Rotate[c, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_1
  241. Sequence(If[a ≤ 1, Rotate[g, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_2
  242. Sequence(Rotate[c_2, α, m_6], α, 1*°, 359*°, 1*°) → arc_2
  243. Cylinder((0, 0.05, 0), (0, 0.1, 0), (((a - 1) * 0.95) * π)) → cyl2_a, f_8, g_8, u
  244. Element(baselist, 2) → cyl2
  245. Sequence(If[a ≤ 2, Rotate[h, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_3
  246. Sequence(Rotate[f_2, α, m_6], α, 1*°, 359*°, 1*°) → arc_3
  247. Cylinder((0, 0.1, 0), (0, 0.15, 0), (((a - 2) * 0.9) * π)) → cyl3_a, h_8, k_8, v
  248. Element(baselist, 3) → cyl_3
  249. Sequence(If[a ≤ 3, Rotate[k, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_4
  250. Sequence(Rotate[k_2, α, m_6], α, 1*°, 359*°, 1*°) → arc_4
  251. Cylinder((0, 0.15, 0), (0, 0.2, 0), (((a - 3) * 0.85) * π)) → cyl4_a, p_2, p_8, w
  252. Element(baselist, 4) → cyl_4
  253. Sequence(If[a ≤ 4, Rotate[p, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_5
  254. Sequence(Rotate[e_4, α, m_6], α, 1*°, 359*°, 1*°) → arc_5
  255. Cylinder((0, 0.2, 0), (0, 0.25, 0), (((a - 4) * 0.8) * π)) → cyl5_a, r_6, q_8, o_1
  256. Element(baselist, 5) → cyl_5
  257. Sequence(If[a ≤ 5, Rotate[q, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_6
  258. Sequence(Rotate[g_4, α, m_6], α, 1*°, 359*°, 1*°) → arc_6
  259. Cylinder((0, 0.25, 0), (0, 0.3, 0), (((a - 5) * 0.75) * π)) → cyl6_a, s_6, r_8, u_1
  260. Element(baselist, 6) → cyl_6
  261. Sequence(If[a ≤ 6, Rotate[r, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_7
  262. Sequence(Rotate[k_4, α, m_6], α, 1*°, 359*°, 1*°) → arc_7
  263. Cylinder((0, 0.3, 0), (0, 0.35, 0), (((a - 6) * 0.7) * π)) → cyl7_a, t_6, s_8, v_1
  264. Element(baselist, 7) → cyl_7
  265. Sequence(If[a ≤ 7, Rotate[s, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_8
  266. Sequence(Rotate[q_4, α, m_6], α, 1*°, 359*°, 1*°) → arc_8
  267. Cylinder((0, 0.35, 0), (0, 0.4, 0), (((a - 7) * 0.65) * π)) → cyl8_a, c_7, t_8, w_1
  268. Element(baselist, 8) → cyl_8
  269. Sequence(If[a ≤ 8, Rotate[t, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_9
  270. Sequence(Rotate[s_4, α, m_6], α, 1*°, 359*°, 1*°) → arc_9
  271. Cylinder((0, 0.4, 0), (0, 0.45, 0), (((a - 8) * 0.6) * π)) → cyl9_a, d_7, c_9, o_2
  272. Element(baselist, 9) → cyl_9
  273. Sequence(If[a ≤ 9, Rotate[c_1, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_10
  274. Sequence(Rotate[c_5, α, m_6], α, 1*°, 359*°, 1*°) → arc_10
  275. Cylinder((0, 0.45, 0), (0, 0.5, 0), (((a - 9) * 0.55) * π)) → cyl10_a, e_7, d_9, u_2
  276. Element(baselist, 10) → cyl_10
  277. Sequence(If[a ≤ 10, Rotate[d_1, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_11
  278. Sequence(Rotate[e_5, α, m_6], α, 1*°, 359*°, 1*°) → arc_11
  279. Cylinder((0, 0.5, 0), (0, 0.55, 0), (((a - 10) * 0.5) * π)) → cyl11_a, f_7, e_9, v_2
  280. Element(baselist, 11) → cyl_11
  281. Sequence(If[a ≤ 11, Rotate[e_1, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_12
  282. Sequence(Rotate[g_5, α, m_6], α, 1*°, 359*°, 1*°) → arc_12
  283. Cylinder((0, 0.55, 0), (0, 0.6, 0), (((a - 11) * 0.45) * π)) → cyl12_a, g_7, f_9, w_2
  284. Element(baselist, 12) → cyl_12
  285. Sequence(If[a ≤ 12, Rotate[f_1, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_13
  286. Sequence(Rotate[k_5, α, m_6], α, 1*°, 359*°, 1*°) → arc_13
  287. Cylinder((0, 0.6, 0), (0, 0.65, 0), (((a - 12) * 0.4) * π)) → cyl13_a, h_7, g_9, o_3
  288. Element(baselist, 13) → cyl_13
  289. Sequence(If[a ≤ 13, Rotate[g_1, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_14
  290. Sequence(Rotate[q_5, α, m_6], α, 1*°, 359*°, 1*°) → arc_14
  291. Cylinder((0, 0.65, 0), (0, 0.7, 0), (((a - 13) * 0.35) * π)) → cyl14_a, k_7, h_9, u_3
  292. Element(baselist, 14) → cyl_14
  293. Sequence(If[a ≤ 14, Rotate[h_1, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_15
  294. Sequence(Rotate[s_5, α, m_6], α, 1*°, 359*°, 1*°) → arc_15
  295. Cylinder((0, 0.7, 0), (0, 0.75, 0), (((a - 14) * 0.3) * π)) → cyl15_a, p_7, k_9, v_3
  296. Element(baselist, 15) → cyl_15
  297. Sequence(If[a ≤ 15, Rotate[k_1, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_16
  298. Sequence(Rotate[c_6, α, m_6], α, 1*°, 359*°, 1*°) → arc_16
  299. Cylinder((0, 0.75, 0), (0, 0.8, 0), (((a - 15) * 0.25) * π)) → cyl16_a, q_7, p_9, w_3
  300. Element(baselist, 16) → cyl_16
  301. Sequence(If[a ≤ 16, Rotate[p_1, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_17
  302. Sequence(Rotate[e_6, α, m_6], α, 1*°, 359*°, 1*°) → arc_17
  303. Cylinder((0, 0.8, 0), (0, 0.85, 0), (((a - 16) * 0.2) * π)) → cyl17_a, r_7, q_9, o_4
  304. Element(baselist, 17) → cyl_17
  305. Sequence(If[a ≤ 17, Rotate[q_1, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_18
  306. Sequence(Rotate[g_6, α, m_6], α, 1*°, 359*°, 1*°) → arc_18
  307. Cylinder((0, 0.85, 0), (0, 0.9, 0), (((a - 17) * 0.15) * π)) → cyl18_a, s_7, r_9, u_4
  308. Element(baselist, 18) → cyl_18
  309. Sequence(If[a ≤ 18, Rotate[r_1, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_19
  310. Sequence(Rotate[k_6, α, m_6], α, 1*°, 359*°, 1*°) → arc_19
  311. Cylinder((0, 0.9, 0), (0, 0.95, 0), (((a - 18) * 0.1) * π)) → cyl19_a, t_7, s_9, v_4
  312. Element(baselist, 19) → cyl_19
  313. Sequence(If[a ≤ 19, Rotate[s_1, α, m_6]], α, 1*°, 180*°, 1*°) → sphere_20
  314. Sequence(Rotate[q_6, α, m_6], α, 1*°, 359*°, 1*°) → arc_20
  315. Cylinder((0, 0.95, 0), (0, 1, 0), (((a - 19) * 0.05) * π)) → cyl20_a, c_8, t_9, w_4
  316. Element(baselist, 20) → cyl_20
  317. Point(yAxis) → I_8
  318. Sphere(I_8, 1) → d