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用单位立方体铺满长方体的体积与单位替换

用单位立方体铺满长方体的体积与单位替换
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2023-03-23 20:00
函数数列立体几何几何作图滑块动画
所属专题 Quader und Würfel - Volumen
该范例演示如何用单位立方体计数来填满长方体，并进一步探究当单位立方体尺寸变化时填充与体积结果是否仍成立。核心数学概念包括：长方体体积=底面积×高、单位体积立方体的“分解计数”思想、单位从1 m^3（或给定体积为1的立方体）到1 mm^3等不同尺度时体积单位与计数方式的对应关系，以及通过几何分割检验“用更大单位体积立方体能否同样铺满”的条件。作图与交互要点：利用多边形面构成立方体/长方体轮廓，借助旋转与拼接完成立方体阵列，随后使用计数逻辑统计能放入的单位块数量，并在必要时对“体积单位”或“个数×单位体积”的推断给出纠错提示；对应GeoGebra构造摘要中使用了 Join、Rotate、Polygon、CountIf、If、Segment、Textfield、Midpoint 等命令，以及如 A_1…A_16、ListA、sliderA/sliderB/sliderC、questionCount、nums、lNums、winkel、lA/lB/lC 等对象来支撑几何构建、参数控制与文本反馈。适合5-6年级立体几何入门到体积理解与单位换算的课堂探究，也可用于开放题讨论与分层练习。

GeoGebra 命令及参数

  1. Join({{1}, nums}) → lNums
  2. Rotate(B + ((sliderB * verzerrung), 0), winkel, B) → C
  3. Rotate(F + ((sliderB * verzerrung), 0), winkel, F) → G
  4. Rotate(E + ((sliderB * verzerrung), 0), winkel, E) → H
  5. Polygon(I, J, K, L) → region, i_{16}, j_{16}, k_{16}, l_{16}
  6. CountIf(IsInRegion[P, region], P, {A_{10}, A_{11}, A_{12}, A_{13}, A_{14}, A_{15}, A_{2}, A_{3}, A_{4}, A_{5}, A_{6}, A_{7}, A_{8}, A_{9}, A_1, A_{16}}) → objectsInRegion
  7. If(bsp ≟ 1, CountIf[x > 1, Bsp1], If[bsp ≟ 2, CountIf[x > 1, Bsp2], If[bsp ≟ 3, CountIf[x > 1, Bsp3], If[bsp ≟ 4, CountIf[x > 1, Bsp4], If[bsp ≟ 5, CountIf[x > 1, Bsp5], If[bsp ≟ 6, CountIf[x > 1, Bsp6], If[bsp ≟ 7, CountIf[x > 1, Bsp7], If[bsp ≟ 8, CountIf[x > 1, Bsp8]]]]]]]]) → double
  8. Rotate(A + ((sliderB * verzerrung), 0), winkel, A) → D
  9. Segment(A, B) → f
  10. Segment(A, D) → g
  11. Segment(D, C) → h
  12. Segment(C, B) → i
  13. Segment(B, F) → j
  14. Segment(F, G) → k
  15. Segment(G, C) → l
  16. Segment(G, H) → m
  17. Segment(H, E) → n
  18. Segment(E, A) → p
  19. Segment(H, D) → q
  20. Segment(F, E) → r
  21. Rotate(B_1 + ((sliderB_1 * verzerrung), 0), winkel, B_1) → C_1
  22. Rotate(A_1 + ((sliderB_1 * verzerrung), 0), winkel, A_1) → D_1
  23. Rotate(F_1 + ((sliderB_1 * verzerrung), 0), winkel, F_1) → G_1
  24. Rotate(E_1 + ((sliderB_1 * verzerrung), 0), winkel, E_1) → H_1
  25. Segment(A_1, B_1) → s
  26. Segment(B_1, F_1) → t
  27. Segment(F_1, E_1) → a
  28. Segment(E_1, A_1) → b
  29. Segment(A_1, D_1) → c
  30. Segment(D_1, H_1) → d
  31. Segment(B_1, C_1) → e
  32. Segment(E_1, H_1) → f_1
  33. Segment(H_1, G_1) → g_1
  34. Segment(F_1, G_1) → h_1
  35. Segment(G_1, C_1) → i_1
  36. Segment(D_1, C_1) → j_1
  37. Polygon(E_1, H_1, G_1, C_1, B_1, A_1) → poly1, e_1, k_1, l_1, c_1, b_1, a_1
  38. Rotate(B_{2} + ((sliderB_1 * verzerrung), 0), winkel, B_{2}) → C_{2}
  39. Rotate(A_{2} + ((sliderB_1 * verzerrung), 0), winkel, A_{2}) → D_{2}
  40. Rotate(F_{2} + ((sliderB_1 * verzerrung), 0), winkel, F_{2}) → G_{2}
  41. Rotate(E_{2} + ((sliderB_1 * verzerrung), 0), winkel, E_{2}) → H_{2}
  42. Segment(A_{2}, B_{2}) → s_{1}
  43. Segment(B_{2}, F_{2}) → t_{1}
  44. Segment(F_{2}, E_{2}) → a_{2}
  45. Segment(E_{2}, A_{2}) → b_{2}
  46. Segment(A_{2}, D_{2}) → c_{2}
  47. Segment(D_{2}, H_{2}) → d_{1}
  48. Segment(B_{2}, C_{2}) → e_{2}
  49. Segment(E_{2}, H_{2}) → f_{2}
  50. Segment(H_{2}, G_{2}) → g_{2}
  51. Segment(F_{2}, G_{2}) → h_{2}
  52. Segment(G_{2}, C_{2}) → i_{2}
  53. Segment(D_{2}, C_{2}) → j_{2}
  54. Polygon(E_{2}, H_{2}, G_{2}, C_{2}, B_{2}, A_{2}) → poly1_{1}, e_{3}, k_{2}, l_{2}, c_{3}, b_{3}, a_{3}
  55. Rotate(B_{3} + ((sliderB_1 * verzerrung), 0), winkel, B_{3}) → C_{3}
  56. Rotate(A_{3} + ((sliderB_1 * verzerrung), 0), winkel, A_{3}) → D_{3}
  57. Rotate(F_{3} + ((sliderB_1 * verzerrung), 0), winkel, F_{3}) → G_{3}
  58. Rotate(E_{3} + ((sliderB_1 * verzerrung), 0), winkel, E_{3}) → H_{3}
  59. Segment(A_{3}, B_{3}) → s_{2}
  60. Segment(B_{3}, F_{3}) → t_{2}
  61. Segment(F_{3}, E_{3}) → a_{4}
  62. Segment(E_{3}, A_{3}) → b_{4}
  63. Segment(A_{3}, D_{3}) → c_{4}
  64. Segment(D_{3}, H_{3}) → d_{2}
  65. Segment(B_{3}, C_{3}) → e_{4}
  66. Segment(E_{3}, H_{3}) → f_{3}
  67. Segment(H_{3}, G_{3}) → g_{3}
  68. Segment(F_{3}, G_{3}) → h_{3}
  69. Segment(G_{3}, C_{3}) → i_{3}
  70. Segment(D_{3}, C_{3}) → j_{3}
  71. Polygon(E_{3}, H_{3}, G_{3}, C_{3}, B_{3}, A_{3}) → poly1_{2}, e_{5}, k_{3}, l_{3}, c_{5}, b_{5}, a_{5}
  72. Rotate(B_{4} + ((sliderB_1 * verzerrung), 0), winkel, B_{4}) → C_{4}
  73. Rotate(A_{4} + ((sliderB_1 * verzerrung), 0), winkel, A_{4}) → D_{4}
  74. Rotate(F_{4} + ((sliderB_1 * verzerrung), 0), winkel, F_{4}) → G_{4}
  75. Rotate(E_{4} + ((sliderB_1 * verzerrung), 0), winkel, E_{4}) → H_{4}
  76. Segment(A_{4}, B_{4}) → s_{3}
  77. Segment(B_{4}, F_{4}) → t_{3}
  78. Segment(F_{4}, E_{4}) → a_{6}
  79. Segment(E_{4}, A_{4}) → b_{6}
  80. Segment(A_{4}, D_{4}) → c_{6}
  81. Segment(D_{4}, H_{4}) → d_{3}
  82. Segment(B_{4}, C_{4}) → e_{6}
  83. Segment(E_{4}, H_{4}) → f_{4}
  84. Segment(H_{4}, G_{4}) → g_{4}
  85. Segment(F_{4}, G_{4}) → h_{4}
  86. Segment(G_{4}, C_{4}) → i_{4}
  87. Segment(D_{4}, C_{4}) → j_{4}
  88. Polygon(E_{4}, H_{4}, G_{4}, C_{4}, B_{4}, A_{4}) → poly1_{3}, e_{7}, k_{4}, l_{4}, c_{7}, b_{7}, a_{7}
  89. Rotate(B_{5} + ((sliderB_1 * verzerrung), 0), winkel, B_{5}) → C_{5}
  90. Rotate(A_{5} + ((sliderB_1 * verzerrung), 0), winkel, A_{5}) → D_{5}
  91. Rotate(F_{5} + ((sliderB_1 * verzerrung), 0), winkel, F_{5}) → G_{5}
  92. Rotate(E_{5} + ((sliderB_1 * verzerrung), 0), winkel, E_{5}) → H_{5}
  93. Segment(A_{5}, B_{5}) → s_{4}
  94. Segment(B_{5}, F_{5}) → t_{4}
  95. Segment(F_{5}, E_{5}) → a_{8}
  96. Segment(E_{5}, A_{5}) → b_{8}
  97. Segment(A_{5}, D_{5}) → c_{8}
  98. Segment(D_{5}, H_{5}) → d_{4}
  99. Segment(B_{5}, C_{5}) → e_{8}
  100. Segment(E_{5}, H_{5}) → f_{5}
  101. Segment(H_{5}, G_{5}) → g_{5}
  102. Segment(F_{5}, G_{5}) → h_{5}
  103. Segment(G_{5}, C_{5}) → i_{5}
  104. Segment(D_{5}, C_{5}) → j_{5}
  105. Polygon(E_{5}, H_{5}, G_{5}, C_{5}, B_{5}, A_{5}) → poly1_{4}, e_{9}, k_{5}, l_{5}, c_{9}, b_{9}, a_{9}
  106. Rotate(B_{6} + ((sliderB_1 * verzerrung), 0), winkel, B_{6}) → C_{6}
  107. Rotate(A_{6} + ((sliderB_1 * verzerrung), 0), winkel, A_{6}) → D_{6}
  108. Rotate(F_{6} + ((sliderB_1 * verzerrung), 0), winkel, F_{6}) → G_{6}
  109. Rotate(E_{6} + ((sliderB_1 * verzerrung), 0), winkel, E_{6}) → H_{6}
  110. Segment(A_{6}, B_{6}) → s_{5}
  111. Segment(B_{6}, F_{6}) → t_{5}
  112. Segment(F_{6}, E_{6}) → a_{10}
  113. Segment(E_{6}, A_{6}) → b_{10}
  114. Segment(A_{6}, D_{6}) → c_{10}
  115. Segment(D_{6}, H_{6}) → d_{5}
  116. Segment(B_{6}, C_{6}) → e_{10}
  117. Segment(E_{6}, H_{6}) → f_{6}
  118. Segment(H_{6}, G_{6}) → g_{6}
  119. Segment(F_{6}, G_{6}) → h_{6}
  120. Segment(G_{6}, C_{6}) → i_{6}
  121. Segment(D_{6}, C_{6}) → j_{6}
  122. Polygon(E_{6}, H_{6}, G_{6}, C_{6}, B_{6}, A_{6}) → poly1_{5}, e_{11}, k_{6}, l_{6}, c_{11}, b_{11}, a_{11}
  123. Rotate(B_{7} + ((sliderB_1 * verzerrung), 0), winkel, B_{7}) → C_{7}
  124. Rotate(A_{7} + ((sliderB_1 * verzerrung), 0), winkel, A_{7}) → D_{7}
  125. Rotate(F_{7} + ((sliderB_1 * verzerrung), 0), winkel, F_{7}) → G_{7}
  126. Rotate(E_{7} + ((sliderB_1 * verzerrung), 0), winkel, E_{7}) → H_{7}
  127. Segment(A_{7}, B_{7}) → s_{6}
  128. Segment(B_{7}, F_{7}) → t_{6}
  129. Segment(F_{7}, E_{7}) → a_{12}
  130. Segment(E_{7}, A_{7}) → b_{12}
  131. Segment(A_{7}, D_{7}) → c_{12}
  132. Segment(D_{7}, H_{7}) → d_{6}
  133. Segment(B_{7}, C_{7}) → e_{12}
  134. Segment(E_{7}, H_{7}) → f_{7}
  135. Segment(H_{7}, G_{7}) → g_{7}
  136. Segment(F_{7}, G_{7}) → h_{7}
  137. Segment(G_{7}, C_{7}) → i_{7}
  138. Segment(D_{7}, C_{7}) → j_{7}
  139. Polygon(E_{7}, H_{7}, G_{7}, C_{7}, B_{7}, A_{7}) → poly1_{6}, e_{13}, k_{7}, l_{7}, c_{13}, b_{13}, a_{13}
  140. Rotate(B_{8} + ((sliderB_1 * verzerrung), 0), winkel, B_{8}) → C_{8}
  141. Rotate(A_{8} + ((sliderB_1 * verzerrung), 0), winkel, A_{8}) → D_{8}
  142. Rotate(F_{8} + ((sliderB_1 * verzerrung), 0), winkel, F_{8}) → G_{8}
  143. Rotate(E_{8} + ((sliderB_1 * verzerrung), 0), winkel, E_{8}) → H_{8}
  144. Segment(A_{8}, B_{8}) → s_{7}
  145. Segment(B_{8}, F_{8}) → t_{7}
  146. Segment(F_{8}, E_{8}) → a_{14}
  147. Segment(E_{8}, A_{8}) → b_{14}
  148. Segment(A_{8}, D_{8}) → c_{14}
  149. Segment(D_{8}, H_{8}) → d_{7}
  150. Segment(B_{8}, C_{8}) → e_{14}
  151. Segment(E_{8}, H_{8}) → f_{8}
  152. Segment(H_{8}, G_{8}) → g_{8}
  153. Segment(F_{8}, G_{8}) → h_{8}
  154. Segment(G_{8}, C_{8}) → i_{8}
  155. Segment(D_{8}, C_{8}) → j_{8}
  156. Polygon(E_{8}, H_{8}, G_{8}, C_{8}, B_{8}, A_{8}) → poly1_{7}, e_{15}, k_{8}, l_{8}, c_{15}, b_{15}, a_{15}
  157. Rotate(B_{9} + ((sliderB_1 * verzerrung), 0), winkel, B_{9}) → C_{9}
  158. Rotate(A_{9} + ((sliderB_1 * verzerrung), 0), winkel, A_{9}) → D_{9}
  159. Rotate(F_{9} + ((sliderB_1 * verzerrung), 0), winkel, F_{9}) → G_{9}
  160. Rotate(E_{9} + ((sliderB_1 * verzerrung), 0), winkel, E_{9}) → H_{9}
  161. Segment(A_{9}, B_{9}) → s_{8}
  162. Segment(B_{9}, F_{9}) → t_{8}
  163. Segment(F_{9}, E_{9}) → a_{16}
  164. Segment(E_{9}, A_{9}) → b_{16}
  165. Segment(A_{9}, D_{9}) → c_{16}
  166. Segment(D_{9}, H_{9}) → d_{8}
  167. Segment(B_{9}, C_{9}) → e_{16}
  168. Segment(E_{9}, H_{9}) → f_{9}
  169. Segment(H_{9}, G_{9}) → g_{9}
  170. Segment(F_{9}, G_{9}) → h_{9}
  171. Segment(G_{9}, C_{9}) → i_{9}
  172. Segment(D_{9}, C_{9}) → j_{9}
  173. Polygon(E_{9}, H_{9}, G_{9}, C_{9}, B_{9}, A_{9}) → poly1_{8}, e_{17}, k_{9}, l_{9}, c_{17}, b_{17}, a_{17}
  174. Rotate(B_{10} + ((sliderB_1 * verzerrung), 0), winkel, B_{10}) → C_{10}
  175. Rotate(A_{10} + ((sliderB_1 * verzerrung), 0), winkel, A_{10}) → D_{10}
  176. Rotate(F_{10} + ((sliderB_1 * verzerrung), 0), winkel, F_{10}) → G_{10}
  177. Rotate(E_{10} + ((sliderB_1 * verzerrung), 0), winkel, E_{10}) → H_{10}
  178. Segment(A_{10}, B_{10}) → s_{9}
  179. Segment(B_{10}, F_{10}) → t_{9}
  180. Segment(F_{10}, E_{10}) → a_{18}
  181. Segment(E_{10}, A_{10}) → b_{18}
  182. Segment(A_{10}, D_{10}) → c_{18}
  183. Segment(D_{10}, H_{10}) → d_{9}
  184. Segment(B_{10}, C_{10}) → e_{18}
  185. Segment(E_{10}, H_{10}) → f_{10}
  186. Segment(H_{10}, G_{10}) → g_{10}
  187. Segment(F_{10}, G_{10}) → h_{10}
  188. Segment(G_{10}, C_{10}) → i_{10}
  189. Segment(D_{10}, C_{10}) → j_{10}
  190. Polygon(E_{10}, H_{10}, G_{10}, C_{10}, B_{10}, A_{10}) → poly1_{9}, e_{19}, k_{10}, l_{10}, c_{19}, b_{19}, a_{19}
  191. Rotate(B_{11} + ((sliderB_1 * verzerrung), 0), winkel, B_{11}) → C_{11}
  192. Rotate(A_{11} + ((sliderB_1 * verzerrung), 0), winkel, A_{11}) → D_{11}
  193. Rotate(F_{11} + ((sliderB_1 * verzerrung), 0), winkel, F_{11}) → G_{11}
  194. Rotate(E_{11} + ((sliderB_1 * verzerrung), 0), winkel, E_{11}) → H_{11}
  195. Segment(A_{11}, B_{11}) → s_{10}
  196. Segment(B_{11}, F_{11}) → t_{10}
  197. Segment(F_{11}, E_{11}) → a_{20}
  198. Segment(E_{11}, A_{11}) → b_{20}
  199. Segment(A_{11}, D_{11}) → c_{20}
  200. Segment(D_{11}, H_{11}) → d_{10}
  201. Segment(B_{11}, C_{11}) → e_{20}
  202. Segment(E_{11}, H_{11}) → f_{11}
  203. Segment(H_{11}, G_{11}) → g_{11}
  204. Segment(F_{11}, G_{11}) → h_{11}
  205. Segment(G_{11}, C_{11}) → i_{11}
  206. Segment(D_{11}, C_{11}) → j_{11}
  207. Polygon(E_{11}, H_{11}, G_{11}, C_{11}, B_{11}, A_{11}) → poly1_{10}, e_{21}, k_{11}, l_{11}, c_{21}, b_{21}, a_{21}
  208. Rotate(B_{12} + ((sliderB_1 * verzerrung), 0), winkel, B_{12}) → C_{12}
  209. Rotate(A_{12} + ((sliderB_1 * verzerrung), 0), winkel, A_{12}) → D_{12}
  210. Rotate(F_{12} + ((sliderB_1 * verzerrung), 0), winkel, F_{12}) → G_{12}
  211. Rotate(E_{12} + ((sliderB_1 * verzerrung), 0), winkel, E_{12}) → H_{12}
  212. Segment(A_{12}, B_{12}) → s_{11}
  213. Segment(B_{12}, F_{12}) → t_{11}
  214. Segment(F_{12}, E_{12}) → a_{22}
  215. Segment(E_{12}, A_{12}) → b_{22}
  216. Segment(A_{12}, D_{12}) → c_{22}
  217. Segment(D_{12}, H_{12}) → d_{11}
  218. Segment(B_{12}, C_{12}) → e_{22}
  219. Segment(E_{12}, H_{12}) → f_{12}
  220. Segment(H_{12}, G_{12}) → g_{12}
  221. Segment(F_{12}, G_{12}) → h_{12}
  222. Segment(G_{12}, C_{12}) → i_{12}
  223. Segment(D_{12}, C_{12}) → j_{12}
  224. Polygon(E_{12}, H_{12}, G_{12}, C_{12}, B_{12}, A_{12}) → poly1_{11}, e_{23}, k_{12}, l_{12}, c_{23}, b_{23}, a_{23}
  225. Rotate(B_{13} + ((sliderB_1 * verzerrung), 0), winkel, B_{13}) → C_{13}
  226. Rotate(A_{13} + ((sliderB_1 * verzerrung), 0), winkel, A_{13}) → D_{13}
  227. Rotate(F_{13} + ((sliderB_1 * verzerrung), 0), winkel, F_{13}) → G_{13}
  228. Rotate(E_{13} + ((sliderB_1 * verzerrung), 0), winkel, E_{13}) → H_{13}
  229. Segment(A_{13}, B_{13}) → s_{12}
  230. Segment(B_{13}, F_{13}) → t_{12}
  231. Segment(F_{13}, E_{13}) → a_{24}
  232. Segment(E_{13}, A_{13}) → b_{24}
  233. Segment(A_{13}, D_{13}) → c_{24}
  234. Segment(D_{13}, H_{13}) → d_{12}
  235. Segment(B_{13}, C_{13}) → e_{24}
  236. Segment(E_{13}, H_{13}) → f_{13}
  237. Segment(H_{13}, G_{13}) → g_{13}
  238. Segment(F_{13}, G_{13}) → h_{13}
  239. Segment(G_{13}, C_{13}) → i_{13}
  240. Segment(D_{13}, C_{13}) → j_{13}
  241. Polygon(E_{13}, H_{13}, G_{13}, C_{13}, B_{13}, A_{13}) → poly1_{12}, e_{25}, k_{13}, l_{13}, c_{25}, b_{25}, a_{25}
  242. Rotate(B_{14} + ((sliderB_1 * verzerrung), 0), winkel, B_{14}) → C_{14}
  243. Rotate(A_{14} + ((sliderB_1 * verzerrung), 0), winkel, A_{14}) → D_{14}
  244. Rotate(F_{14} + ((sliderB_1 * verzerrung), 0), winkel, F_{14}) → G_{14}
  245. Rotate(E_{14} + ((sliderB_1 * verzerrung), 0), winkel, E_{14}) → H_{14}
  246. Segment(A_{14}, B_{14}) → s_{13}
  247. Segment(B_{14}, F_{14}) → t_{13}
  248. Segment(F_{14}, E_{14}) → a_{26}
  249. Segment(E_{14}, A_{14}) → b_{26}
  250. Segment(A_{14}, D_{14}) → c_{26}
  251. Segment(D_{14}, H_{14}) → d_{13}
  252. Segment(B_{14}, C_{14}) → e_{26}
  253. Segment(E_{14}, H_{14}) → f_{14}
  254. Segment(H_{14}, G_{14}) → g_{14}
  255. Segment(F_{14}, G_{14}) → h_{14}
  256. Segment(G_{14}, C_{14}) → i_{14}
  257. Segment(D_{14}, C_{14}) → j_{14}
  258. Polygon(E_{14}, H_{14}, G_{14}, C_{14}, B_{14}, A_{14}) → poly1_{13}, e_{27}, k_{14}, l_{14}, c_{27}, b_{27}, a_{27}
  259. Rotate(B_{15} + ((sliderB_1 * verzerrung), 0), winkel, B_{15}) → C_{15}
  260. Rotate(A_{15} + ((sliderB_1 * verzerrung), 0), winkel, A_{15}) → D_{15}
  261. Rotate(F_{15} + ((sliderB_1 * verzerrung), 0), winkel, F_{15}) → G_{15}
  262. Rotate(E_{15} + ((sliderB_1 * verzerrung), 0), winkel, E_{15}) → H_{15}
  263. Segment(A_{15}, B_{15}) → s_{14}
  264. Segment(B_{15}, F_{15}) → t_{14}
  265. Segment(F_{15}, E_{15}) → a_{28}
  266. Segment(E_{15}, A_{15}) → b_{28}
  267. Segment(A_{15}, D_{15}) → c_{28}
  268. Segment(D_{15}, H_{15}) → d_{14}
  269. Segment(B_{15}, C_{15}) → e_{28}
  270. Segment(E_{15}, H_{15}) → f_{15}
  271. Segment(H_{15}, G_{15}) → g_{15}
  272. Segment(F_{15}, G_{15}) → h_{15}
  273. Segment(G_{15}, C_{15}) → i_{15}
  274. Segment(D_{15}, C_{15}) → j_{15}
  275. Polygon(E_{15}, H_{15}, G_{15}, C_{15}, B_{15}, A_{15}) → poly1_{14}, e_{29}, k_{15}, l_{15}, c_{29}, b_{29}, a_{29}
  276. If(bsp ≟ 1, CountIf[x ≟ 0, Bsp1], If[bsp ≟ 2, CountIf[x ≟ 0, Bsp2], If[bsp ≟ 3, CountIf[x ≟ 0, Bsp3], If[bsp ≟ 4, CountIf[x ≟ 0, Bsp4], If[bsp ≟ 5, CountIf[x ≟ 0, Bsp5], If[bsp ≟ 6, CountIf[x ≟ 0, Bsp6], If[bsp ≟ 7, CountIf[x ≟ 0, Bsp7], If[bsp ≟ 8, CountIf[x ≟ 0, Bsp8]]]]]]]]) → every
  277. Textfield(aInput) → InputBox1
  278. Midpoint(A, B) → M
  279. Midpoint(B, C) → N
  280. Midpoint(A, E) → O
  281. Rotate(B_{16} + ((sliderB_1 * verzerrung), 0), winkel, B_{16}) → C_{16}
  282. Rotate(F_{16} + ((sliderB_1 * verzerrung), 0), winkel, F_{16}) → G_{16}
  283. Rotate(E_{16} + ((sliderB_1 * verzerrung), 0), winkel, E_{16}) → H_{16}
  284. Segment(A_{16}, B_{16}) → s_{15}
  285. Segment(B_{16}, F_{16}) → t_{15}
  286. Segment(F_{16}, E_{16}) → a_{31}
  287. Segment(E_{16}, A_{16}) → b_{31}
  288. Segment(B_{16}, C_{16}) → e_{31}
  289. Segment(E_{16}, H_{16}) → f_{16}
  290. Segment(H_{16}, G_{16}) → g_{16}
  291. Segment(F_{16}, G_{16}) → h_{16}
  292. Segment(G_{16}, C_{16}) → i_{17}
  293. Polygon(E_{16}, H_{16}, G_{16}, C_{16}, B_{16}, A_{16}) → poly1_{15}, e_{30}, k_{17}, l_{17}, c_{30}, b_{30}, a_{30}
  294. Rotate(A_{16} + ((sliderB_1 * verzerrung), 0), winkel, A_{16}) → P
  295. Segment(A_{16}, P) → m_1
  296. Segment(P, C_{16}) → n_1
  297. Segment(P, H_{16}) → p_1
  298. Polygon(A, B, C, G, H, E) → poly2, q_1, r_1, m_2, n_2, p_2, q_2

AI 绘图提示语参考

绘制一个长方体，并用单位立方体填充它。首先，创建长方体的六个面，然后使用旋转和平移操作将这些面复制并排列成一个网格。接着，计算并显示在不同单位立方体大小下能容纳多少个单位立方体，以及这些单位立方体的总体积。
以上提示语为根据原始绘图命令整理而来，仅供参考。