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组合体表面积探究：立方体与棱柱的拼接

组合体表面积探究：立方体与棱柱的拼接
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2018-03-06 10:04
多边形立体几何几何作图滑块动画
本范例演示一个由立方体与四棱柱拼接而成的组合体的表面积计算。核心数学概念是立体几何中的表面积、全等（congruence）以及组合体表面积与各面面积的关系。作图要点：使用GeoGebra的Point、Intersect、Cube、Prism命令创建三维对象，包括立方体ABCD-EFGH和棱柱BIJK-LMNO，并定义了多个面（如faceABCD、faceBIJK等）和棱（如edgeAD、edgeAB等），通过随机实验（Random Experiments）和单位圆、正弦等元素辅助理解。适合中学高年级或大学低年级学生用于空间想象和表面积计算的练习，也可作为教师演示组合体表面积分解的直观教具。

GeoGebra 命令及参数

  1. Point(yAxis) → A
  2. Intersect(yAxis, zAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE_1, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Point(xAxis) → I
  6. Point(Circle[I, Distance[B, I], Segment[B, I]]) → J
  7. Cube(B, I, J) → b, K, faceJKON, faceLMNO, edgeBK, edgeBI, edgeIJ, edgeJK, edgeBL, edgeKO, edgeLO, edgeLM, L, edgeIM, edgeMN, edgeJN, edgeNO, M, N, O, faceBIJK, faceBKOL, faceBIML, faceIJNM
  8. Prism(faceBKOL, d) → e, T, edgeLT, edgeBU, edgeKV, edgeOW_1, edgeTU, edgeUV, edgeVW, edgeTW, U, V, W, faceBLTU, faceBKVU, faceKOWV, faceLOWT, faceTUVW
  9. Point(edgeAB) → P
  10. Prism(A, P, Q, E) → c, R, edgeAQ, edgeAE, edgePR, edgeQS, edgeER, edgeRS, edgeES, S, faceAPQ, faceAERP, facePQSR, faceAESQ, faceERS, edgeAP, edgePQ
  11. Prism(faceKOWV, g) → h, D_1, edge8, edge9, edge11, edge10, edge12, edge14, edge15, edge13, E_1, F_1, G_1, face6, face8, face9, face7, face10
  12. Prism(faceJKON, i) → j, H_1, edge17, edge16, edge18, edge19, edge20, edge22, edge23, edge21, I_1, J_1, K_1, face11, face12, face14, face13, face15
  13. Point(xAxis) → Z
  14. Point(Circle[Z, Distance[C, Z], Segment[C, Z]]) → A_1
  15. Cube(C, Z, A_1) → f, B_1, face5, face16, edge1, edgeCZ, edge3, edge5, edge2, edge7, edge25, edge24, C_1, edge4, edge26, edge6, edge27, L_1, M_1, N_1, face1, face3, face2, face4
  16. Prism(face5, l) → m, S_1, edge37, edge36, edge38, edge39, edge40, edge42, edge43, edge41, T_1, U_1, V_1, face22, face23, face25, face24, face26

AI 绘图提示语参考

绘制一个由立方体和棱柱组合而成的立体图形。首先画一个立方体ABCD-EFGH，然后在棱BI上画一个棱柱BIJK-LMNO，接着在棱AB上画一个棱柱APQ-ERS，最后在棱BI上画一个棱柱KOWV-D_1E_1F_1G_1。确保所有棱柱和立方体的面和边正确连接。
以上提示语为根据原始绘图命令整理而来，仅供参考。