积极 AI Logo 积极 AI

二项式展开立方体模型

二项式展开立方体模型
几何画板及绘图内容加载中，请稍等……
2016-11-08 07:37
向量函数立体几何几何作图
该范例通过三维立方体及其棱、面、顶点等几何元素，直观演示二项式展开的几何意义。核心数学概念是二项式定理与立体几何的结合，将(a+b)^3的展开项与立方体的体积分割对应起来。作图要点：使用GeoGebra的Vector、Cube、Prism命令构建立方体，并定义多个向量（vector_0至vector_8）和点（A至K），以及面（faceABCD等）和棱（edgeAD等）对象，通过三维空间中的几何构造展示展开式的各项。适合高中或大学低年级学生，用于理解二项式展开的代数与几何联系，也可作为数学建模或可视化教学的素材。

GeoGebra 命令及参数

  1. Vector((-4, -4, -4)) → vector_0
  2. Vector((0, 0, 0), (-1, -1, -1)) → vector_1
  3. Vector((0, 0, 0), (1, -1, 1)) → vector_6
  4. Vector((0, 0, 0), (-1, -1, 1)) → vector_5
  5. Vector((0, 0, 0), (-1, 1, 1)) → vector_8
  6. Vector((0, 0, 0), (1, 1, 1)) → vector_7
  7. Vector((0, 0, 0), (-1, 1, -1)) → vector_4
  8. Vector((0, 0, 0), (1, 1, -1)) → vector_3
  9. Vector((0, 0, 0), (1, -1, -1)) → vector_2
  10. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  11. Cube(I, J, K) → b, L, faceKLPO, faceMNOP, edgeIL, edgeIJ, edgeJK, edgeKL, edgeIM, edgeLP, edgeMP, edgeMN, M, edgeJN, edgeNO, edgeKO, edgeOP, N, O, P, faceIJKL, faceILPM, faceIJNM, faceJKON
  12. Prism(Q, R, S, T, Z) → c, U, edgeQR, edgeRS, edgeST, edgeQT, edgeQZ, edgeRU, edgeSV, edgeTW, edgeUZ, edgeUV, V, edgeVW, edgeWZ, W, faceQRST, faceQRUZ, faceRSVU, faceSTWV, faceQTWZ, faceUVWZ
  13. Prism(A_1, B_1, C_1, D_1, H_1) → d, E_1, edge1, edge4, edge6, edge2, edge3, edge5, edge7, edge8, edge9, edge11, F_1, edge12, edge10, G_1, face1, face2, face4, face5, face3, face6
  14. Prism(I_1, J_1, K_1, L_1, M_1) → e, N_1, edge13, edge16, edge18, edge14, edge15, edge17, edge19, edge20, edge21, edge23, O_1, edge24, edge22, P_1, face7, face8, face10, face11, face9, face12
  15. Prism(Q_1, R_1, S_1, T_1, U_1) → f, V_1, edge25, edge28, edge30, edge26, edge27, edge29, edge31, edge32, edge33, edge35, W_1, edge36, edge34, Z_1, face13, face14, face16, face17, face15, face18
  16. Prism(A_2, B_2, C_2, D_2, E_2) → g, F_2, edge37, edge40, edge42, edge38, edge39, edge41, edge43, edge44, edge45, edge47, G_2, edge48, edge46, H_2, face19, face20, face22, face23, face21, face24
  17. Prism(I_2, J_2, K_2, L_2, M_2) → h, N_2, edge49, edge52, edge54, edge50, edge51, edge53, edge55, edge56, edge57, edge59, O_2, edge60, edge58, P_2, face25, face26, face28, face29, face27, face30