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立方体三维可视化

立方体三维可视化
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2015-11-09 12:06
多边形立体几何几何作图
所属专题 Algebra II|CH7: Polynomial Functions
这个GeoGebra范例演示了一个三维立方体的构造与可视化，展示了如何在三维空间中通过几何命令构建多面体模型。涉及的核心数学概念包括立体几何、空间坐标系、多边形和棱柱的生成，以及重心或质心的计算原理。作图要点方面，使用了GeoGebra的Intersect命令求交点、Point命令创建关键点、Polygon命令绘制多边形面、Cube和Prism命令生成立方体和棱柱结构；对象包括从A到R的多个点，以及poly1、poly2等多边形，辅助构建完整模型。此范例适合高中或大学低年级的立体几何教学，用于帮助学生理解三维几何形状的构造过程和性质，也可用于教师演示或自主学习。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Point(xAxis) → C
  4. Point(yAxis) → F
  5. Point(yAxis) → G
  6. Polygon(B, C, D, E) → poly1, b, c, d, e
  7. Polygon(B, A, F, E) → poly2, b_1, a, f, e_1
  8. Polygon(F, G, H, E) → poly3, f_1, g, h, e_2
  9. Polygon(D, E, H, I) → poly4, d_1, e_3, h_1, i
  10. Point(Circle[J, Distance[C, J], Segment[C, J]]) → S
  11. Cube(C, J, S) → j, T, faceSTZW, faceUVWZ, edgeCT, edgeCJ, edgeJS, edgeST, edgeCU, edgeTZ, edgeUZ, edgeUV, U, edgeJV, edgeVW, edgeSW, edgeWZ, V, W, Z, faceCJST, faceCTZU, faceCJVU, faceJSWV
  12. Prism(poly2, -4) → k, A_1, edge2, edge1, edge4, edge3, edge5, edge7, edge8, edge6, B_1, C_1, D_1, face1, face2, face4, face3, face5
  13. Prism(poly4, -4) → l, E_1, edge9, edge10, edge11, edge12, edge13, edge15, edge16, edge14, F_1, G_1, H_1, face6, face8, face9, face7, face10
  14. Prism(poly3, -4) → m, I_1, edge18, edge19, edge20, edge17, edge21, edge23, edge24, edge22, J_1, K_1, L_1, face13, face14, face12, face11, face15
  15. Polygon(J, K, N, M) → poly5, j_1, k_1, n, m_1
  16. Prism(poly5, 2) → o, V_1, edge25, edge26, edge28, edge27, edge29, edge31, edge32, edge30, W_1, Z_1, A_2, face16, face18, face19, face17, face20
  17. Polygon(O, N, K, L) → poly6, o_1, n_1, k_2, l_1
  18. Prism(poly6, 2) → p, B_2, edge36, edge35, edge33, edge34, edge37, edge39, edge40, edge38, C_2, D_2, E_2, face24, face22, face21, face23, face25
  19. Polygon(N, Q, P, M) → poly7, n_2, q, p_1, m_2
  20. Prism(poly7, 2) → r, F_2, edge42, edge44, edge43, edge41, edge45, edge47, edge48, edge46, G_2, H_2, I_2, face28, face29, face27, face26, face30
  21. Polygon(N, O, R, Q) → poly8, n_3, o_2, r_1, q_1
  22. Prism(poly8, 2) → s, J_2, edge49, edge50, edge52, edge51, edge53, edge55, edge56, edge54, K_2, L_2, M_2, face31, face33, face34, face32, face35