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立方体展开图 by Guillermo Bautista

立方体展开图 by Guillermo Bautista
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2020-03-03 10:07
多边形立体几何几何作图
①本范例演示了立方体的一个展开图；②涉及的核心数学概念包括立体几何、多边形构造；③作图要点——从下方『构造摘要』提炼用到了Polygon（多边形）、Line（线段）、Rotate（旋转）、Point（点）、Vector（向量）、Translate（平移）等GeoGebra命令/对象；④适合高中阶段学习立体几何的学生或用于教学演示。

GeoGebra 命令及参数

  1. Polygon(A, B, 4, xOyPlane) → poly1, f, g, h, i, C, D
  2. Polygon(D, C, 4, xOyPlane) → poly2, j, k, l, m, E, F
  3. Polygon(F, E, 4, xOyPlane) → poly3, n, p_1, q, r, G, H
  4. Polygon(H, G, 4, xOyPlane) → poly4, s, t, a, b, I, J
  5. Polygon(D, F, 4, xOyPlane) → poly5, c, d, e, f_1, K, L
  6. Polygon(E, C, 4, xOyPlane) → poly6, g_1, h_1, i_1, j_1, M, N
  7. Line(D, F) → k_1
  8. Rotate(poly5, p, k_1) → poly5'
  9. Rotate(poly5, 90°, k_1) → poly5'_1
  10. Line(D, C) → l_1
  11. Rotate(poly1, (-(p - π / 2)), l_1) → poly1'
  12. Rotate(poly1, (-(90°)), l_1) → poly1'_1
  13. Line(C, E) → m_1
  14. Rotate(poly6, (-(p - π)), m_1) → poly6'
  15. Rotate(poly6, (-(90°)), m_1) → poly6'_1
  16. Line(F, E) → n_1
  17. Rotate(poly6'_1, (-(p - (3 * π / 2))), n_1) → q1
  18. Rotate(poly2, (-(p - (3 * π / 2))), n_1) → poly2'
  19. Rotate(poly1'_1, (-(p - (3 * π / 2))), n_1) → q2
  20. Rotate(poly5'_1, (-(p - (3 * π / 2))), n_1) → q3
  21. Polygon(G, E, 4, xOyPlane) → poly7, q_1, r_1, s_1, t_1, O, P
  22. Polygon(F, H, 4, xOyPlane) → poly8, a_1, b_1, c_1, d_1, Q, R
  23. Rotate(poly8, 90°, k_1) → poly8'
  24. Rotate(poly7, (-(90°)), m_1) → poly7'
  25. Rotate(poly2, (-(90°)), n_1) → poly2'_1
  26. Point(zAxis) → S
  27. Point(zAxis) → T
  28. Vector(S, T) → u
  29. Translate(poly3, u) → poly3'
  30. Line(Q, P) → e_1
  31. Rotate(poly7, (-(90°)), m_1) → poly7'_1
  32. Rotate(poly7'_1, (-(p - (2 * π))), e_1) → q4
  33. Rotate(poly8, 90°, k_1) → poly8'_1
  34. Rotate(poly8'_1, (-(p - (2 * π))), e_1) → q5
  35. Rotate(poly2, (-(90°)), n_1) → poly2'_2
  36. Rotate(poly2'_2, (-(p - (2 * π))), e_1) → q6
  37. Polygon(U, V, W, Z) → q7, u_1, v, w, z_1
  38. Rotate(q7, (-(p - (2 * π))), e_1) → q7'
  39. Rotate(poly3, (-(p - (2 * π))), e_1) → poly3'_1