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立方体中的十二个菱形

立方体中的十二个菱形
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2019-07-21 22:52
多边形立体几何几何作图
①本范例演示了如何在立方体内部构造十二个相互关联的菱形；②涉及的核心数学概念包括立体几何、多边形性质、角度计算、几何变换；③作图要点提炼自GeoGebra命令：使用了Intersect（交集）、Point（点）、Circle（圆）、Rotate（旋转）、Angle（角度）、Cube（立方体）、Midpoint（中点）、Polygon（多边形）等命令，以及u, A, B, c, C, C', α, C'', β, a, D, E, F, G, H, faceCC'C''D, faceCDHE, faceCC'FE, faceC'C''GF, faceC''DHG, faceEFGH, edgeCD, edgeCC', edgeC'C'', edgeC''D, edgeCE, edgeDH, edgeEH, edgeEF, edgeC'F, edgeFG, edgeC''G, edgeGH, I, J, K, L, M, N, O等对象；④适合高中阶段学生学习和理解空间几何、多边形构造，也可用于数学演示和教学。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Point(c, 1 - u) → C
  5. Rotate(C, 90°, A) → C'
  6. Angle(C, A, C') → α
  7. Rotate(C', 90°, A) → C''
  8. Angle(C', A, C'') → β
  9. Cube(C, C', C'') → a, D, faceC''DHG, faceEFGH, edgeCD, edgeCC', edgeC'C'', edgeC''D, edgeCE, edgeDH, edgeEH, edgeEF, E, edgeC'F, edgeFG, edgeC''G, edgeGH, F, G, H, faceCC'C''D, faceCDHE, faceCC'FE, faceC'C''GF
  10. Midpoint(edgeCD) → I
  11. Midpoint(edgeC''D) → J
  12. Midpoint(edgeGH) → K
  13. Midpoint(edgeFG) → L
  14. Midpoint(edgeEH) → M
  15. Midpoint(edgeC''G) → N
  16. Midpoint(edgeC'C'') → O
  17. Midpoint(edgeCC') → P
  18. Midpoint(edgeDH) → Q
  19. Midpoint(edgeCE) → R
  20. Midpoint(edgeEF) → S
  21. Polygon(C, J, G, S) → q1, c_1, j, g, s
  22. Polygon(C', I, H, L) → q2, c', i, h, l
  23. Polygon(E, K, C'', P) → q3, e, k, c'', p
  24. Polygon(F, R, D, N) → q4, f, r, d, n
  25. Midpoint(edgeC'F) → T
  26. Polygon(E, Q, C'', T) → q5, e_1, q, m, t
  27. Polygon(H, J, C', S) → q6, h_1, j_1, b, s_1
  28. Polygon(E, L, C'', I) → q7, e_2, l_1, f_1, i_1
  29. Polygon(F, K, D, P) → q8, f_2, k_1, d_1, p_1
  30. Polygon(G, M, C, O) → q9, g_1, m_1, c_2, o
  31. Polygon(F, M, D, O) → q10, f_3, m_2, d_2, o_1
  32. Polygon(C', N, H, R) → q11, n_1, n_2, h_2, r_1
  33. Polygon(G, T, C, Q) → q12, g_2, t_1, c_3, q_1