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正交框架演示

正交框架演示
几何画板及绘图内容加载中，请稍等……
2018-07-06 15:00
多边形数列解析几何
①本范例演示了正交框架的几何构造与性质；②涉及的核心数学概念包括解析几何、多边形构造、数列应用；③作图要点：使用 GeoGebra 命令如 Cube（立方体）、Polygon（多边形）、Sequence（数列）等构建框架；④适合高中数学教学，用于理解空间几何与解析几何的结合应用。

GeoGebra 命令及参数

  1. Cube(C1, A1, B1) → D1, E1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, F1, X1, Y1, Z1, AA1, G1, H1, I1, J1, K1, L1, M1
  2. Cube(C2, A2, B2) → D2, E2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2, F2, X2, Y2, Z2, AA2, G2, H2, I2, J2, K2, L2, M2
  3. Cube(C3, A3, B3) → D3, E3, N3, O3, P3, Q3, R3, S3, T3, U3, V3, W3, F3, X3, Y3, Z3, AA3, G3, H3, I3, J3, K3, L3, M3
  4. Cube(C4, A4, B4) → D4, E4, N4, O4, P4, Q4, R4, S4, T4, U4, V4, W4, F4, X4, Y4, Z4, AA4, G4, H4, I4, J4, K4, L4, M4
  5. Cube(C5, A5, B5) → D5, E5, N5, O5, P5, Q5, R5, S5, T5, U5, V5, W5, F5, X5, Y5, Z5, AA5, G5, H5, I5, J5, K5, L5, M5
  6. Cube(C6, A6, B6) → D6, E6, N6, O6, P6, Q6, R6, S6, T6, U6, V6, W6, F6, X6, Y6, Z6, AA6, G6, H6, I6, J6, K6, L6, M6
  7. Cube(C7, A7, B7) → D7, E7, N7, O7, P7, Q7, R7, S7, T7, U7, V7, W7, F7, X7, Y7, Z7, AA7, G7, H7, I7, J7, K7, L7, M7
  8. Cube(C8, A8, B8) → D8, E8, N8, O8, P8, Q8, R8, S8, T8, U8, V8, W8, F8, X8, Y8, Z8, AA8, G8, H8, I8, J8, K8, L8, M8
  9. Polygon(C1, E1, B2, A2) → q1, c1, e1, b2, a2
  10. Polygon(C1, F1, G2, A2) → q2, c1_1, f1, g2, a2_1
  11. Polygon(F1, G2, H2, I1) → q3, f1_1, g2_1, h2, i1
  12. Polygon(E1, B2, H2, I1) → q4, e1_1, b2_1, h2_1, i1_1
  13. Sequence(PolyLine[C1 - (i, 0, 0), E1 - (i, 0, 0), I1 - (i, 0, 0), F1 - (i, 0, 0), C1 - (i, 0, 0)], i, 1, a - 3) → lista_1
  14. Polygon(F3, G4, A4, C3) → q5, f3, g4, a4, c3
  15. Polygon(F3, G4, H4, I3) → q6, f3_1, g4_1, h4, i3
  16. Polygon(E3, B4, H4, I3) → q7, e3, b4, h4_1, i3_1
  17. Polygon(C3, A4, B4, E3) → q8, c3_1, a4_1, b4_1, e3_1
  18. Sequence(PolyLine[C3 - (i, 0, 0), E3 - (i, 0, 0), I3 - (i, 0, 0), F3 - (i, 0, 0), C3 - (i, 0, 0)], i, 1, a - 3) → lista_2
  19. Polygon(C5, A6, G6, F5) → q9, c5, a6, g6, f5
  20. Polygon(F5, G6, H6, I5) → q10, f5_1, g6_1, h6, i5
  21. Polygon(E5, B6, H6, I5) → q11, e5, b6, h6_1, i5_1
  22. Polygon(C5, A6, B6, E5) → q12, c5_1, a6_1, b6_1, e5_1
  23. Polygon(C7, A8, G8, F7) → q13, c7, a8, g8, f7
  24. Polygon(F7, G8, H8, I7) → q14, f7_1, g8_1, h8, i7
  25. Polygon(E7, B8, H8, I7) → q15, e7, b8, h8_1, i7_1
  26. Polygon(C7, A8, B8, E7) → q16, c7_1, a8_1, b8_1, e7_1
  27. Sequence(PolyLine[C5 - (i, 0, 0), E5 - (i, 0, 0), I5 - (i, 0, 0), F5 - (i, 0, 0), C5 - (i, 0, 0)], i, 1, a - 3) → lista_3
  28. Sequence(PolyLine[C7 - (i, 0, 0), E7 - (i, 0, 0), I7 - (i, 0, 0), F7 - (i, 0, 0), C7 - (i, 0, 0)], i, 1, a - 3) → lista_4
  29. Polygon(F1, C5, E5, I1) → q17, f1_2, c5_2, e5_2, i1_2
  30. Polygon(F1, G1, A5, C5) → q18, f1_3, g1, a5, c5_3
  31. Polygon(H1, G1, A5, B5) → q19, h1, g1_1, a5_1, b5
  32. Polygon(I1, H1, B5, E5) → q20, i1_3, h1_1, b5_1, e5_3
  33. Polygon(F2, G2, A6, C6) → q21, f2, g2_2, a6_2, c6
  34. Polygon(F2, I2, E6, C6) → q22, f2_1, i2, e6, c6_1
  35. Polygon(G2, H2, B6, A6) → q23, g2_3, h2_2, b6_2, a6_3
  36. Polygon(H2, I2, E6, B6) → q24, h2_3, i2_1, e6_1, b6_3
  37. Polygon(F3, G3, A7, C7) → q25, f3_2, g3, a7, c7_2
  38. Polygon(F3, I3, E7, C7) → q26, f3_3, i3_2, e7_2, c7_3
  39. Polygon(G3, H3, B7, A7) → q27, g3_1, h3, b7, a7_1
  40. Polygon(H3, I3, E7, B7) → q28, h3_1, i3_3, e7_3, b7_1
  41. Polygon(F4, G4, A8, C8) → q29, f4, g4_2, a8_2, c8
  42. Polygon(F4, I4, E8, C8) → q30, f4_1, i4, e8, c8_1
  43. Polygon(G4, H4, B8, A8) → q31, g4_3, h4_2, b8_2, a8_3
  44. Polygon(I4, H4, B8, E8) → q32, i4_1, h4_3, b8_3, e8_1
  45. Sequence(PolyLine[A5 + (0, 0, i), C5 + (0, 0, i), E5 + (0, 0, i), B5 + (0, 0, i), A5 + (0, 0, i)], i, 1, c - 3) → lista_5
  46. Sequence(PolyLine[A6 + (0, 0, i), C6 + (0, 0, i), E6 + (0, 0, i), B6 + (0, 0, i), A6 + (0, 0, i)], i, 1, c - 3) → lista_6
  47. Sequence(PolyLine[A7 + (0, 0, i), C7 + (0, 0, i), E7 + (0, 0, i), B7 + (0, 0, i), A7 + (0, 0, i)], i, 1, c - 3) → lista_7
  48. Sequence(PolyLine[A8 + (0, 0, i), C8 + (0, 0, i), E8 + (0, 0, i), B8 + (0, 0, i), A8 + (0, 0, i)], i, 1, c - 3) → lista_8
  49. Polygon(E1, I1, F3, C3) → q33, e1_2, i1_4, f3_4, c3_2
  50. Polygon(I1, H1, G3, F3) → q34, i1_5, h1_2, g3_2, f3_5
  51. Polygon(B1, H1, G3, A3) → q35, b1, h1_3, g3_3, a3
  52. Polygon(B1, E1, C3, A3) → q36, b1_1, e1_3, c3_3, a3_1
  53. Polygon(I2, H2, G4, F4) → q37, i2_2, h2_4, g4_4, f4_2
  54. Polygon(E2, I2, F4, C4) → q38, e2, i2_3, f4_3, c4
  55. Polygon(B2, H2, G4, A4) → q39, b2_2, h2_5, g4_5, a4_2
  56. Polygon(E2, B2, A4, C4) → q40, e2_1, b2_3, a4_3, c4_1
  57. Polygon(I5, H5, G7, F7) → q41, i5_2, h5, g7, f7_2
  58. Polygon(E5, I5, F7, C7) → q42, e5_4, i5_3, f7_3, c7_4
  59. Polygon(B5, H5, G7, A7) → q43, b5_2, h5_1, g7_1, a7_2
  60. Polygon(B5, E5, C7, A7) → q44, b5_3, e5_5, c7_5, a7_3
  61. Polygon(I6, H6, G8, F8) → q45, i6, h6_2, g8_2, f8
  62. Polygon(E6, I6, F8, C8) → q46, e6_2, i6_1, f8_1, c8_2
  63. Polygon(B6, H6, G8, A8) → q47, b6_4, h6_3, g8_3, a8_4
  64. Polygon(B6, E6, C8, A8) → q48, b6_5, e6_3, c8_3, a8_5
  65. Sequence(PolyLine[A3 + (0, i, 0), C3 + (0, i, 0), F3 + (0, i, 0), G3 + (0, i, 0), A3 + (0, i, 0)], i, 1, b - 3) → lista_9
  66. Sequence(PolyLine[A4 + (0, i, 0), C4 + (0, i, 0), F4 + (0, i, 0), G4 + (0, i, 0), A4 + (0, i, 0)], i, 1, b - 3) → lista_{10}
  67. Sequence(PolyLine[A7 + (0, i, 0), C7 + (0, i, 0), F7 + (0, i, 0), G7 + (0, i, 0), A7 + (0, i, 0)], i, 1, b - 3) → lista_{11}
  68. Sequence(PolyLine[A8 + (0, i, 0), C8 + (0, i, 0), F8 + (0, i, 0), G8 + (0, i, 0), A8 + (0, i, 0)], i, 1, b - 3) → lista_{12}