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正八边形的尺寸

正八边形的尺寸
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2018-02-26 19:50
多边形向量几何作图
所属专题 Folding paper, doing geometry figures
这个范例演示了正八边形的构造及其尺寸关系。涉及的核心数学概念包括多边形、向量和几何作图。通过使用Polygon、Translate、Rotate等GeoGebra命令，可以构造出正八边形并探索其边长和角度。适合初中及以上学生或教师使用。

GeoGebra 命令及参数

  1. Polygon(A, C, D, B) → vierhoek1, a, c, d, b
  2. Segment(DD, E) → f
  3. Vector((0, -0.15)) → u
  4. Polygon(B, DD, E, D) → vierhoek2, b_1, dd, e, d_1
  5. Polygon(A, C, E, DD) → vierhoek3, a_1, c_1, e_1, dd_1
  6. If(s < 1, vierhoek3, If[1 < s ≤ 2, Polygon[Translate[A, Vector[((s - 1) * u)]], Translate[C, Vector[((s - 1) * u)]], Translate[E, Vector[((s - 1) * u)]], Translate[DD, Vector[((s - 1) * u)]]], Polygon[Translate[A, u], Translate[C, u], Translate[E, u], Translate[DD, u]]]) → vierhoek4
  7. Vector(D, B) → v
  8. Translate(afbeelding1, Vector[(1.25 * ((s - 1) * v))]) → afbeelding1'
  9. Segment(B, E) → g
  10. CircleArc(B, DD, D) → h
  11. Segment(DD, D) → i
  12. Polygon(A2, A1, D1, D2) → vierhoek5, a2, a1, d1, d2
  13. Mirror(D, d1) → DB
  14. Mirror(DD, a2) → DDB
  15. CircleArc(D2, DB, D) → k
  16. CircleArc(A2, DD, DDB) → p
  17. Polygon(B, A2, A1, E, D1, D2) → veelhoek1, b_2, a2_1, a1_1, e_2, d1_1, d2_1
  18. Polygon(D1, D, D2) → driehoek1, d2_2, d1_2, d_2
  19. Rotate(D1, (((-(s - 3)) * 180))°, d1) → D1'
  20. Rotate(D, (((-(s - 3)) * 180))°, d1) → D'
  21. Rotate(D2, (((-(s - 3)) * 180))°, d1) → D2'
  22. Polygon(D1', D', D2') → driehoek1', d2', d1', d'
  23. Polygon(D2, DB, D1) → driehoek2, d1_3, d2_3, db
  24. Midpoint(B, E) → M
  25. Rotate(D2, 180°, M) → D2'_1
  26. Rotate(DB, 180°, M) → DB'
  27. Rotate(D1, 180°, M) → D1'_1
  28. Polygon(D2'_1, DB', D1'_1) → driehoek2', d1'_1, d2'_1, db'
  29. Polygon(B, B1, B2) → driehoek4, b2, b_3, b1
  30. Polygon(A2, DD, A1) → driehoek3, a1_2, a2_2, dd_2
  31. Rotate(A2, (((-(s - 3)) * 180))°, a2) → A2'
  32. Rotate(DD, (((-(s - 3)) * 180))°, a2) → DD'
  33. Rotate(A1, (((-(s - 3)) * 180))°, a2) → A1'
  34. Polygon(A2', DD', A1') → driehoek3', a1', a2', dd'
  35. Polygon(B2, B1, A2, A1, C1, C2, D1, D2) → veelhoek2, b2_1, b1_1, a2_3, a1_3, c1, c2, d1_4, d2_4
  36. Polygon(B1, C1, C2, B2) → vierhoek6, b1_2, c1_1, c2_1, b2_2
  37. Segment(DDB, DB) → j
  38. Rotate(B, (((s - 5) * 180))°, b_3) → B'
  39. Rotate(B1, (((s - 5) * 180))°, b_3) → B1'
  40. Rotate(B2, (((s - 5) * 180))°, b_3) → B2'
  41. Polygon(B', B1', B2') → driehoek4', b2', b', b1'
  42. Polygon(B2, B1, A2, A1, C1, C2, D1, D2) → veelhoek3, b2_3, b1_3, a2_4, a1_4, c1_2, c2_2, d1_5, d2_5
  43. Rotate(C1, (((-(s - 5)) * 180))°, c1) → C1'
  44. Rotate(E, (((-(s - 5)) * 180))°, c1) → E'
  45. Rotate(C2, (((-(s - 5)) * 180))°, c1) → C2'
  46. Polygon(C1', E', C2') → driehoek5', c2', c1', e'
  47. Rotate(DDB, 90°, M) → DDB'
  48. Rotate(DB, 90°, M) → DB'_1
  49. Segment(DDB', DB'_1) → j'
  50. Polygon(B1, DB'_1, B2) → driehoek5, b2_4, b1_4, db'_1
  51. Polygon(C1, DDB', C2) → driehoek6, c2_3, c1_3, ddb'
  52. Rotate(B1, (((-(s - 6)) * 45))°, M) → B1'_1
  53. Rotate(C1, (((-(s - 6)) * 45))°, M) → C1'_1
  54. Rotate(C2, (((-(s - 6)) * 45))°, M) → C2'_1
  55. Rotate(B2, (((-(s - 6)) * 45))°, M) → B2'_1
  56. Polygon(B1'_1, C1'_1, C2'_1, B2'_1) → vierhoek6', b1'_1, c1'_1, c2'_1, b2'_1
  57. Mirror(B2, M) → E1
  58. Mirror(B1, M) → E2
  59. Mirror(B, b2_2) → BB
  60. Mirror(BB, M) → EE
  61. CircleArc(B1, BB, B) → q
  62. CircleArc(C1, E, EE) → r
  63. Segment(D2, D) → l
  64. Segment(D1, D) → m
  65. Segment(DD, A1) → n
  66. Segment(DD, A2) → t
  67. Segment(B, B2) → f_1
  68. Segment(B, B1) → g_1
  69. Segment(E, C1) → h_1
  70. Segment(E, C2) → i_1
  71. Polygon(B, B1, B2) → driehoek7, b2_5, b_4, b1_5