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正方形与等边三角形

正方形与等边三角形
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2019-03-21 00:46
多边形三角函数几何作图
所属专题 Cutting up squares
①本范例演示正方形与等边三角形的几何关系与构造；②涉及核心数学概念包括多边形、几何变换、对称性、角度等；③作图要点提炼自构造摘要，使用了Intersect（交点）、Point（点）、Polygon（多边形）、Segment（线段）、Midpoint（中点）、Circle（圆）、Ray（射线）、OrthogonalLine（垂线）、Rotate（旋转）、Line（直线）等GeoGebra命令与对象；④适合高中数学教学，用于几何作图与变换教学。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 3) → poly1, a, a_1, b, C
  4. Segment(A, B) → c
  5. Segment(B, C) → d
  6. Segment(C, A) → e
  7. Midpoint(d) → D
  8. Midpoint(e) → E
  9. Circle(D, C) → f
  10. Ray(A, D) → g
  11. Intersect(f, g) → F_1, F
  12. Midpoint(A, F) → G
  13. Circle(G, F) → h
  14. Ray(B, C) → i
  15. Intersect(h, i) → H,
  16. Circle(D, H) → k
  17. Intersect(k, c, 1) → J
  18. Circle(J, Segment[C, D]) → p
  19. Intersect(p, c, 1) → K
  20. Segment(J, D) → j
  21. OrthogonalLine(E, j) → l
  22. Intersect(l, j) → N
  23. OrthogonalLine(K, j) → m
  24. Intersect(m, j) → R
  25. Segment(E, N) → n
  26. Segment(K, R) → q
  27. Polygon(C, D, N, E) → poly2, c_1, d_1, n_1, e_1
  28. Polygon(D, B, K, R) → poly3, d_2, b_1, k_1, r
  29. Polygon(J, K, R) → poly4, r_1, j_1, k_2
  30. Polygon(A, J, N, E) → poly5, a_2, j_2, n_2, e_2
  31. Rotate(C, (-α), D) → C'_1
  32. Rotate(D, (-α), D) → D'
  33. Rotate(N, (-α), D) → N'_1
  34. Rotate(E, (-α), D) → E'_1
  35. Polygon(C'_1, D', N'_1, E'_1) → poly2', c', d', n', e'_1
  36. Rotate(J, α, K) → J'_1
  37. Rotate(K, α, K) → K'
  38. Rotate(R, α, K) → R'
  39. Polygon(J'_1, K', R') → poly4', r', j', k'
  40. Rotate(A, α, K') → A'
  41. Rotate(J, α, K') → J'
  42. Rotate(N, α, K') → N'
  43. Rotate(E, α, K') → E'
  44. Polygon(A', J', N', E') → poly5', a', j'_1, n'_1, e'
  45. Intersect(b, e) → I
  46. Intersect(a_1, d) → L
  47. Intersect(b, e) → M
  48. Intersect(a_1, d) → O
  49. Point(poly1) → P
  50. Line(N, R) → s
  51. Circle(D', N') → t
  52. Line(N, D') → f_1
  53. Circle(D', N) → g_1
  54. Intersect(g_1, f_1, 2) → Q
  55. Polygon(Q, R, 4) → poly6, q_1, r_2, h_1, i_1, S, T
  56. Circle(Q, D') → p_1
  57. Point(poly6) → U
  58. Polygon(D', Q, U, B) → poly7, d'_1, q_2, u, b_2
  59. Circle(K', J) → s_1
  60. Point(poly6) → V
  61. Polygon(K', V, S) → poly8, s_2, k'_1, v
  62. Polygon(B, U, T, V) → poly9, b_3, u_1, t_1, v_1
  63. Rotate(B, α - 360°, V) → B'
  64. Rotate(U, α - 360°, V) → U'
  65. Rotate(T, α - 360°, V) → T'
  66. Rotate(V, α - 360°, V) → V'
  67. Polygon(B', U', T', V') → poly9', b', u', t', v'