积极 AI Logo 积极 AI

七巧板拼图

七巧板拼图
几何画板及绘图内容加载中，请稍等……
2020-07-11 12:31
多边形角变换几何作图
①本范例演示如何使用七巧板拼出各种图形；②涉及的核心数学概念包括几何图形拼接、对称、旋转、平移等；③作图要点：从下方『构造摘要』提炼用到了 Point（点）、Segment（线段）、Polygon（多边形）、Rotate（旋转）、Circle（圆）等 GeoGebra 命令/对象；④适合初中生学习几何作图和空间想象能力。

GeoGebra 命令及参数

  1. Point(Circle[C, a]) → D
  2. Segment(C, D) → b
  3. Semicircle(C, D) → c
  4. Midpoint(b) → E
  5. OrthogonalLine(E, b) → d
  6. Intersect(c, d, 1) → F
  7. Polygon(D, F, C) → poly1, c_1, d_1, f
  8. Point(Circle[G, a]) → H
  9. Segment(G, H) → e
  10. Semicircle(G, H) → g
  11. Midpoint(e) → I
  12. OrthogonalLine(I, e) → h
  13. Intersect(g, h, 1) → J
  14. Polygon(G, H, J) → poly2, j, g_1, h_1
  15. Point(Circle[A, a / 2]) → B
  16. Segment(A, B) → i
  17. OrthogonalLine(A, i) → k
  18. Circle(A, B) → p
  19. Intersect(p, k, 2) → K
  20. Polygon(A, B, K) → poly3, k_1, a_1, b_1
  21. Point(Circle[L, a / 2]) → M
  22. Segment(L, M) → l
  23. Semicircle(L, M) → q
  24. Midpoint(l) → N
  25. OrthogonalLine(N, l) → m
  26. Intersect(q, m, 1) → O
  27. Polygon(L, M, O) → poly4, o, l_1, m_1
  28. Point(Circle[P, a / 2]) → Q
  29. Segment(P, Q) → n
  30. Semicircle(P, Q) → r
  31. Midpoint(n) → R
  32. OrthogonalLine(R, n) → s
  33. Intersect(r, s, 1) → S
  34. Polygon(P, Q, S) → poly5, s_1, p_1, q_1
  35. Point(Circle[T, (a * sqrt(2) / 4)]) → U
  36. Segment(T, U) → t
  37. OrthogonalLine(T, t) → e_1
  38. OrthogonalLine(U, t) → f_1
  39. Circle(T, U) → r_1
  40. Circle(U, T) → t_1
  41. Intersect(t_1, f_1, 2) → V
  42. Intersect(r_1, e_1, 2) → W
  43. Polygon(T, U, V, W) → poly6, t_2, u, v, w
  44. Point(Circle[Z, a / 2]) → A_1
  45. Segment(Z, A_1) → i_1
  46. Rotate(Z, 315°, A_1) → Z'
  47. Angle(Z', A_1, Z) → α
  48. Ray(A_1, Z') → j_1
  49. Circle(A_1, (a * sqrt(2) / 4)) → c_2
  50. Intersect(c_2, j_1, 1) → B_1
  51. Line(Z, j_1) → n_1
  52. Line(B_1, i_1) → a_2
  53. Intersect(n_1, a_2) → C_1
  54. Polygon(A_1, B_1, C_1, Z) → poly7, a_3, b_2, c_3, z
  55. Point(Circle[D_1, a]) → E_1