风筝形与维度

风筝形与维度
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2018-02-26 17:44
①本范例演示风筝形的几何构造及其维度特性;②涉及核心数学概念包括多边形、角度、几何变换(旋转、镜像)、中位线等;③构造过程中运用了Polygon(多边形)、Segment(线段)、CircleArc(圆弧)、Rotate(旋转)、LineBisector(角平分线)、Intersect(交点)、Mirror(镜像)、OrthogonalLine(垂线)等GeoGebra命令;④适合高中数学几何学习,用于理解多边形性质及变换应用。

GeoGebra 命令及参数

  1. Polygon(A, C, D, B) → vierhoek1, a, c, d, b
  2. Segment(B, E) → f
  3. CircleArc(B, DD, D) → e
  4. Polygon(A, C, E, B) → vierhoek2, a_1, c_1, e_1, b_1
  5. Polygon(B, E, D) → driehoek1, d_1, b_2, e_2
  6. Rotate(B, (((s - 1) * 180))°, d_1) → B'
  7. Rotate(E, (((s - 1) * 180))°, d_1) → E'
  8. Rotate(D, (((s - 1) * 180))°, d_1) → D'
  9. Polygon(B', E', D') → driehoek1', d', b', e'
  10. Polygon(DD, E, B) → driehoek2, b_3, dd, e_3
  11. LineBisector(DD, C) → g
  12. Intersect(g, a_1) → F
  13. Intersect(g, e_1) → G
  14. Segment(F, G) → h
  15. CircleArc(D, DD, C) → k
  16. Polygon(B, A, F, G) → vierhoek3, b_4, a_2, f_1, g_1
  17. Polygon(F, C, E, G) → vierhoek4, f_2, c_2, e_4, g_2
  18. Rotate(F, (((-(s - 3)) * 180))°, f_1) → F'
  19. Rotate(C, (((-(s - 3)) * 180))°, f_1) → C'
  20. Rotate(E, (((-(s - 3)) * 180))°, f_1) → E'_1
  21. Rotate(G, (((-(s - 3)) * 180))°, f_1) → G'
  22. Polygon(F', C', E'_1, G') → vierhoek4', f', c', e'_1, g'
  23. Mirror(E, f_1) → EE
  24. Polygon(DD, F, G, EE) → vierhoek5, dd_1, f_3, g_3, ee
  25. Intersect(b_3, h) → H
  26. Polygon(DD, H, G, B) → vierhoek6, dd_2, h_1, g_4, b_5
  27. Segment(DD, H) → i
  28. OrthogonalLine(DD, f_1) → j
  29. Intersect(j, f_1) → I
  30. Segment(DD, I) → l
  31. Polygon(B, DD, I, G) → vierhoek7, b_6, dd_3, i_1, g_5
  32. Intersect(b_6, dd_3) → J
  33. Polygon(J, A, F, I) → vierhoek8, j_1, a_3, f_4, i_2
  34. Rotate(J, (((s - 5) * 180))°, i_2) → J'
  35. Rotate(A, (((s - 5) * 180))°, i_2) → A'
  36. Rotate(F, (((s - 5) * 180))°, i_2) → F'_1
  37. Rotate(I, (((s - 5) * 180))°, i_2) → I'
  38. Polygon(J', A', F'_1, I') → vierhoek8', j', a', f'_1, i'
  39. Polygon(J, I, H) → driehoek3, h_2, j_2, i_3
  40. Polygon(DD, I, G, EE) → vierhoek9, dd_4, i_4, g_6, ee_1
  41. CircleArc(DD, A, EE) → p
  42. Segment(B, D) → m
  43. Segment(E, D) → n
  44. Segment(DD, C) → q
  45. Intersect(q, h) → L
  46. Angle(G, L, DD) → α
  47. Intersect(f_1, h_1) → M
  48. Intersect(i, f_1) → N
  49. Segment(N, O) → r
  50. Segment(F, C) → t
  51. Segment(E, C) → k_1
  52. Segment(A, DD) → l_1
  53. Segment(A, C) → m_1
  54. Segment(B, L) → n_1
  55. Segment(I, F) → p_1

AI 绘图提示语参考

绘制一个菱形风筝,包含四边形ABCD、四边形ABEF、三角形BDE、三角形BDE'、四边形BEGF、四边形BEGF'、四边形BDEG、四边形BDEG'、四边形BDEH、四边形BDEH'、四边形BDEI、四边形BDEI'、四边形BDEJ、四边形BDEJ'、四边形BDEK、四边形BDEK'。首先画出四边形ABCD,然后依次构造四边形ABEF、三角形BDE、四边形BEGF、四边形BEGF'、四边形BDEG、四边形BDEG'、四边形BDEH、四边形BDEH'、四边形BDEI、四边形BDEI'、四边形BDEJ、四边形BDEJ'、四边形BDEK、四边形BDEK'。
以上提示语为根据原始绘图命令整理而来,仅供参考。