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旗帜周长与面积动态演示

旗帜周长与面积动态演示
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2015-12-29 07:28
圆多边形向量微积分几何作图
① 该范例演示如何通过几何作图构造一面旗帜形状，并实时计算其周长与面积。② 涉及核心数学概念包括周长、面积、微积分求积分、二维向量、交点求解、二次方程及缩放变换。③ 作图要点：使用 Segment、Point、Circle、Intersect、OrthogonalLine、Polygon、PointIn 等命令，配合大量点对象（A、B、C、D、E、F、G、H、I、J、K、L、M、N、O、P、Q、R、S、T、U、V、W、Z、A_1、B_1、C_1、D_1 等）构建旗帜轮廓并标记内部区域。④ 适合高中几何、微积分及向量教学，也可作为大学几何建模与动态演示的教学素材。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. Segment(A, C) → b
  3. Segment(C, D) → c
  4. Segment(D, B) → d
  5. Point(b) → E
  6. Circle(E, e / 2) → f
  7. Point(d) → F
  8. Circle(F, e / 2) → g
  9. Point(a) → G
  10. Circle(G, e / 2) → h
  11. Point(c) → H
  12. Circle(H, e / 2) → k
  13. Intersect(f, b) → I, J
  14. Intersect(h, a) → K, L
  15. Intersect(d, xAxis) → M
  16. Intersect(d, xAxis) → N
  17. Intersect(d, xAxis) → O
  18. Intersect(d, xAxis) → P
  19. Intersect(d, xAxis) → Q
  20. Intersect(d, xAxis) → R
  21. Intersect(d, xAxis) → S
  22. Intersect(k, c) → T, U
  23. Intersect(d, xAxis) → V
  24. Intersect(d, xAxis) → W
  25. Intersect(d, xAxis) → Z
  26. Intersect(d, xAxis) → A_1
  27. Segment(B, D) → i
  28. Intersect(d, i) → B_1
  29. Intersect(d, i) → C_1
  30. Intersect(d, i) → D_1
  31. OrthogonalLine(I, b) → j
  32. OrthogonalLine(J, b) → l
  33. Intersect(j, d) → E_1
  34. Intersect(l, d) → F_1
  35. Segment(I, E_1) → m
  36. Segment(J, F_1) → n
  37. Intersect(b, n) → G_1
  38. Segment(K, T) → p
  39. Segment(U, L) → q
  40. Intersect(p, m) → H_1
  41. Intersect(q, m) → I_1
  42. Intersect(p, n) → J_1
  43. Intersect(q, n) → K_1
  44. Intersect(a, p) → L_1
  45. Polygon(I, H_1, J_1, G_1, L_1, L, I_1, E_1, F_1, K_1, U, T) → poly1, i_1, t, j_1, g_1, h_1, l_1, l_2, i_2, e_1, f_1, k_1, u
  46. PointIn(poly1) → Pointpoly1
  47. Segment(I, G_1) → r
  48. Segment(L_1, H_1) → a_1
  49. Segment(I, H_1) → b_1
  50. Segment(L_1, L) → c_1
  51. Intersect(a_1, b_1) → N_1
  52. Segment(L_1, N_1) → q_1
  53. Segment(L, I_1) → r_1
  54. Segment(I_1, E_1) → s_1
  55. Segment(K_1, U) → t_1
  56. Segment(G_1, J_1) → a_2
  57. Segment(I, N_1) → b_2
  58. Segment(K_1, F_1) → c_2
  59. Segment(J_1, T) → d_2