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元素H的几何构造与变换

元素H的几何构造与变换
几何画板及绘图内容加载中，请稍等……
2020-05-14 00:44
向量解析几何几何作图
本范例演示了元素H在几何变换中的构造与应用。核心数学概念包括向量变换、几何作图与三维空间中的点定位。作图要点涉及使用GeoGebra命令如Rotate、Segment、Intersect等来构建元素H的图形，并结合Circle、Plane等对象进行空间定位。该范例适合高中生学习几何变换与解析几何，适用于数学教学与自主探索。

GeoGebra 命令及参数

  1. Rotate(B, 45°, A) → B'
  2. Segment(A, B') → f
  3. Intersect(f, yAxis) → C
  4. Circle(C, 0.1) → c
  5. Segment(A, C) → g
  6. Segment(C, B) → h
  7. Intersect(c, g, 1) → D
  8. Intersect(c, h, 1) → E
  9. Circle(O, straal) → d
  10. Intersect(d, xAxis, 1) → F
  11. Intersect(d, xAxis, 2) → G
  12. Semicircle(F, G) → e
  13. Surface((sqrt(straal^(2) - h^(2)) * cos(t)), (sqrt(straal^(2) - h^(2)) * sin(t)), h + (1.5 * straal), t, 0°, 180°, h, 0, straal) → a
  14. Surface((sqrt(straal^(2) - h^(2)) * cos(t)), (sqrt(straal^(2) - h^(2)) * sin(t)), h + (1.5 * straal), t, 0°, 360°, h, 0, straal) → b
  15. Surface((straal * cos(t)), (straal * sin(t)), hh, t, 0°, 180°, hh, 0, (1.5 * straal)) → i
  16. Surface((straal * cos(t)), (straal * sin(t)), hh, t, 0°, 360°, hh, 0, (1.5 * straal)) → j
  17. Segment(L, M) → k
  18. Segment(L, A) → l
  19. Segment(M, B) → m
  20. CircleArc(N, J, P) → p
  21. CircleArc(N, P, I) → q
  22. Point(q) → Q
  23. Point(q) → R
  24. Point(q) → S
  25. Point(q) → T
  26. Point(q) → U
  27. Line(P, k) → r
  28. Line(Q, k) → s
  29. Line(R, k) → t
  30. Line(S, k) → f_1
  31. Line(T, k) → g_1
  32. Line(U, k) → h_1
  33. Intersect(r, l) → V
  34. Intersect(l, s) → W
  35. Intersect(l, t) → Z
  36. Intersect(l, f_1) → A_1
  37. Intersect(l, g_1) → B_1
  38. Intersect(l, h_1) → C_1
  39. Polygon(V, W, Q, P) → vierhoek1, v, w, q_1, p_1
  40. Polygon(W, Z, R, Q) → vierhoek2, w_1, z_1, r_1, q_2
  41. Polygon(Z, A_1, S, R) → vierhoek3, z_2, a_1, s_1, r_2
  42. Polygon(A_1, B_1, T, S) → vierhoek4, i_1, b_1, t_1, s_2
  43. Polygon(B_1, C_1, U, T) → vierhoek5, j_1, c_1, u, t_2
  44. Polygon(C_1, H, I, U) → vierhoek6, k_1, h_2, i_2, u_1
  45. Plane(O, C, P) → sym
  46. Mirror(V, sym) → V'
  47. Polygon(M, V', V, L) → vierhoek7, m_1, v', v_1, l_1
  48. Polygon(L, A, C, D_1) → vierhoek8, l_2, a_2, c_2, d_1
  49. Mirror(vierhoek5, sym) → vierhoek5'
  50. Mirror(vierhoek8, sym) → vierhoek8'
  51. Mirror(vierhoek1, sym) → vierhoek1'
  52. Mirror(vierhoek2, sym) → vierhoek2'
  53. Mirror(vierhoek3, sym) → vierhoek3'
  54. Mirror(vierhoek4, sym) → vierhoek4'
  55. Polygon(H, A, F, I) → vierhoek9, h_3, a_3, f_2, i_3
  56. Mirror(vierhoek9, sym) → vierhoek9'
  57. Mirror(vierhoek6, sym) → vierhoek6'
  58. Polygon(L, M, D_1) → driehoek1, n_1, l_3, m_2
  59. Segment(G, B) → e_1
  60. Segment(A, F) → g_2