斜圆锥

斜圆锥
几何画板及绘图内容加载中,请稍等……
2020-02-24 05:03
这个范例展示了斜圆锥的几何构造。它涉及圆锥、立体几何和向量等核心数学概念。通过使用GeoGebra命令如Circle、Line、Intersect、Vector等,可以动态地展示斜圆锥的生成过程。适合高中数学教学和学习立体几何的学生。

GeoGebra 命令及参数

  1. Circle(O_r, 0.5) → d
  2. Line(O_r, xAxis) → a
  3. Circle(O_r, 1) → c_1
  4. Point(c_1) → Girar
  5. Intersect(c_1, a, 2) → U
  6. Angle(U, O_r, Girar) → phi
  7. Point(d) → B_1
  8. Intersect(d, a, 2) → M_2
  9. Angle(M_2, O_r, B_1) → theta
  10. Vector(O_ , O) → u
  11. Translate(X_r, u) → X
  12. Vector(O, X) → v_x
  13. Translate(Y_r, u) → Y
  14. Vector(O, Y) → v_y
  15. Translate(Z_r, u) → Z
  16. Vector(O, Z) → v_z
  17. Circle(O, Zoom, xOyPlane) → e
  18. Line(O, yAxis) → b_1
  19. Line(Y, O) → f
  20. Line(O, X) → g
  21. Line(Z, O) → j
  22. Line(X, v_y) → h
  23. Translate(Y, v_z) → B_2
  24. Translate(X, v_z) → C_2
  25. Point(xAxis) → B
  26. Circle(O_ , B) → c
  27. Intersect(c, yAxis, 2) → F
  28. Intersect(c, xAxis, 2) → A
  29. AngularBisector(F, O_ , A) → b
  30. Intersect(c, b, 2) → H
  31. AngularBisector(H, O_ , A) → k
  32. AngularBisector(H, O_ , F) → l
  33. Intersect(c, l, 2) → I
  34. Intersect(c, k, 2) → J
  35. Translate((x(F) * v_x) + (y(F) * v_y), u) → B_ 
  36. Translate((x(A) * v_x) + (y(A) * v_y), u) → L
  37. Translate((x(H) * v_x) + (y(H) * v_y), u) → M
  38. Translate((x(I) * v_x) + (y(I) * v_y), u) → N
  39. Translate((x(J) * v_x) + (y(J) * v_y), u) → P
  40. Mirror(B_ , O) → A_3
  41. Mirror(I, yAxis) → W
  42. Mirror(J, yAxis) → D_1
  43. Mirror(A, yAxis) → E_1
  44. Polygon(A, B, S) → P_1, l_1, g_1, e_1
  45. Dilate(B, 0.4, S) → E'_2
  46. Circle(F_1, Distance[A, B] / 2) → p_1
  47. OrthogonalLine(F_1, yAxis) → q_1
  48. OrthogonalLine(A, q_1) → r_2
  49. OrthogonalLine(S, q_1) → b_3
  50. Intersect(q_1, b_3) → Z_1
  51. Segment(Z_1, S) → c_3
  52. Translate((x(S) * v_y), u) → C_b
  53. Intersect(b_3, xAxis) → E
  54. Segment(S, E) → q
  55. Point(q) → G
  56. Line(G, xAxis) → r
  57. Intersect(e_1, r) → K
  58. Intersect(g_1, r) → V
  59. Segment(K, V) → s
  60. OrthogonalLine(V, r) → a_1
  61. OrthogonalLine(K, r) → i_1
  62. Intersect(q_1, i_1) → A_1
  63. Intersect(q_1, a_1) → C_1
  64. Midpoint(A_1, C_1) → G_1
  65. Circle(G_1, C_1) → k_1
  66. Segment(V, C_1) → j_1
  67. Segment(A_1, K) → m_1
  68. Intersect(c, yAxis, 1) → H_1
  69. If(Distance[E, O_ ] > Distance[B, O_ ], Distance[E, O_ ], Distance[B, O_ ]) → m_p
  70. Circle(O_ , m_p) → r_1
  71. Intersect(r_1, xAxis, 2) → I_1
  72. OrthogonalLine(I_1, xAxis) → i
  73. Intersect(r_1, yAxis, 1) → K_1
  74. OrthogonalLine(K_1, yAxis) → s_1
  75. Intersect(i, s_1) → L_1
  76. Translate((x(L_1) * v_x) + (y(L_1) * v_y), u) → M_1
  77. Mirror(M_1, O) → D
  78. Translate((x(L_1) * v_x) - (y(L_1) * v_y), u) → N_1
  79. Mirror(N_1, O) → O_1
  80. Translate(D, Vector[(Distance[G, E] * v_z)]) → D'
  81. Translate(N_1, Vector[(Distance[G, E] * v_z)]) → N_1'
  82. Translate(M_1, Vector[(Distance[G, E] * v_z)]) → M_1'
  83. Translate(O_1, Vector[(Distance[G, E] * v_z)]) → O_1'
  84. Segment(O_ , E) → t_1
  85. Segment(G, K) → b_2
  86. Segment(Z_1, G_1) → g_2
  87. Segment(Z_1, F_1) → h_2
  88. Circle(F_1, Distance[A, B] / 2) → p_2
  89. Circle(F_1, Distance[A, B] / 2) → q_2
  90. Circle(G_1, C_1) → s_2
  91. Intersect(l_1, c_3) → V_1
  92. Segment(Z_1, V_1) → l_2
  93. Circle(O, Distance[A, B] / 2, zAxis) → p
  94. Vector(O, Q) → v
  95. CurveCartesian(x(O) + (Distance[A, B] / 2 * cos(i)), y(O) + (Distance[A, B] / 2 * sin(i)), z(O), i, 0, 6.283185307179586) → m
  96. Sequence((x(O) + (Distance[A, B] / 2 * cos(i)), y(O) + (Distance[A, B] / 2 * sin(i)), z(O)), i, 0, 6.28319, 0.12566370614359174) → liste1
  97. Sequence(Polygon[Element[liste1, i], Element[liste1, i + 1], Q], i, 1, Length[liste1]) → liste2
  98. Plane(T, Line[O, R]) → n
  99. OrthogonalLine(Q, n) → t
  100. Intersect(t, f) → J_1
  101. Segment(Q, J_1) → d_1
  102. Segment(O, J_1) → f_1
  103. Segment(O - (Distance[A, B] / 2, 0, 0), Q) → h_1
  104. Segment(O + (Distance[A, B] / 2, 0, 0), Q) → n_1
  105. OrthogonalLine(Q, n) → a_2
  106. Line(Q_1, f) → c_2
  107. Intersect(c_2, n_1) → R_1
  108. Intersect(h_1, c_2) → S_1
  109. Point(liste2) → T_1
  110. Segment(Q, O) → d_2
  111. Intersect(d_2, c_2) → U_1
  112. Circle(U_1, Distance[U_1, R_1], zAxis) → e_2
  113. Circle(U_1, Distance[U_1, R_1], zAxis) → f_2
  114. Point(liste2) → A_2
  115. Segment(S_1, R_1) → i_2
  116. Segment(O, J_1) → j_2
  117. Segment(O, D_2) → k_2
  118. Segment(O, E_2) → m_2

AI 绘图提示语参考

绘制一个斜圆锥,首先画一个圆d,然后画一条与x轴平行的直线a,接着在圆c1上取点Girar,并与直线a相交得到点U,通过U点画出圆d的切线。接着画出向量u,利用向量u平移点O得到点X,再画出向量v_x和v_y,利用向量v_x和v_y平移点O得到点Y和Z,然后画出xOy平面上的圆e,接着画出y轴上的直线b1,再画出直线Y到O的直线f,直线O到X的直线g,直线Z到O的直线j,直线X到v_y的直线h,然后平移Y和X得到B_2和C_2,接着画出x轴上的点B,以B为圆心画圆c,与y轴和x轴相交得到点F和A,通过F和A画出角平分线b,再画出c与b的交点H,通过H画出角平分线k和l,再画出c与k和l的交点I和J,然后平移B_2、I、J得到B_、M、N和P,接着镜像B_、I、J、A、E_1、D_1、W、E'_2、P_1、l_1、g_1、e_1、p_1、q_1和r_2。
以上提示语为根据原始绘图命令整理而来,仅供参考。