“Rosetón 1”几何构造：角与双曲线相关轨迹的作图示例

GeoGebra 命令及参数

1. Vector(A, B) → u
2. OrthogonalVector(u) → v
3. Polygon(A, B, 4) → poly1, n, r, t, a, N, O
4. PointIn(poly1) → Puntopoly1
5. Centroid(poly1) → C
6. PointIn(poly1) → D
7. Circle(C, D) → c
8. LineBisector(A, B) → f
9. OrthogonalLine(C, f) → g
10. LineBisector(F, G) → h
11. Intersect(f, h) → L
12. Mirror(M, f) → M'
13. LineBisector(M, G) → i
14. Intersect(eq1, i) → P
15. Polygon(M, F, M') → t1, m', m, f_1
16. Rotate(M, 45°, C) → M'_{1}
17. Rotate(F, 45°, C) → F'
18. Rotate(M', 45°, C) → M''
19. Polygon(M'_{1}, F', M'') → t1', m'', m'_{1}, f'
20. Rotate(M'_{1}, 45°, C) → Q
21. Rotate(F', 45°, C) → F''
22. Rotate(M'', 45°, C) → M'''
23. Polygon(Q, F'', M''') → t1'', m''', q, f''
24. Mirror(M, g) → M'_{2}
25. Mirror(F, g) → F'_{1}
26. Mirror(M', g) → M''_{1}
27. Polygon(M'_{2}, F'_{1}, M''_{1}) → t1'_{1}, m''_{1}, m'_{2}, f'_{1}
28. Mirror(Q, C) → Q'
29. Mirror(F'', C) → F'''
30. Mirror(M''', C) → R
31. Polygon(Q', F''', R) → t1''', r_1, q', f'''
32. Rotate(Q', 45°, C) → Q''
33. Rotate(F''', 45°, C) → S
34. Rotate(R, 45°, C) → R'
35. Polygon(Q'', S, R') → t2, r', q'', s
36. Rotate(Q', -45°, C) → Q''_{1}
37. Rotate(F''', -45°, C) → T
38. Rotate(R, -45°, C) → R'_{1}
39. Polygon(Q''_{1}, T, R'_{1}) → t3, r'_{1}, q''_{1}, t_1
40. Mirror(Q''_{1}, f) → U
41. Mirror(T, f) → T'
42. Mirror(R'_{1}, f) → V
43. Polygon(U, T', V) → t3', v_1, u_1, t'
44. Rotate(E, 8°, C) → E'
45. Rotate(E', 30°, C) → E''
46. Rotate(E'', 15°, C) → E'''
47. Rotate(E''', 30°, C) → K
48. LineBisector(E'', E') → j
49. Intersect(j, g_1) → W
50. CircleArc(C, E', E'') → e_1
51. Polygon(E'', W, E') → t4, l, b, w
52. Rotate(E'', 45°, C) → E'''_{1}
53. Rotate(W, 45°, C) → W'
54. Rotate(E', 45°, C) → E''_{1}
55. Polygon(E'''_{1}, W', E''_{1}) → t4', h_1, e'''_{1}, w'
56. Mirror(E', f) → E''_{2}
57. Mirror(E'', f) → E'''_{2}
58. Segment(E''_{2}, E'''_{2}) → w'_{1}
59. Mirror(E'', f) → E'''_{3}
60. Mirror(W, f) → W'_{1}
61. Mirror(E', f) → E''_{3}
62. Polygon(E'''_{3}, W'_{1}, E''_{3}) → t4'_{1}, e''_{3}, e'''_{3}, i_1
63. Mirror(E'''_{1}, f) → A_1
64. Rotate(e_1, 45°, C) → k_1
65. Mirror(k_1, f) → p_1
66. Mirror(E'''_{1}, f) → B_1
67. Mirror(W', f) → W''
68. Mirror(E''_{1}, f) → C_1
69. Polygon(B_1, W'', C_1) → t4'', j_1, b_1, l_1
70. Mirror(e_1, f) → q_1
71. Mirror(e_1, g) → s_1
72. Mirror(s_1, f) → c_2
73. Mirror(k_1, g) → d_2
74. Mirror(d_2, f) → e_2
75. Mirror(E'''_{1}, g) → D_1
76. Mirror(W', g) → W''_{1}
77. Mirror(E''_{1}, g) → o
78. Polygon(D_1, W''_{1}, o) → t4''_{1}, m_1, n_1, w''_{1}
79. Mirror(E'''_{1}, C) → F_1
80. Mirror(W', C) → W''_{2}
81. Mirror(E''_{1}, C) → G_1
82. Polygon(F_1, W''_{2}, G_1) → t4''_{2}, a_1, f_2, w''_{2}
83. Mirror(E'''_{3}, g) → H_1
84. Mirror(W'_{1}, g) → I_1
85. Mirror(E''_{3}, g) → J_1
86. Polygon(H_1, I_1, J_1) → t5, g_2, h_2, i_2
87. Mirror(E'', g) → E'''_{4}
88. Mirror(W, g) → W'_{2}
89. Mirror(E', g) → E''_{4}
90. Polygon(E'''_{4}, W'_{2}, E''_{4}) → t4'_{2}, e''_{4}, e'''_{4}, w'_{2}
91. Rotate(K_1, 22.5°, C) → L_1
92. Rotate(L_1, 90°, C) → M_1
93. Line(M'', M) → j_2
94. Angle(D, C, H) → α
95. CurveCartesian(((1 - t)^(3) * N_1) + (((3 * t) * (1 - t)^(2)) * O_1) + (((3 * (1 - t)) * t^(2)) * P_1) + (t^(3) * M_1), t, 0, 1) → o_1
96. Mirror(o_1, j) → w_1
97. Mirror(o_1, f) → a_2
98. Mirror(w_1, f) → b_2
99. Rotate(o_1, 45°, C) → k_2
100. Rotate(w_1, 45°, C) → l_2
101. Mirror(k_2, f) → m_2
102. Mirror(l_2, f) → n_2
103. Mirror(l_2, g) → p_2
104. Mirror(k_2, g) → q_2
105. Mirror(q_2, f) → r_2
106. Mirror(p_2, f) → s_2
107. Mirror(w_1, g) → t_2
108. Mirror(o_1, g) → u_2
109. Mirror(t_2, f) → v_2
110. Mirror(u_2, f) → w_2
111. Polygon(M, G, M') → t6, f_3, m_3, g_3
112. Rotate(M, 45°, C) → M'_{3}
113. Rotate(G, 45°, C) → G'
114. Rotate(M', 45°, C) → M''_{2}
115. Polygon(M'_{3}, G', M''_{2}) → t6', m''_{2}, m'_{3}, g'
116. Rotate(M, 90°, C) → M'_{4}
117. Rotate(G, 90°, C) → G'_{1}
118. Rotate(M', 90°, C) → M''_{3}
119. Polygon(M'_{4}, G'_{1}, M''_{3}) → t6'_{1}, m''_{3}, m'_{4}, g'_{1}
120. Mirror(M, g) → M'_{5}
121. Mirror(G, g) → G'_{2}
122. Mirror(M', g) → M''_{4}
123. Polygon(M'_{5}, G'_{2}, M''_{4}) → t6'_{2}, m''_{4}, m'_{5}, g'_{2}
124. Rotate(M, 135°, C) → M'_{6}
125. Rotate(G, 135°, C) → G'_{3}
126. Rotate(M', 135°, C) → M''_{5}
127. Polygon(M'_{6}, G'_{3}, M''_{5}) → t6'_{3}, m''_{5}, m'_{6}, g'_{3}
128. Rotate(M, -45°, C) → M'_{7}
129. Rotate(G, -45°, C) → G'_{4}
130. Rotate(M', -45°, C) → M''_{6}
131. Polygon(M'_{7}, G'_{4}, M''_{6}) → t6'_{4}, m''_{6}, m'_{7}, g'_{4}
132. Rotate(M, -90°, C) → M'_{8}
133. Rotate(G, -90°, C) → G'_{5}
134. Rotate(M', -90°, C) → M''_{7}
135. Polygon(M'_{8}, G'_{5}, M''_{7}) → t6'_{5}, m''_{7}, m'_{8}, g'_{5}
136. Rotate(M, -135°, C) → M'_{9}
137. Rotate(G, -135°, C) → G'_{6}
138. Rotate(M', -135°, C) → M''_{8}
139. Polygon(M'_{9}, G'_{6}, M''_{8}) → t6'_{6}, m''_{8}, m'_{9}, g'_{6}