Banca Boat (版本2)：几何作图与对称性探索

GeoGebra 命令及参数

1. Point(yAxis) → A
2. Segment(D, E) → i
3. CircumcircleArc(B, F, D) → c
4. Segment(A, B) → f
5. Mirror(B, yAxis) → B'
6. Mirror(F, yAxis) → F'
7. Mirror(D, yAxis) → D'
8. CircumcircleArc(B', F', D') → c'
9. Mirror(A, yAxis) → A'
10. Mirror(B, yAxis) → B'_{1}
11. Segment(A', B'_{1}) → f'
12. Mirror(D, yAxis) → D'_{1}
13. Mirror(E, yAxis) → E'
14. Segment(D'_{1}, E') → i'
15. Line(F, zAxis) → g
16. Line(B, g) → h
17. Line(D, g) → j
18. Intersect(h, p) → C
19. Intersect(g, p) → G
20. Intersect(j, p) → H
21. Mirror(C, eq1) → C'
22. Mirror(G, eq1) → G'
23. Mirror(H, eq1) → H'
24. Line(E, g) → k
25. Point(k) → I
26. Plane(H, G, C) → q
27. Intersect(k, q) → J
28. Midpoint(D, E) → K
29. Line(K, j) → l
30. Intersect(l, q) → L
31. CircumcircleArc(H, L, I) → e
32. Mirror(e, eq1) → e'
33. CircumcircleArc(C, G, H) → d
34. Mirror(I, r) → I'
35. Mirror(e', r) → e''
36. Mirror(e, r) → e'_{1}
37. Mirror(d, eq1) → d'
38. Polygon(B, B', D', D) → q1, b, b', m, d_1
39. Polygon(A, B, B') → t1, n, a, b_1
40. Polygon(E, D'_{1}, D) → t2, d_2, e_1, d'_{1}
41. LineBisector(B, F) → s
42. LineBisector(D, F, xOyPlane) → t
43. Intersect(s, t) → M
44. Segment(H, D) → g_1
45. Line(M, k) → f_1
46. Angle(D, M, B, space) → α
47. Segment(C, B) → h_1
48. Surface(h_1, α, f_1) → o
49. Mirror(M, yAxis) → M'
50. Mirror(f_1, eq1) → i_1
51. Segment(C', B'_{1}) → j_1
52. Segment(H', D'_{1}) → k_1
53. Surface(k_1, α, i_1) → u
54. Segment(I, E) → l_1
55. Segment(H', J) → m_1
56. Polygon(L, D, E, J) → q2, l_2, d_3, e_2, j_2
57. Mirror(q2, eq1) → q2'
58. Mirror(K, r) → K'
59. Mirror(q2', r) → q2''
60. Mirror(q2, r) → q2'_{1}
61. Point(e) → N
62. Point(e) → O
63. Point(e) → P
64. Point(e) → Q
65. Point(e) → R
66. Point(e) → S
67. Point(e) → T
68. Point(e) → U
69. Point(e) → V
70. Point(e) → W
71. Point(e) → Z
72. Point(e) → A_1
73. Polygon(I, O, Z, A_1, L, J, P, Q, R, S, T, U, V, W) → poly1, i_2, w, z_1, a_1, l_3, j_3, o_1, p_1, q_1, r_1, s_1, t_1, u_1, v
74. Mirror(poly1, eq1) → poly1'
75. Mirror(poly1, r) → poly1'_{1}
76. Mirror(poly1', r) → poly1''
77. Point(e) → B_1
78. Point(e) → C_1
79. Point(e) → D_1
80. Point(e) → E_1
81. Point(e) → F_1
82. Point(e) → G_1
83. Point(e) → H_1
84. Point(e) → I_1
85. Point(e) → J_1
86. Point(e) → K_1
87. Point(e) → L_1
88. Point(e) → M_1
89. Point(e) → N_1
90. Polygon(N_1, B_1, K_1, L_1, M_1, L, D, H, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1) → poly2, n_1, q_2, r_2, s_2, t_2, l_4, d_4, h_3, c_1, f_2, g_2, h_2, k_2, m_2, n_2, p_2
91. Mirror(poly2, eq1) → poly2'
92. Mirror(poly2, r) → poly2'_{1}
93. Mirror(poly2', r) → poly2''
94. Mirror(c', yAxis) → c''
95. Point(yAxis) → O_1
96. Line(O_1, xAxis) → b_2
97. OrthogonalLine(O_1, q1) → c_2
98. Intersect(c_2, q) → P_1
99. Line(P_1, b_2) → f_3
100. Intersect(f_3, d, 2) → Q_1
101. Intersect(f_3, d', 1) → R_1
102. Segment(Q_1, R_1) → g_3
103. Plane(O_1, Q_1, R_1) → p_3
104. PointIn(p_3) → S_1
105. PointIn(p_3) → T_1
106. CircumcircleArc(Q_1, S_1, T_1) → c_3
107. Mirror(c_3, eq1) → e_3
108. Mirror(T_1, eq1) → U_1
109. Mirror(e_3, r) → k_3
110. Mirror(c_3, r) → q_3
111. Mirror(Q_1, r) → V_1
112. Mirror(R_1, r) → W_1
113. Segment(V_1, W_1) → i_3
114. Mirror(T_1, r) → Z_1
115. Mirror(U_1, r) → A_2
116. Midpoint(A_2, U_1) → B_2
117. Midpoint(A_2, B_2) → C_2
118. Midpoint(B_2, U_1) → D_2
119. Line(A_2, U_1) → a_2
120. Sphere(A_2, C_2) → v_1
121. Sphere(U_1, D_2) → w_1
122. Intersect(a_2, v_1, 1) → E_2
123. Intersect(a_2, w_1, 2) → F_2
124. Segment(E_2, A_2) → m_3
125. Segment(A_2, C_2) → n_3
126. Segment(C_2, B_2) → r_3
127. Segment(B_2, D_2) → s_3
128. Segment(D_2, U_1) → t_3
129. Segment(U_1, F_2) → a_3
130. Mirror(A_2, eq1) → G_2
131. Mirror(C_2, eq1) → H_2
132. Segment(G_2, H_2) → b_3
133. Mirror(E_2, eq1) → I_2
134. Mirror(A_2, eq1) → J_2
135. Segment(I_2, J_2) → f_4
136. Mirror(C_2, eq1) → K_2
137. Mirror(B_2, eq1) → L_2
138. Segment(K_2, L_2) → g_4
139. Mirror(B_2, eq1) → M_2
140. Mirror(D_2, eq1) → N_2
141. Segment(M_2, N_2) → h_4
142. Mirror(D_2, eq1) → O_2
143. Mirror(U_1, eq1) → P_2
144. Segment(O_2, P_2) → i_4
145. Mirror(U_1, eq1) → Q_2
146. Mirror(F_2, eq1) → R_2
147. Segment(Q_2, R_2) → j_4
148. Mirror(U_1, eq1) → S_2
149. Mirror(A_2, eq1) → T_2
150. Mirror(F_2, eq1) → U_2
151. Mirror(E_2, eq1) → V_2
152. Midpoint(R_1, Q_1) → W_2
153. OrthogonalLine(W_2, q) → k_4
154. Intersect(k_4, q1) → Z_2
155. Midpoint(V_1, W_1) → A_3
156. Ray(W_2, A_3) → m_4
157. Intersect(m_4, e_2) → B_3
158. Rotate(B_3, -90°, g_3) → C_3
159. Midpoint(A_3, W_2) → D_3
160. Rotate(D_3, -90°, g_3) → E_3
161. Point(zAxis) → F_3
162. Point(yAxis) → G_3
163. Line(F_3, G_3) → n_4
164. Line(E_3, n_4) → p_4
165. Line(C_3, p_4) → q_4
166. Intersect(n_4, k_4) → H_3
167. Point(q_4) → I_3
168. Sphere(C_3, Z_2) → o_2
169. Intersect(q_4, o_2, 1) → J_3
170. Line(J_3, k_4) → r_4
171. Intersect(p_4, r_4) → K_3
172. Polygon(J_3, K_3, E_3, C_3) → q3, s_4, t_4, a_4, b_4
173. Midpoint(J_3, K_3) → L_3
174. Midpoint(C_3, E_3) → M_3
175. Midpoint(J_3, L_3) → N_3
176. Midpoint(C_3, M_3) → O_3
177. Segment(N_3, O_3) → c_4
178. Midpoint(O_3, N_3) → P_3
179. Midpoint(M_3, L_3) → Q_3
180. Midpoint(M_3, E_3) → R_3
181. Midpoint(L_3, K_3) → S_3
182. Midpoint(R_3, S_3) → T_3
183. Midpoint(O_3, P_3) → U_3
184. Midpoint(M_3, Q_3) → V_3
185. Midpoint(Q_3, L_3) → W_3
186. Midpoint(P_3, N_3) → Z_3
187. Midpoint(O_3, U_3) → A_4
188. Midpoint(M_3, V_3) → B_4
189. Midpoint(U_3, P_3) → C_4
190. Midpoint(V_3, Q_3) → D_4
191. Midpoint(Q_3, W_3) → E_4
192. Midpoint(c_4) → F_4
193. Midpoint(Z_3, F_4) → G_4
194. Midpoint(Z_3, N_3) → H_4
195. Midpoint(W_3, L_3) → I_4
196. Polygon(O_3, M_3, A_4) → t3, g_5, o_3, h_5
197. Polygon(A_4, B_4, M_3) → t4, i_5, j_5, k_5
198. Polygon(A_4, V_3, B_4) → t5, l_5, m_5, v_3
199. Polygon(A_4, U_3, V_3) → t6, n_5, p_5, u_3
200. Polygon(C_4, V_3, U_3) → t7, q_5, r_5, s_5
201. Polygon(C_4, D_4, V_3) → t8, t_5, a_5, b_5
202. Polygon(C_4, Q_3, D_4) → t9, c_5, d_5, e_5
203. Polygon(C_4, F_4, Q_3) → t10, f_6, g_6, h_6
204. Polygon(F_4, G_4, Q_3) → t11, i_6, j_6, k_6
205. Polygon(G_4, E_4, Q_3) → t12, l_6, m_6, n_6
206. Polygon(G_4, W_3, E_4) → t13, p_6, q_6, w_3
207. Polygon(G_4, Z_3, W_3) → t14, r_6, s_6, z_3
208. Polygon(Z_3, H_4, W_3) → t15, t_6, a_6, b_6
209. Polygon(H_4, I_4, W_3) → t16, c_6, d_6, e_6
210. Polygon(H_4, L_3, I_4) → t17, f_7, g_7, h_7
211. Polygon(H_4, N_3, L_3) → t18, i_7, j_7, k_7
212. Midpoint(E_3, K_3) → J_4
213. Midpoint(E_3, J_4) → K_4
214. Midpoint(E_3, K_4) → L_4
215. Midpoint(K_4, J_4) → M_4
216. Midpoint(J_4, K_3) → N_4
217. Midpoint(J_4, N_4) → O_4
218. Midpoint(N_4, K_3) → P_4
219. Polygon(M_3, E_3, L_4, B_4) → q5, e_4, f_5, q_7, r_7
220. Polygon(B_4, V_3, K_4, L_4) → q6, s_7, t_7, a_7, b_7
221. Polygon(V_3, D_4, M_4, K_4) → q7, c_7, d_7, e_7, f_8
222. Polygon(D_4, Q_3, J_4, M_4) → q8, g_8, h_8, i_8, j_8
223. Polygon(Q_3, E_4, O_4, J_4) → q9, k_8, l_8, o_4, m_8
224. Polygon(E_4, W_3, N_4, O_4) → q10, n_8, p_8, q_8, r_8
225. Polygon(W_3, I_4, P_4, N_4) → q11, s_8, t_8, a_8, b_8
226. Polygon(I_4, L_3, K_3, P_4) → q12, c_8, d_8, e_8, f_9
227. Sphere(C_3, O_3) → u_2
228. Sphere(E_3, R_3) → v_2
229. Intersect(q_4, u_2, 2) → Q_4
230. Intersect(p_4, v_2, 2) → R_4
231. Sphere(J_3, N_3) → w_2
232. Sphere(K_3, S_3) → u_4
233. Intersect(q_4, w_2, 1) → S_4
234. Intersect(p_4, u_4, 1) → T_4
235. Sphere(Q_4, C_3) → v_4
236. Intersect(q_4, v_4, 2) → U_4
237. Sphere(R_4, E_3) → w_4
238. Intersect(p_4, w_4, 2) → V_4
239. Midpoint(U_4, V_4) → W_4
240. Midpoint(U_4, W_4) → Z_4
241. Midpoint(O_3, Z_4) → A_5
242. Midpoint(M_3, W_4) → B_5
243. Polygon(M_3, B_5, R_4, E_3) → q13, p_7, g_9, h_9, i_9
244. Polygon(A_5, M_3, O_3) → t19, n_9, p_9, q_9
245. Polygon(A_5, B_5, M_3) → t20, r_9, s_9, t_9
246. Polygon(J_3, N_3, A_5, Q_4) → q4, l_7, m_7, n_7, j_9
247. Sphere(C_3, Q_4) → o_5
248. Intersect(k_4, o_5, 1) → C_5
249. Segment(S_4, U_4) → k_9
250. Segment(T_4, V_4) → l_9
251. Segment(Z_2, C_5) → m_9
252. Segment(J_3, K_3) → a_9
253. Segment(Q_4, R_4) → b_9