十边形和十一边形星星

GeoGebra 命令及参数

1. ConstructionStep() → stap
2. Point(xAxis) → A
3. Rotate(A, 18°) → A'
4. Polygon(A, A', 20) → veelhoek1, f, p, q, r, s, t, a, b, c, d, e, g, f_1, B, C, D, E, F, G, H, I, J, h, K, L, M, N, P, Q, R, S, T, i, j, k, l, m, n
5. Segment(O, A) → g_1
6. Sequence(Segment[Rotate[O, (nn * 36°)], Rotate[A, (nn * 36°)]], nn, 1, 10) → l1
7. Circle(O, 4) → c_{15}
8. Sequence(Segment[Rotate[O, (nn * 36°)], Rotate[A', (nn * 36°)]], nn, 1, 10) → l2
9. Mirror(l1, y = 4) → l1'
10. Circle((0, 8), 4) → d_{15}
11. Mirror(l2, y = 4) → l2'
12. Mirror(veelhoek1, y = 4) → veelhoek1'
13. Ray(O, B) → h_1
14. Mirror(O, y = 4) → O'
15. Mirror(B, y = 4) → B'
16. Ray(O', B') → i_1
17. Ray(O, D) → j_1
18. Mirror(O, y = 4) → O'_1
19. Mirror(D, y = 4) → D'
20. Ray(O'_1, D') → k_1
21. Intersect(j_1, k_1) → V
22. Rotate(W, ((-(360°))) / 11, U) → W'
23. Polygon(W', W, 11) → veelhoek2, l_1, b_1, c_1, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, m_1, H_1, n_1, p_1, q_1, r_1, s_1, t_1, a_1
24. Ray(U, G_1) → d_1
25. Ray(O', B') → e_1
26. Ray(O, B) → f_2
27. Ray(U, F_1) → g_2
28. Ray(U, H_1) → h_2
29. Circle(U, 4) → c_2
30. Segment(U, B') → i_2
31. Rotate(U, (360°) / 11, U) → U'
32. Rotate(B', (360°) / 11, U) → B''
33. Segment(U', B'') → j_2
34. Rotate(U, (2 * (360°) / 11), U) → U'_1
35. Rotate(B', (2 * (360°) / 11), U) → B''_1
36. Segment(U'_1, B''_1) → k_2
37. Sequence(Segment[Rotate[U, (nn * (360°) / 11), U'_1], Rotate[B', (nn * (360°) / 11), U'_1]], nn, 1, 11) → l3
38. Sequence(Segment[Rotate[U, (360°) / 22 + (nn * (360°) / 11), U'_1], Rotate[B', (360°) / 22 + (nn * (360°) / 11), U'_1]], nn, 1, 11) → l4
39. Circle(U, B') → e_{15}
40. Mirror(l3, y = 8) → l3'
41. Mirror(l4, y = 8) → l4'
42. Point(yAxis) → I_1
43. Point(yAxis) → J_1
44. Rotate(J_1, 18°, I_1) → K_1
45. Polygon(J_1, K_1, 20) → veelhoek3, l_2, b_2, d_2, e_2, f_3, g_3, h_3, i_3, j_3, k_3, l_3, m_2, m_3, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, n_2, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, p_2, q_2, r_2, s_2, t_2, a_2
46. Polygon(O, RO, RB, I_1) → vierhoek1, n_3, p_3, q_3, r_3
47. Mirror(U, y = 8) → UU
48. Midpoint(q_3) → F_2
49. Segment(UU, F_2) → s_3
50. Rotate(F_2, (360°) / 11, UU) → G_2
51. Ray(UU, G_2) → t_3
52. Intersect(q_3, t_3) → H_2
53. Rotate(F_2, (360°) / 22, UU) → I_2
54. Ray(UU, I_2) → a_3
55. Intersect(a_3, q_3) → J_2
56. Segment(UU, H_2) → g_{15}
57. Segment(UU, J_2) → h_{15}
58. Circle(J_2, H_2) → c_3
59. Intersect(c_3, a_3, 1) → K_2
60. Circle(UU, K_2) → d_3
61. Rotate(K_2, ((-(360°))) / 11, UU) → L_2
62. Polygon(L_2, K_2, 11) → veelhoek4, b_3, m_4, n_4, M_2, N_2, O_2, P_2, Q_2, R_2, S_2, T_2, e_3, U_2, f_4, g_4, h_4, i_4, j_4, k_4, l_4
63. Ray(UU, P_2) → p_4
64. Ray(O', V_2) → q_4
65. Intersect(q_4, p_4) → W_2
66. Rotate(Q_2, ((-(360°))) / 22, UU) → Z_2
67. Ray(UU, Z_2) → r_4
68. Intersect(s_3, g_{15}) → D_{10}
69. Segment(D_{10}, W_2) → i_{15}
70. Ray(O', A_3) → s_4
71. Intersect(r_4, s_4) → B_3
72. Segment(O', B_3) → t_4
73. Segment(UU, B_3) → a_4
74. Polygon(B_3, W_2, 5) → veelhoek5, b_4, c_4, d_4, e_4, f_5, C_3, D_3, E_3
75. Polygon(D_3, C_3, 10) → veelhoek6, g_5, q_5, F_3, G_3, H_3, I_3, J_3, K_3, L_3, M_3, h_5, i_5, j_5, k_5, l_5, m_5, n_5, p_5
76. Distance(O', G_3) → straal
77. Circle(I_1, straal) → c_5
78. Segment(I_1, L_1) → r_5
79. Intersect(c_5, r_5, 1) → N_3
80. Intersect(c_5, r_3, 1) → O_3
81. Polygon(O_3, N_3, 10) → veelhoek7, s_5, i_6, P_3, Q_3, R_3, S_3, T_3, U_3, V_3, W_3, t_5, a_5, b_5, d_5, e_5, f_6, g_6, h_6
82. Circle(O', W_2) → c_6
83. Ray(O', F_3) → j_6
84. Intersect(c_6, j_6) → Z_3,
85. Polygon(C_3, W_2, P_2, O_2, Z_3, F_3) → veelhoek8, k_6, w_2, l_6, o_2, z_3, m_6
86. Ray(UU, N_2) → n_6
87. Intersect(r_5, n_6) → A_4
88. Rotate(O_3, (360°) / 20, I_1) → B_4
89. Ray(I_1, B_4) → p_6
90. Polygon(N_3, O_3, 5) → veelhoek9, q_6, r_6, s_6, t_6, a_6, C_4, D_4, E_4
91. Polygon(G_3, F_3, 5) → veelhoek10, b_6, d_6, e_6, f_7, g_7, F_4, G_4, H_4
92. Midpoint(G_4, D_4) → I_4
93. Polygon(F_3, F_4, I_4, H_4, G_3) → veelhoek11, h_7, i_7, j_7, k_7, l_7
94. Polygon(N_3, O_3, C_4, I_4, E_4) → veelhoek12, m_7, o_3, n_7, p_7, q_7
95. Polygon(O_2, N_2, A_4, I_4, Z_3) → veelhoek13, r_7, s_7, t_7, a_7, b_7
96. Ray(I_1, P_3) → c_7
97. Ray(UU, M_2) → d_7
98. Ray(I_1, P_3) → e_7
99. Circle(H_2, J_2) → c_8
100. Point(e_7) → J_4
101. Polygon(M_2, K_2, J_2, H_2, J_4) → veelhoek14, f_8, g_8, h_8, i_8, j_8
102. Polygon(A_4, N_2, M_2, J_4, P_3, N_3) → veelhoek15, k_8, l_8, m_8, n_8, p_8, q_8
103. Ray(UU, L_2) → r_8
104. Intersect(q_3, r_8) → K_4
105. Mirror(L_2, q_3) → L_4
106. Mirror(K_2, q_3) → M_4
107. Polygon(K_2, L_2, K_4, L_4, M_4, J_2) → veelhoek16, s_8, t_8, a_8, b_8, d_8, e_8
108. Mirror(J_4, q_3) → N_4
109. Polygon(P_3, J_4, H_2, N_4, Q_3) → veelhoek17, f_9, g_9, h_9, i_9, j_9
110. Circle(UU, W_2) → c_9
111. Ray(UU, Q_2) → k_9
112. Intersect(c_9, k_9, 1) → O_4
113. Polygon(Q_2, P_2, W_2, B_3, O_4) → veelhoek18, l_9, m_9, n_9, p_9, o_4
114. Mirror(M_2, vert) → P_4
115. Mirror(K_2, vert) → Q_4
116. Mirror(J_2, vert) → R_4
117. Mirror(H_2, vert) → S_4
118. Mirror(J_4, vert) → T_4
119. Polygon(P_4, Q_4, R_4, S_4, T_4) → veelhoek14', q_9, r_9, s_9, t_9, a_9
120. Mirror(P_3, vert) → U_4
121. Mirror(J_4, vert) → V_4
122. Mirror(H_2, vert) → W_4
123. Mirror(N_4, vert) → Z_4
124. Mirror(Q_3, vert) → A_5
125. Polygon(U_4, V_4, W_4, Z_4, A_5) → veelhoek17', u_4, v_4, w_4, z_4, b_9
126. Mirror(A_4, vert) → B_5
127. Mirror(N_2, vert) → C_5
128. Mirror(M_2, vert) → D_5
129. Mirror(J_4, vert) → E_5
130. Mirror(P_3, vert) → F_5
131. Mirror(N_3, vert) → G_5
132. Polygon(B_5, C_5, D_5, E_5, F_5, G_5) → veelhoek15', d_9, e_9, f_{10}, g_{10}, h_{10}, i_{10}
133. Mirror(O_2, vert) → H_5
134. Mirror(N_2, vert) → I_5
135. Mirror(A_4, vert) → J_5
136. Mirror(I_4, vert) → K_5
137. Mirror(Z_3, vert) → L_5
138. Polygon(H_5, I_5, J_5, K_5, L_5) → veelhoek13', j_{10}, k_{10}, l_{10}, m_{10}, n_{10}
139. Mirror(N_3, vert) → M_5
140. Mirror(O_3, vert) → N_5
141. Mirror(C_4, vert) → O_5
142. Mirror(I_4, vert) → P_5
143. Mirror(E_4, vert) → Q_5
144. Polygon(M_5, N_5, O_5, P_5, Q_5) → veelhoek12', p_{10}, q_{10}, o_5, r_{10}, s_{10}
145. Mirror(C_3, vert) → R_5
146. Mirror(W_2, vert) → S_5
147. Mirror(P_2, vert) → T_5
148. Mirror(O_2, vert) → U_5
149. Mirror(Z_3, vert) → V_5
150. Mirror(F_3, vert) → W_5
151. Polygon(R_5, S_5, T_5, U_5, V_5, W_5) → veelhoek8', t_{10}, a_{10}, b_{10}, u_5, v_5, w_5
152. Mirror(F_3, vert) → Z_5
153. Mirror(F_4, vert) → A_6
154. Mirror(I_4, vert) → B_6
155. Mirror(H_4, vert) → C_6
156. Mirror(G_3, vert) → D_6
157. Polygon(Z_5, A_6, B_6, C_6, D_6) → veelhoek11', z_5, c_{10}, d_{10}, e_{10}, f_{11}
158. Mirror(veelhoek6, vert) → veelhoek6'
159. Mirror(veelhoek7, vert) → veelhoek7'
160. Mirror(Q_2, vert) → E_6
161. Mirror(P_2, vert) → F_6
162. Mirror(W_2, vert) → G_6
163. Mirror(B_3, vert) → H_6
164. Mirror(O_4, vert) → I_6
165. Polygon(E_6, F_6, G_6, H_6, I_6) → veelhoek18', g_{11}, h_{11}, i_{11}, j_{11}, k_{11}
166. Mirror(veelhoek5, vert) → veelhoek5'
167. Mirror(Q_2, hor) → J_6
168. Mirror(P_2, hor) → K_6
169. Mirror(W_2, hor) → L_6
170. Mirror(B_3, hor) → M_6
171. Mirror(O_4, hor) → N_6
172. Polygon(J_6, K_6, L_6, M_6, N_6) → veelhoek18'_1, l_{11}, m_{11}, n_{11}, p_{11}, q_{11}
173. Mirror(E_6, hor) → O_6
174. Mirror(F_6, hor) → P_6
175. Mirror(G_6, hor) → Q_6
176. Mirror(H_6, hor) → R_6
177. Mirror(I_6, hor) → S_6
178. Polygon(O_6, P_6, Q_6, R_6, S_6) → veelhoek18'', o_6, r_{11}, s_{11}, t_{11}, a_{11}
179. Mirror(R_5, hor) → T_6
180. Mirror(S_5, hor) → U_6
181. Mirror(T_5, hor) → V_6
182. Mirror(U_5, hor) → W_6
183. Mirror(V_5, hor) → Z_6
184. Mirror(W_5, hor) → A_7
185. Polygon(T_6, U_6, V_6, W_6, Z_6, A_7) → veelhoek8'', b_{11}, u_6, v_6, w_6, z_6, c_{11}
186. Mirror(C_3, hor) → B_7
187. Mirror(W_2, hor) → C_7
188. Mirror(P_2, hor) → D_7
189. Mirror(O_2, hor) → E_7
190. Mirror(Z_3, hor) → F_7
191. Mirror(F_3, hor) → G_7
192. Polygon(B_7, C_7, D_7, E_7, F_7, G_7) → veelhoek8'_1, d_{11}, e_{11}, f_{12}, g_{12}, h_{12}, i_{12}
193. Mirror(H_5, hor) → H_7
194. Mirror(I_5, hor) → I_7
195. Mirror(J_5, hor) → J_7
196. Mirror(K_5, hor) → K_7
197. Mirror(L_5, hor) → L_7
198. Polygon(H_7, I_7, J_7, K_7, L_7) → veelhoek13'', j_{12}, k_{12}, l_{12}, m_{12}, n_{12}
199. Mirror(B_5, hor) → M_7
200. Mirror(C_5, hor) → N_7
201. Mirror(D_5, hor) → O_7
202. Mirror(E_5, hor) → P_7
203. Mirror(F_5, hor) → Q_7
204. Mirror(G_5, hor) → R_7
205. Polygon(M_7, N_7, O_7, P_7, Q_7, R_7) → veelhoek15'', p_{12}, q_{12}, o_7, r_{12}, s_{12}, t_{12}
206. Mirror(P_4, hor) → S_7
207. Mirror(Q_4, hor) → T_7
208. Mirror(R_4, hor) → U_7
209. Mirror(S_4, hor) → V_7
210. Mirror(T_4, hor) → W_7
211. Polygon(S_7, T_7, U_7, V_7, W_7) → veelhoek14'', a_{12}, b_{12}, u_7, v_7, w_7
212. Mirror(K_2, hor) → Z_7
213. Mirror(L_2, hor) → A_8
214. Mirror(K_4, hor) → B_8
215. Mirror(L_4, hor) → C_8
216. Mirror(M_4, hor) → D_8
217. Mirror(J_2, hor) → E_8
218. Polygon(Z_7, A_8, B_8, C_8, D_8, E_8) → veelhoek16', z_7, c_{12}, d_{12}, e_{12}, f_{13}, g_{13}
219. Mirror(M_2, hor) → F_8
220. Mirror(K_2, hor) → G_8
221. Mirror(J_2, hor) → H_8
222. Mirror(H_2, hor) → I_8
223. Mirror(J_4, hor) → J_8
224. Polygon(F_8, G_8, H_8, I_8, J_8) → veelhoek14'_1, h_{13}, i_{13}, j_{13}, k_{13}, l_{13}
225. Mirror(A_4, hor) → K_8
226. Mirror(N_2, hor) → L_8
227. Mirror(M_2, hor) → M_8
228. Mirror(J_4, hor) → N_8
229. Mirror(P_3, hor) → O_8
230. Mirror(N_3, hor) → P_8
231. Polygon(K_8, L_8, M_8, N_8, O_8, P_8) → veelhoek15'_1, m_{13}, n_{13}, p_{13}, q_{13}, o_8, r_{13}
232. Mirror(N_3, hor) → Q_8
233. Mirror(O_3, hor) → R_8
234. Mirror(C_4, hor) → S_8
235. Mirror(I_4, hor) → T_8
236. Mirror(E_4, hor) → U_8
237. Polygon(Q_8, R_8, S_8, T_8, U_8) → veelhoek12'_1, s_{13}, t_{13}, a_{13}, b_{13}, u_8
238. Mirror(O_2, hor) → V_8
239. Mirror(N_2, hor) → W_8
240. Mirror(A_4, hor) → Z_8
241. Mirror(I_4, hor) → A_9
242. Mirror(Z_3, hor) → B_9
243. Polygon(V_8, W_8, Z_8, A_9, B_9) → veelhoek13'_1, v_8, w_8, z_8, c_{13}, d_{13}
244. Mirror(F_3, hor) → C_9
245. Mirror(F_4, hor) → D_9
246. Mirror(I_4, hor) → E_9
247. Mirror(H_4, hor) → F_9
248. Mirror(G_3, hor) → G_9
249. Polygon(C_9, D_9, E_9, F_9, G_9) → veelhoek11'_1, e_{13}, f_{14}, g_{14}, h_{14}, i_{14}
250. Mirror(M_5, hor) → H_9
251. Mirror(N_5, hor) → I_9
252. Mirror(O_5, hor) → J_9
253. Mirror(P_5, hor) → K_9
254. Mirror(Q_5, hor) → L_9
255. Polygon(H_9, I_9, J_9, K_9, L_9) → veelhoek12'', j_{14}, k_{14}, l_{14}, m_{14}, n_{14}
256. Mirror(Z_5, hor) → M_9
257. Mirror(A_6, hor) → N_9
258. Mirror(B_6, hor) → O_9
259. Mirror(C_6, hor) → P_9
260. Mirror(D_6, hor) → Q_9
261. Polygon(M_9, N_9, O_9, P_9, Q_9) → veelhoek11'', p_{14}, q_{14}, o_9, r_{14}, s_{14}
262. Mirror(P_3, hor) → R_9
263. Mirror(J_4, hor) → S_9
264. Mirror(H_2, hor) → T_9
265. Mirror(N_4, hor) → U_9
266. Mirror(Q_3, hor) → V_9
267. Polygon(R_9, S_9, T_9, U_9, V_9) → veelhoek17'_1, t_{14}, a_{14}, b_{14}, u_9, v_9
268. Mirror(U_4, hor) → W_9
269. Mirror(V_4, hor) → Z_9
270. Mirror(W_4, hor) → A_{10}
271. Mirror(Z_4, hor) → B_{10}
272. Mirror(A_5, hor) → C_{10}
273. Polygon(W_9, Z_9, A_{10}, B_{10}, C_{10}) → veelhoek17'', w_9, z_9, c_{14}, d_{14}, e_{14}
274. Mirror(veelhoek7, hor) → veelhoek7'_1
275. Mirror(veelhoek7'_1, vert) → veelhoek19
276. Mirror(veelhoek4, hor) → veelhoek4'