美国长老会标志的几何构造

GeoGebra 命令及参数

1. Vector(A, B) → u
2. OrthogonalVector(u) → v
3. LineBisector(A, B) → m
4. Line(A, B) → s
5. OrthogonalLine(A, s) → b
6. Polygon(A, B, 4) → poly1, f, h, j, k, D, E
7. Midpoint(E, A) → J
8. OrthogonalLine(J, m) → i
9. OrthogonalLine(L_2, b) → h_3
10. Intersect(m, h_3) → M_2
11. OrthogonalLine(V, b) → g_3
12. OrthogonalLine(K, i) → l
13. OrthogonalLine(U, l) → c
14. OrthogonalLine(F, l) → n
15. Intersect(m, n) → H
16. Mirror(n, i) → n'
17. Intersect(m, n') → W
18. Line(A_1, I) → f_1
19. Intersect(g_3, f_1) → L_3
20. Intersect(f_1, h_3) → N_2
21. Intersect(f_1, g_3) → K_2
22. Line(Z, P) → d
23. Intersect(d, g_3) → J_2
24. Polygon(Z, J_2, K_2, I_2, M_2, N_2) → poly4, z_2, i_3, j_3, k_3, l_3, m_3
25. CurveCartesian(((1 - t)^(4) * Z) + (((4 * (1 - t)^(3)) * t) * O_2) + (((6 * (1 - t)^(2)) * t^(2)) * P_2) + (((4 * (1 - t)) * t^(3)) * M_2) + (t^(4) * N_2), t, 0, 1) → w
26. Intersect(m_3, w) → Q_2, R_2, S_2, T_2
27. Mirror(T_2, m) → J_3
28. LineBisector(G_3, D_3) → h_4
29. Intersect(m, h_4) → V_2
30. OrthogonalLine(B, u, xOyPlane) → g
31. Mirror(J, m) → J'
32. Intersect(m, i) → C
33. Mirror(l, m) → l'
34. OrthogonalLine(G, l) → p
35. Intersect(l, n) → Q
36. LineBisector(R, P) → q
37. OrthogonalLine(L, l) → r
38. OrthogonalLine(M, l) → t
39. OrthogonalLine(S, l) → a
40. Line(O, d) → e
41. Intersect(d, r) → B_1
42. Intersect(e, i) → C_1
43. Intersect(e, p) → D_1
44. Polygon(L, B_1, P, O, C_1, K) → poly2, l_1, b_1, p_1, o_1, c_1, k_1
45. Intersect(f_1, i) → E_1
46. Intersect(e, f_1) → F_1
47. Intersect(f_1, p) → G_1
48. Polygon(E_1, C, H, O, D_1, G_1) → poly3, e_1, c_2, h_1, o_2, d_1, g_1
49. Mirror(L, m) → L'
50. Mirror(B_1, m) → H_1
51. Mirror(P, m) → P'
52. Mirror(O, m) → O'
53. Mirror(C_1, m) → I_1
54. Mirror(K, m) → K'
55. Polygon(L', H_1, P', O', I_1, K') → poly2', i_1, j_1, p', o', m_1, k'
56. Mirror(E_1, m) → J_1
57. Mirror(C, m) → C'
58. Mirror(H, m) → H'
59. Mirror(O, m) → O'_1
60. Mirror(D_1, m) → K_1
61. Mirror(G_1, m) → L_1
62. Polygon(J_1, C', H', O'_1, K_1, L_1) → poly3', n_1, c', h', o'_1, q_1, r_1
63. Intersect(e, t) → M_1
64. Mirror(M_1, m) → N_1
65. CircleArc(P_1, M_1, N_1) → s_1
66. Mirror(O_1, m) → Q_1
67. Semicircle(Q_1, O_1) → t_1
68. Polygon(M, M_1, C, O_1, S) → q1, a_1, f_2, i_2, j_2, k_2
69. Mirror(M, m) → M'
70. Mirror(M_1, m) → R_1
71. Mirror(O_1, m) → S_1
72. Mirror(S, m) → S'
73. Mirror(M, m) → M'_1
74. Mirror(M_1, m) → T_1
75. Mirror(C, m) → C'_1
76. Mirror(O_1, m) → U_1
77. Mirror(S, m) → S'_1
78. Polygon(M'_1, T_1, C'_1, U_1, S'_1) → q1', m'_1, g_2, c'_1, u_1, s'_1
79. Polygon(T, W_1, Z_1, U) → q2, t_2, w_1, z_1, u_2
80. Mirror(T, m) → T'
81. Mirror(W_1, m) → A_2
82. Mirror(Z_1, m) → B_2
83. Mirror(U, m) → U'
84. Polygon(T', A_2, B_2, U') → q2', t', a_2, b_2, u'
85. LineBisector(V_1, W_1) → h_2
86. Intersect(h_2, t) → C_2
87. CircleArc(C_2, V_1, W_1) → d_2
88. Polygon(W_1, Z_1, D_2, V_1) → q3, l_2, m_2, n_2, v_1
89. Translate(d_2, Vector[(0.038 * v)]) → e_2
90. Mirror(e_2, m) → p_2
91. Mirror(W_1, m) → E_2
92. Mirror(Z_1, m) → F_2
93. Mirror(D_2, m) → G_2
94. Mirror(V_1, m) → H_2
95. Polygon(E_2, F_2, G_2, H_2) → q3', q_2, r_2, s_2, f_3
96. Mirror(d_2, m) → c_3
97. CurveCartesian(((1 - t)^(4) * R_2) + (((4 * (1 - t)^(3)) * t) * U_2) + (((6 * (1 - t)^(2)) * t^(2)) * J_2) + (((4 * (1 - t)) * t^(3)) * M_2) + (t^(4) * N_2), t, 0, 1) → v_2
98. Mirror(w, m) → w'
99. Mirror(v_2, m) → w_2
100. Mirror(Z, m) → Z'
101. Mirror(J_2, m) → W_2
102. Mirror(K_2, m) → Z_2
103. Mirror(I_2, m) → A_3
104. Mirror(M_2, m) → B_3
105. Mirror(N_2, m) → C_3
106. Polygon(Z', W_2, Z_2, A_3, B_3, C_3) → poly4', z', n_3, p_3, a_3, b_3, q_3
107. Midpoint(D_3, T_2) → E_3
108. Centroid(poly1) → F_3
109. Polygon(A_1, D_3, V_2, J_3, L_3) → poly5, r_3, s_3, t_3, d_3, e_3
110. CurveCartesian(((1 - t)^(4) * E_3) + (((4 * (1 - t)^(3)) * t) * G_3) + (((6 * (1 - t)^(2)) * t^(2)) * H_3) + (((4 * (1 - t)) * t^(3)) * K_3) + (t^(4) * J_3), t, 0, 1) → o_3
111. OrthogonalLine(N_3, b) → f_4
112. OrthogonalLine(M_3, b) → g_4
113. LineBisector(N_3, M_3) → i_4
114. Intersect(l, i_4) → O_3
115. Intersect(q, f_4) → P_3
116. Intersect(q, g_4) → Q_3
117. OrthogonalLine(R, s) → j_4
118. Intersect(j_4, i_4) → R_3
119. Spline({P_3, T_3, Q_3, R}, 4) → u_3
120. Spline({P_3, S_3, V_3, U_3}, 4) → v_3
121. OrthogonalLine(W_3, q) → k_4
122. Intersect(l, g_4) → Z_3
123. Intersect(k_4, l) → C_4
124. LineBisector(B_4, U_3) → l_4
125. Intersect(l_4, p) → D_4
126. Intersect(l_4, l') → E_4
127. Vector(D_4, E_4) → w_3
128. CircleArc(F_4, U_3, B_4) → c_4
129. Polygon(Q, R, U_3, B_4, O_3, A_4) → poly6, m_4, n_4, p_4, q_4, r_4, s_4
130. Spline({O_3, A_4, Q}, 3) → d_4
131. Line(P_3, U_3) → a_4
132. Intersect(a_4, u_3) → G_4, H_4, F_5
133. LineBisector(P_3, H_4) → t_4
134. Intersect(t_4, o_1) → I_4
135. CircleArc(I_4, P_3, H_4) → e_4
136. Intersect(a_4, v_3) → J_4, K_4, L_4, M_4, N_4
137. LineBisector(U_3, K_4) → b_4
138. Intersect(b_4, d_4) → O_4
139. CircleArc(O_4, U_3, K_4) → c_5
140. Mirror(u_3, m) → o_4
141. Mirror(v_3, m) → u_4
142. Mirror(Q, m) → Q'
143. Mirror(R, m) → R'
144. Mirror(U_3, m) → P_4
145. Mirror(B_4, m) → Q_4
146. Mirror(O_3, m) → R_4
147. Mirror(A_4, m) → S_4
148. Polygon(Q', R', P_4, Q_4, R_4, S_4) → poly6', q', r', h_5, i_5, j_5, k_5
149. Mirror(d_4, m) → v_4
150. Mirror(e_4, m) → d_5
151. Mirror(c_5, m) → e_5
152. Mirror(c_4, m) → p_5
153. Mirror(U_3, m) → T_4
154. Mirror(K_4, m) → U_4
155. Segment(T_4, U_4) → l_5
156. Mirror(H_4, m) → V_4
157. Mirror(P_3, m) → W_4
158. Segment(V_4, W_4) → m_5
159. Intersect(c_5, g_4) → Z_4,
160. Segment(K_4, Z_4) → n_5
161. Intersect(e_4, i_4) → A_5,
162. Segment(H_4, A_5) → q_5
163. Mirror(K_4, m) → B_5
164. Mirror(Z_4, m) → C_5
165. Segment(B_5, C_5) → r_5
166. Mirror(H_4, m) → D_5
167. Mirror(A_5, m) → E_5
168. Segment(D_5, E_5) → s_5
169. Segment(F_5, P_3) → g_5
170. Segment(U_3, K_4) → f_5
171. Intersect(q_5, a_4) → G_5
172. Segment(G_5, P_3) → t_5
173. Mirror(G_5, m) → H_5
174. Mirror(P_3, m) → I_5
175. Segment(H_5, I_5) → a_5
176. Mirror(H_4, m) → J_5