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三星Logo的数学构造

三星Logo的数学构造
几何画板及绘图内容加载中，请稍等……
2019-09-10 20:08
圆多边形角向量几何作图
①本范例演示了如何使用二维向量、角度、面积、圆等数学概念构造三星公司标志；②涉及核心概念包括向量运算、正交、反射、多边形构造、相似三角形等；③通过GeoGebra命令如Vector, OrthogonalVector, Polygon, Mirror等实现图形的精确绘制；④适合高中数学教学，用于展示几何作图与变换的应用。

GeoGebra 命令及参数

  1. Vector(A, B) → u
  2. OrthogonalVector(u) → v
  3. OrthogonalLine(I, v, xOyPlane) → f
  4. OrthogonalLine(M', f, xOyPlane) → n
  5. Intersect(f, n) → W
  6. OrthogonalLine(A, f, xOyPlane) → i_4
  7. Intersect(f, i_4) → V
  8. OrthogonalLine(B, f, xOyPlane) → t
  9. Intersect(f, t) → D_1
  10. Polygon(W, K_5, I_5, O_5) → q3, w, h_6, i_6, o_5
  11. LineBisector(O_5, M_5) → j_6
  12. Intersect(i_6, j_6) → Q_5
  13. OrthogonalLine(N, f, xOyPlane) → p
  14. Intersect(f, p) → Z
  15. LineBisector(K_5, L_5, xOyPlane) → g_6
  16. Intersect(g_6, j_6) → N_6
  17. Midpoint(Q_5, N_6) → O_6
  18. Midpoint(D_1, O') → P_5
  19. Mirror(U_5, P_5) → V_5
  20. Mirror(D_6, P_5) → K_6
  21. OrthogonalLine(O', f, xOyPlane) → s
  22. Intersect(f, s) → C_1
  23. Mirror(T_5, P_5) → W_5
  24. LineBisector(G_1, J_1) → f_3
  25. OrthogonalLine(J, f, xOyPlane) → g
  26. Intersect(f, g) → P
  27. Midpoint(A, P) → V_1
  28. Mirror(B_2, V_1) → G_2
  29. Mirror(J, C) → J'
  30. Mirror(K, D) → K'
  31. Mirror(L, E) → L'
  32. Mirror(N, G) → N'
  33. OrthogonalLine(J', f, xOyPlane) → h
  34. OrthogonalLine(K, f, xOyPlane) → i
  35. OrthogonalLine(K', f, xOyPlane) → j
  36. OrthogonalLine(L, f, xOyPlane) → k
  37. OrthogonalLine(L', f, xOyPlane) → l
  38. OrthogonalLine(M, f, xOyPlane) → m
  39. OrthogonalLine(N', f, xOyPlane) → q
  40. OrthogonalLine(O, f, xOyPlane) → r
  41. Intersect(f, h) → Q
  42. Intersect(f, i) → R
  43. Intersect(f, j) → S
  44. Intersect(f, k) → T
  45. Intersect(f, l) → U
  46. Intersect(f, q) → A_1
  47. Intersect(f, r) → B_1
  48. CircleArc(R_1, L_1, H_1, xOyPlane) → d
  49. Mirror(d, V_1) → d'
  50. Segment(M_1, B_2) → b
  51. Mirror(Z_1, V_1) → D_2
  52. Mirror(R_1, V_1) → E_2
  53. Mirror(J_1, V_1) → I_2
  54. Mirror(B_2, V_1) → P_2
  55. Mirror(R_2, V_1) → V_2
  56. Mirror(Q_1, V_1) → W_2
  57. Translate(d, Vector[(0.44 * u)]) → d'_1
  58. Translate(d', Vector[(0.44 * u)]) → d''
  59. Translate(Q_1, Vector[(0.44 * u)]) → B_3
  60. Translate(R_1, Vector[(0.44 * u)]) → C_3
  61. Translate(B_2, Vector[(0.44 * u)]) → D_3
  62. Translate(J_1, Vector[(0.44 * u)]) → F_3
  63. Translate(M_1, Vector[(0.44 * u)]) → I_3
  64. Translate(R_2, Vector[(0.44 * u)]) → J_3
  65. Translate(M_1, Vector[(0.44 * u)]) → L_3
  66. Translate(R_2, Vector[(0.44 * u)]) → M_3
  67. Translate(M_1, Vector[(0.44 * u)]) → O_3
  68. Translate(R_2, Vector[(0.44 * u)]) → P_3
  69. Translate(Q_1, Vector[(0.44 * u)]) → R_3
  70. Translate(N_1, Vector[(0.44 * u)]) → T_3
  71. Translate(Q_1, Vector[(0.44 * u)]) → U_3
  72. Translate(L_1, Vector[(0.44 * u)]) → V_3
  73. Translate(N_1, Vector[(0.44 * u)]) → W_3
  74. Translate(G_1, Vector[(0.44 * u)]) → Z_3
  75. Translate(H_1, Vector[(0.44 * u)]) → A_4
  76. Translate(B_2, Vector[(44 * u)]) → C_4
  77. Translate(J_1, Vector[(0.44 * u)]) → D_4
  78. Translate(V_2, Vector[(0.44 * u)]) → E_4
  79. Translate(B_2, Vector[(0.44 * u)]) → G_4
  80. Translate(K_1, Vector[(0.44 * u)]) → H_4
  81. Segment(V_2, J_1) → a_4
  82. Segment(H_1, L_1) → b_4
  83. Midpoint(K_4, L_4) → M_4
  84. Polygon(J', K_4, L_4, K, J_4, N_4, I_4) → poly2, j', d_4, e_4, k_5, f_5, g_5, h_5
  85. Midpoint(P_4, Q_4) → W_4
  86. Polygon(K', S, P_4, U_4, O_4, R_4, Z_4, T_4, T, L, S_4, V_4, Q_4) → poly3, k', n_5, p_5, u_4, o_4, s_5, i_5, z_4, j_5, t_5, l_5, m_5, v_4
  87. Midpoint(B_1, N') → C_5
  88. Mirror(A_5, C_5) → D_5
  89. Mirror(B_5, C_5) → E_5
  90. Mirror(F_5, C_5) → G_5
  91. Polygon(N', A_1, E_5, G_5, D_5, B_1, O, B_5, F_5, A_5) → poly4, n', f_6, q_5, e_5, r_5, d_5, a_5, o_1, b_5, c_5
  92. Mirror(O_5, g_6) → H_5
  93. Mirror(I_5, g_6) → J_5
  94. Mirror(q3, g_6) → q3'
  95. CircleArc(O_6, O_5, M_5, xOyPlane) → c_6
  96. Mirror(c_6, g_6) → d_6
  97. Polygon(M_5, N_5, H_5, O_5) → q4, k_6, l_6, m_6, n_6
  98. Translate(c_6, Vector[(0.29 * u)]) → e_6
  99. Translate(d_6, Vector[(0.3 * u)]) → p_6
  100. Mirror(e_6, P_5) → q_6
  101. Mirror(p_6, P_5) → r_6
  102. Mirror(N, H_5) → N'_1
  103. Mirror(R_5, P_5) → S_5
  104. Mirror(Z_5, P_5) → A_6
  105. Mirror(I_6, P_5) → J_6
  106. CircleArc(L_6, D_6, I_6, xOyPlane) → s_6
  107. Mirror(s_6, P_5) → t_6
  108. Polygon(U_5, Z_5, W_5, E_6, F_6, G_6, H_6, M_6, K_6) → poly6, i_7, j_7, k_7, l_7, m_7, n_7, p_7, q_7, r_7
  109. Polygon(T_5, A_6, I_6, K_6, U_5, R_5) → poly5, a_6, b_6, f_7, g_7, u_5, h_7
  110. Polygon(I_6, A_6, V_5, S_5, B_6, C_6, D_6) → poly7, s_7, t_7, v_5, a_7, b_7, c_7, d_7
  111. Segment(I_6, D_6) → e_7
  112. Segment(K_6, I_6) → g_8
  113. LineBisector(G_1, H_1, xOyPlane) → a
  114. Mirror(d, a) → d'_2
  115. Mirror(d', V_1) → d''_1
  116. Mirror(d'_2, V_1) → c
  117. Translate(d'_2, Vector[(0.44 * u)]) → d'_3
  118. Translate(c, Vector[(0.44 * u)]) → c'
  119. Mirror(D_2, a) → W_1
  120. Mirror(E_2, a) → S_2
  121. Mirror(W_1, V_1) → P_1
  122. Mirror(E_2, V_1) → J_2
  123. Mirror(O_1, a) → L_2
  124. Mirror(J_1, a) → N_2
  125. Mirror(K_2, a) → O_2
  126. Mirror(M_2, V_1) → Q_2
  127. Mirror(T_2, V_1) → U_2
  128. Mirror(T_2, a) → A_2
  129. Mirror(I_1, a) → H_2
  130. Polygon(O_1, T_2, E_2, S_2, A_2, L_2, H_2, F_1, E_1, I_1) → poly1, e, n_1, f_1, g_1, h_1, i_1, j_1, k_1, l_1, m_1
  131. Mirror(poly1, V_1) → poly1'
  132. Polygon(K_2, B_2, Q_2, L_2, A_2, M_2) → poly8, k_2, b_2, q_2, l_2, a_2, m_2
  133. CircleArc(Z_2, R_1, S_1, xOyPlane) → e_1
  134. Mirror(e_1, V_1) → p_1
  135. Translate(poly1, Vector[(0.44 * u)]) → poly1'_1
  136. Translate(poly1', Vector[(0.44 * u)]) → poly1''
  137. Translate(poly8, Vector[(0.44 * u)]) → poly8'
  138. Translate(V_1, Vector[(0.44 * u)]) → A_3
  139. Translate(I_1, Vector[(0.44 * u)]) → E_3
  140. Translate(O_1, Vector[(0.44 * u)]) → G_3
  141. Segment(E_3, G_3) → q_1
  142. Translate(E_1, Vector[(0.44 * u)]) → H_3
  143. Translate(I_1, Vector[(0.44 * u)]) → K_3
  144. Segment(H_3, K_3) → r_1
  145. Translate(F_1, Vector[(0.44 * u)]) → N_3
  146. Translate(E_1, Vector[(0.44 * u)]) → Q_3
  147. Segment(N_3, Q_3) → s_1
  148. Translate(H_2, Vector[(0.44 * u)]) → S_3
  149. Translate(F_1, Vector[(0.44 * u)]) → B_4
  150. Segment(S_3, B_4) → t_1
  151. Translate(L_2, Vector[(0.44 * u)]) → F_4
  152. Translate(H_2, Vector[(0.44 * u)]) → P_6
  153. Segment(F_4, P_6) → a_1
  154. Translate(A_2, Vector[(0.44 * u)]) → Q_6
  155. Translate(L_2, Vector[(0.44 * u)]) → R_6
  156. Segment(Q_6, R_6) → b_1
  157. Translate(S_2, Vector[(0.44 * u)]) → S_6
  158. Translate(A_2, Vector[(0.44 * u)]) → T_6
  159. Translate(E_2, Vector[(0.44 * u)]) → U_6
  160. Translate(S_2, Vector[(0.44 * u)]) → V_6
  161. Translate(T_2, Vector[(0.44 * u)]) → W_6
  162. Translate(E_2, Vector[(0.44 * u)]) → Z_6
  163. Segment(W_6, Z_6) → h_2
  164. Translate(O_1, Vector[(0.44 * u)]) → A_7
  165. Translate(T_2, Vector[(0.44 * u)]) → B_7
  166. Segment(A_7, B_7) → e'
  167. Mirror(E_3, A_3) → C_7
  168. Mirror(G_3, A_3) → D_7
  169. Segment(C_7, D_7) → i_2
  170. Mirror(H_3, A_3) → E_7
  171. Mirror(K_3, A_3) → F_7
  172. Segment(E_7, F_7) → j_2
  173. Mirror(N_3, A_3) → G_7
  174. Mirror(Q_3, A_3) → H_7
  175. Segment(G_7, H_7) → n_2
  176. Mirror(S_3, A_3) → I_7
  177. Mirror(B_4, A_3) → J_7
  178. Segment(I_7, J_7) → p_2
  179. Mirror(F_4, A_3) → K_7
  180. Mirror(P_6, A_3) → L_7
  181. Segment(K_7, L_7) → r_2
  182. Mirror(Q_6, A_3) → M_7
  183. Mirror(R_6, A_3) → N_7
  184. Segment(M_7, N_7) → s_2
  185. Mirror(S_6, A_3) → O_7
  186. Mirror(T_6, A_3) → P_7
  187. Segment(O_7, P_7) → t_2
  188. Segment(U_6, W_6) → d_2
  189. Mirror(U_6, A_3) → Q_7
  190. Mirror(W_6, A_3) → R_7
  191. Segment(Q_7, R_7) → e_2
  192. Translate(I_1, Vector[(0.44 * u)]) → S_7
  193. Translate(O_1, Vector[(0.44 * u)]) → T_7
  194. Segment(S_7, T_7) → g_3
  195. Translate(O_1, Vector[(0.44 * u)]) → U_7
  196. Translate(T_2, Vector[(0.44 * u)]) → V_7
  197. Segment(U_7, V_7) → e'_1
  198. Translate(e_1, Vector[(0.44 * u)]) → d_3
  199. Mirror(d_3, A_3) → h_3
  200. Translate(R_1, Vector[(0.44 * u)]) → W_7
  201. Translate(S_1, Vector[(0.44 * u)]) → Z_7
  202. Segment(W_7, Z_7) → i_3
  203. Mirror(W_7, A_3) → A_8
  204. Mirror(Z_7, A_3) → B_8
  205. Segment(A_8, B_8) → j_3
  206. Mirror(e_9, V_1) → k_3
  207. Translate(k_3, Vector[(0.44 * u)]) → p_3
  208. Mirror(p_3, A_3) → q_3
  209. Line(A, M_4) → l_3
  210. Intersect(l_3, b_2) → C_8
  211. Intersect(b_2, l_3) → D_8
  212. LineBisector(D_8, R_2, xOyPlane) → m_3
  213. OrthogonalLine(C_2, f, xOyPlane) → n_3
  214. Intersect(n_3, m_3) → E_8
  215. CircleArc(E_8, R_2, D_8, xOyPlane) → r_3
  216. Polygon(R_2, Q_2, D_8) → t1, d_8, s_3, t_3
  217. Mirror(r_3, V_1) → c_4
  218. Mirror(t1, V_1) → t1'
  219. Translate(t1, Vector[(0.44 * u)]) → t1'_1
  220. Translate(r_3, Vector[(0.44 * u)]) → f_4
  221. Mirror(f_4, A_3) → g_4
  222. Mirror(t1'_1, A_3) → t3
  223. Segment(Q_7, O_7) → a_3
  224. Segment(U_6, V_6) → b_3
  225. Mirror(D_8, V_1) → F_8
  226. Mirror(R_2, V_1) → G_8
  227. Segment(F_8, G_8) → h_4
  228. Line(V, B) → j_4
  229. Midpoint(A, D_1) → J_8
  230. Segment(G_1, H_1) → k_4
  231. Segment(E_2, C_2) → l_4
  232. Segment(O_7, Q_7) → m_4
  233. Segment(N_7, L_8) → n_4
  234. Mirror(N_7, A_3) → M_8
  235. Mirror(L_8, A_3) → N_8
  236. Segment(M_8, N_8) → p_4
  237. CurveCartesian(((1 - t)^(4) * V) + (((4 * (1 - t)^(3)) * t) * K_8) + (((6 * (1 - t)^(2)) * t^(2)) * H_8) + (((4 * (1 - t)) * t^(3)) * I_8) + (t^(4) * B), t, 0, 1) → u_1
  238. Mirror(u_1, J_8) → v_1
  239. Mirror(d_6, g_6) → e_3
  240. Mirror(I_1, V_1) → O_8
  241. Mirror(O_1, V_1) → P_8
  242. Segment(O_8, P_8) → c_1
  243. Segment(E_2, C_2) → d_1
  244. LineBisector(K_6, M_6, xOyPlane) → r_4
  245. Line(D_1, C_1) → s_4
  246. Intersect(r_4, s_4) → Q_8
  247. Segment(Q_2, R_2) → t_4
  248. CircleArc(R_8, K_6, M_6, xOyPlane) → c_8
  249. Segment(K_6, M_6) → h_8
  250. Segment(G_1, H_1) → i_8
  251. Segment(S_8, T_8) → j_8
  252. Mirror(S_8, V_1) → U_8
  253. Mirror(T_8, V_1) → V_8
  254. Segment(U_8, V_8) → k_8
  255. Translate(S_8, Vector[(0.44 * u)]) → W_8
  256. Translate(T_8, Vector[(0.44 * u)]) → Z_8
  257. Segment(W_8, Z_8) → l_8
  258. Translate(U_8, Vector[(0.44 * u)]) → A_9
  259. Translate(V_8, Vector[(0.44 * u)]) → B_9
  260. Segment(A_9, B_9) → m_8
  261. Segment(C_9, D_9) → n_8
  262. Mirror(C_9, V_1) → E_9
  263. Mirror(D_9, V_1) → F_9
  264. Segment(E_9, F_9) → c_2
  265. Segment(G_9, H_9) → p_8
  266. Segment(I_9, J_9) → f_2

AI 绘图提示语参考

使用二维向量和角度构造三星标志，首先绘制两个正交向量，然后创建它们的正交线并找到交点，接着用这些点构建多边形和圆，最后通过镜像和角平分线调整形状，形成标志的最终轮廓。
以上提示语为根据原始绘图命令整理而来，仅供参考。