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Mathematical Construction of Samsung Logo

Mathematical Construction of Samsung Logo
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2019-09-10 20:08
CirclePolygonAngleVectorGeometric Construction
This example demonstrates how to construct the Samsung logo using mathematical concepts like 2D vectors, angles, area, and circles. It involves core ideas such as vector operations, orthogonality, reflection, and polygon construction. GeoGebra commands like Vector, OrthogonalVector, and Mirror are used to achieve the drawing. Suitable for high school mathematics education to showcase applications of geometric constructions and transformations.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Construct the Samsung logo using 2D vectors and angles by first creating two orthogonal vectors, then drawing their perpendicular lines and finding intersections, building polygons and circles with these points, and finally adjusting shapes through reflections and angle bisectors to form the final logo outline.
The prompt above was compiled from the original drawing commands and is for reference only.