MathPlotAI Logo MathPlotAI

Banca Boat (Version 2): Geometric Construction and Symmetry Exploration

Banca Boat (Version 2): Geometric Construction and Symmetry Exploration
Loading the math board and drawing, please wait…
2022-10-22 20:38
TriangleCirclePolygonAngleGeometric Construction
This example demonstrates how to create complex figures through geometric construction and symmetry. Key mathematical concepts include triangles, circles, polygons, and symmetry. Construction involves GeoGebra commands such as Point, Segment, CircumcircleArc, Mirror, etc. Suitable for middle or high school students to learn geometric construction and symmetry principles.

GeoGebra Commands & Parameters

  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

AI Drawing Prompt Reference

Draw a boat model composed of triangles, circles, and symmetry. Start by creating point A on the y-axis, then draw triangles and arcs using points A, B, D, etc. Use the y-axis as the symmetry axis to create symmetric points B', D', etc. Construct symmetric shapes using these points and line segments. Finally, use intersection points and midpoints to form other elements, creating a complex geometric figure.
The prompt above was compiled from the original drawing commands and is for reference only.