MathPlotAI Logo MathPlotAI

Cross Section & Relative Position

Cross Section & Relative Position
Loading the math board and drawing, please wait…
2019-05-12 01:44
PolygonSolid GeometryGeometric Construction
This example demonstrates the dynamic changes in the cross-sectional shapes of 3D geometric solids (like a cube) and their relative positions. It involves core mathematical concepts such as polygons, similar triangles, solid geometry, and geometric construction. The construction utilizes GeoGebra commands/objects like Polygon, Intersect, OrthogonalLine, Point, Plane, CircleArc, Circle, Line, Segment, PointIn, and Cube. It is suitable for high school and above students studying solid geometry, geometric construction, and spatial reasoning, as well as for demonstrating related topics.

GeoGebra Commands & Parameters

  1. Polygon(C, D, B, A) → q1, c, d, b, a
  2. Intersect(b, yAxis) → E
  3. Intersect(c, yAxis) → F
  4. Intersect(xAxis, d) → G
  5. Intersect(a, xAxis) → H
  6. OrthogonalLine(E, xOyPlane) → f
  7. OrthogonalLine(G, xOyPlane) → g
  8. OrthogonalLine(F, xOyPlane) → h
  9. OrthogonalLine(H, xOyPlane) → i
  10. Point(f) → I
  11. Point(yAxis) → J
  12. Plane(E, J, I) → e
  13. CircleArc(E, I, J) → k_2
  14. Point(k_2) → P_2
  15. Plane(A, B, P_2) → j
  16. Circle(A, 4, j) → p
  17. Circle(B, 4, j) → q
  18. Line(P_2, b) → l
  19. Intersect(l, p) → L, M
  20. Intersect(l, q) → N, O
  21. Polygon(A, B, N, P_2, L) → poly1, a_1, b_1, n, k_5, l_1
  22. Point(i) → P
  23. Point(xAxis) → Q
  24. CircleArc(H, Q, P) → k_3
  25. Point(k_3) → P_3
  26. Plane(C, A, P_3) → m
  27. Line(P_3, a) → s
  28. Circle(C, 4, m) → t
  29. Circle(A, 4, m) → c_1
  30. Intersect(s, t) → S, T
  31. Intersect(s, c_1) → U, V
  32. Polygon(C, A, U, P_3, S) → poly2, c_2, a_2, u, r_1, s_1
  33. Point(g) → W
  34. Point(xAxis) → Z
  35. CircleArc(G, W, Z) → k_1
  36. Point(k_1) → P_1
  37. Plane(B, D, P_1) → o
  38. Line(P_1, d) → f_1
  39. Circle(B, 4, o) → e_1
  40. Circle(D, 4, o) → g_1
  41. Intersect(f_1, e_1) → B_1, C_1
  42. Intersect(f_1, g_1) → D_1, E_1
  43. Polygon(B, D, D_1, P_1, B_1) → poly3, b_2, d_2, h_1, i_1, j_1
  44. Point(h) → F_1
  45. Point(yAxis) → G_1
  46. CircleArc(F, F_1, G_1) → k_4
  47. Point(k_4) → P_4
  48. Plane(D, C, P_4) → k
  49. Line(P_4, c) → r
  50. Circle(D, 4, k) → d_1
  51. Circle(C, 4, k) → p_1
  52. Intersect(r, d_1) → K, R
  53. Intersect(r, p_1) → A_1, H_1
  54. Point(r) → I_1
  55. Polygon(D, C, A_1, I_1, K) → poly4, d_3, c_3, m_1, n_1, k_6
  56. Point(zAxis) → J_1
  57. Point(zAxis) → K_1
  58. Segment(J_1, K_1) → q_1
  59. PointIn(poly2) → A_2
  60. PointIn(poly2) → B_2
  61. PointIn(poly2) → C_2
  62. PointIn(poly2) → D_2
  63. PointIn(poly1) → E_2
  64. PointIn(poly1) → F_2
  65. PointIn(poly1) → G_2
  66. PointIn(poly1) → H_2
  67. PointIn(poly3) → I_2
  68. PointIn(poly3) → J_2
  69. PointIn(poly3) → K_2
  70. PointIn(poly3) → L_2
  71. Polygon(I_2, J_2, K_2, L_2) → q4, r_2, s_2, t_2, e_2
  72. PointIn(poly4) → M_2
  73. PointIn(poly4) → N_2
  74. PointIn(poly4) → O_2
  75. Point(zAxis) → R_2
  76. PointIn(poly4) → S_2
  77. Polygon(N_2, O_2, S_2, M_2) → q5, f_3, o_2, g_3, h_3
  78. Polygon(F_2, G_2, H_2, E_2) → q6, i_3, j_3, l_3, m_3
  79. Polygon(B_2, C_2, D_2, A_2) → q7, n_3, p_3, q_3, r_3
  80. Point(zAxis) → L_1
  81. Plane(L_1, xOyPlane) → w
  82. PointIn(w) → R_1
  83. PointIn(w) → S_1
  84. Point(Circle[S_1, Distance[R_1, S_1], Segment[R_1, S_1]]) → T_1
  85. Cube(R_1, S_1, T_1) → u_1, U_1, face5, face6, edge2, edge1, edge4, edge6, edge3, edge8, edge10, edge9, V_1, edge5, edge11, edge7, edge12, W_1, Z_1, T_2, face1, face3, face2, face4
  86. PointIn(q1) → U_2
  87. PointIn(q1) → V_2
  88. PointIn(q1) → W_2
  89. PointIn(q1) → Z_2
  90. Point(zAxis) → B_3
  91. Segment(A_3, B_3) → s_3
  92. Point(c_2) → C_3
  93. Line(C_3, s_3) → t_3
  94. Segment(A_3, C_3) → a_3
  95. Point(t_3) → D_3
  96. Line(D_3, a_3) → b_3
  97. Line(B_3, b_3) → e_3
  98. Intersect(t_3, e_3) → E_3
  99. Point(t_3) → F_3
  100. Line(F_3, b_3) → t_1
  101. Point(b_3) → M_1
  102. Intersect(t_1, zAxis) → N_1
  103. Intersect(b_1, j_1) → O_1
  104. Point(b_2) → Q_1
  105. Point(d_3) → Q_2
  106. OrthogonalLine(O_1, q1) → f_2
  107. OrthogonalLine(Q_2, q1) → g_2
  108. OrthogonalLine(Q_1, q1) → h_2
  109. Intersect(e_3, h_2) → G_3
  110. Intersect(t_1, h_2) → H_3
  111. Segment(O_1, A_3) → i_2
  112. Line(N_1, i_2) → j_2
  113. Line(B_3, i_2) → l_2
  114. Intersect(f_2, j_2) → I_3
  115. Intersect(g_2, j_2) → J_3
  116. Intersect(l_2, g_2) → L_3
  117. Segment(D_3, F_3) → m_2
  118. Segment(C_3, E_3) → n_2
  119. Point(m_2) → P_5
  120. Point(n_2) → P_6
  121. Plane(P_5, xOyPlane) → v
  122. PointIn(v) → O_3
  123. Polygon(O_3, P_5, 4, xOyPlane) → poly5, p_2, q_2, f_4, g_4, Q_3, R_3
  124. Plane(P_6, xOyPlane) → o_1
  125. PointIn(o_1) → K_3
  126. Polygon(K_3, P_6, 4, xOyPlane) → poly6, h_4, i_4, j_4, l_4, T_3, U_3
  127. PointIn(poly5) → N_3
  128. PointIn(poly5) → M_3
  129. PointIn(poly5) → V_3
  130. PointIn(poly5) → W_3
  131. Polygon(M_3, N_3, W_3, V_3) → q2, m_4, n_4, w_3, v_3
  132. OrthogonalLine(M_3, poly6) → p_4
  133. OrthogonalLine(V_3, poly6) → q_4
  134. OrthogonalLine(W_3, poly6) → r_4
  135. OrthogonalLine(N_3, poly6) → s_4
  136. Intersect(q_4, poly6) → Z_3
  137. Intersect(p_4, poly6) → A_4
  138. Intersect(r_4, poly6) → B_4
  139. Intersect(s_4, poly6) → C_4
  140. Polygon(A_4, C_4, B_4, Z_3) → q3, a_4, c_4, b_4, z_3
  141. Intersect(edge3, edge2) → D_4
  142. Intersect(edge10, edge12) → E_4
  143. Segment(D_4, E_4) → t_4
  144. Intersect(edge4, edge6) → F_4
  145. Segment(E_4, F_4) → d_4
  146. Point(edge9) → G_4
  147. Segment(F_4, G_4) → e_4
  148. Point(j_3) → H_4
  149. Point(l_3) → I_4
  150. Segment(H_4, I_4) → f_5
  151. Intersect(i_3, j_3) → J_4
  152. Segment(I_4, J_4) → g_5
  153. Intersect(m_3, i_3) → K_4
  154. Segment(J_4, K_4) → h_5
  155. Intersect(r_3, q_3) → L_4
  156. Point(p_3) → M_4
  157. Segment(L_4, M_4) → i_5
  158. Point(p_3) → N_4
  159. Intersect(r_3, n_3) → O_4
  160. Segment(N_4, O_4) → j_5
  161. Segment(N_4, M_4) → l_5
  162. Intersect(r_2, s_2) → Q_4
  163. PointIn(poly3) → R_4
  164. Segment(Q_4, R_4) → m_5
  165. Intersect(s_2, t_2) → S_4
  166. Point(r_2) → T_4
  167. Segment(S_4, T_4) → n_5
  168. Segment(R_4, S_4) → p_5
  169. Point(v_3) → U_4
  170. Point(v_3) → V_4
  171. Segment(U_4, V_4) → q_5
  172. Intersect(n_4, w_3) → W_4
  173. Segment(W_4, V_4) → r_5
  174. Intersect(m_4, n_4) → Z_4
  175. Segment(W_4, Z_4) → s_5
  176. Intersect(a_4, z_3) → A_5
  177. Point(z_3) → B_5
  178. Intersect(c_4, b_4) → C_5
  179. Intersect(a_4, c_4) → D_5
  180. Intersect(h_3, g_3) → E_5
  181. Point(g_3) → F_5
  182. Segment(E_5, F_5) → c_5
  183. Intersect(f_3, h_3) → G_5
  184. Segment(F_5, G_5) → d_5
  185. Intersect(f_3, o_2) → H_5
  186. Segment(G_5, H_5) → e_5
  187. Point(z_3) → I_5
  188. Point(z_3) → J_5
  189. Segment(I_5, J_5) → t_5
  190. Point(b_4) → K_5
  191. Segment(J_5, K_5) → a_5
  192. Point(c_4) → L_5
  193. Segment(K_5, L_5) → b_5
  194. Intersect(edge9, edge3) → M_5
  195. Intersect(edge6, edge2) → N_5
  196. Segment(M_5, N_5) → f_6
  197. Intersect(edge11, edge7) → O_5
  198. Segment(N_5, O_5) → g_6
  199. Point(edge4) → Q_5
  200. Segment(O_5, Q_5) → h_6
  201. Intersect(edge5, edge1) → R_5
  202. Intersect(f_6, edge3) → S_5
  203. Segment(R_5, S_5) → i_6
  204. Intersect(f_6, edge2) → T_5
  205. Segment(S_5, T_5) → j_6
  206. Intersect(h_6, g_6) → U_5
  207. Segment(T_5, U_5) → l_6
  208. Intersect(edge5, edge11) → V_5
  209. Segment(U_5, R_5) → m_6

AI Drawing Prompt Reference

Draw a cube and its three different plane sections. First, draw a cube, then draw section polygons on three different planes. Start by drawing a section polygon on the xOy plane, followed by section polygons on the yOz and xOz planes. Ensure each section polygon intersects with the corresponding face of the cube.
The prompt above was compiled from the original drawing commands and is for reference only.