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Buildings Logic Game

Buildings Logic Game
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2018-11-08 21:32
PolygonVectorCoordinate GeometryTransformationGeometric Construction
This example demonstrates geometric constructions and transformations, revealing properties of parallelograms, reflections, etc. Core concepts include vectors, polygons, reflections, and geometric transformations. It uses commands like Intersect, Polygon, Midpoint, Segment, Vector, Translate, Prism, Line in GeoGebra. Suitable for high school mathematics teaching, focusing on geometric construction and logical reasoning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Polygon(A, B, 4) → poly_{frame}, f_2, g_2, h_2, i_2, C, D
  3. Midpoint(A, B) → E
  4. Midpoint(B, C) → F
  5. Midpoint(C, D) → G
  6. Midpoint(D, A) → H
  7. Midpoint(A, E) → I
  8. Midpoint(E, B) → J
  9. Midpoint(B, F) → K
  10. Midpoint(F, C) → L
  11. Midpoint(C, G) → M
  12. Midpoint(G, D) → N
  13. Midpoint(D, H) → O
  14. Midpoint(H, A) → P
  15. Segment(N, I) → j_2
  16. Segment(G, E) → k_2
  17. Segment(M, J) → l_1
  18. Segment(O, L) → m_1
  19. Segment(H, F) → n_1
  20. Segment(P, K) → p_1
  21. Polygon(Q, R, 4) → poly1, q, r, s, t, S, T
  22. Vector(D, N) → u
  23. Vector(D, O) → v
  24. Translate(poly1, u) → poly2
  25. Translate(poly2, u) → poly3
  26. Translate(poly3, u) → poly4
  27. Translate(poly1, v) → poly5
  28. Translate(poly5, v) → poly9
  29. Translate(poly9, v) → poly13
  30. Translate(poly2, v) → poly6
  31. Translate(poly6, v) → poly10
  32. Translate(poly10, v) → poly14
  33. Translate(poly3, v) → poly7
  34. Translate(poly7, v) → poly11
  35. Translate(poly11, v) → poly15
  36. Translate(poly4, v) → poly8
  37. Translate(poly8, v) → poly12
  38. Translate(poly12, v) → poly16
  39. Prism(poly1, (0.6 * a_1)) → a, U, edgeQU, edgeRV, edgeSW, edgeTZ, edgeUV, edgeVW, edgeWZ, edgeUZ, V, W, Z, face1_a, face3_a, face4_a, face2_a, face5_a
  40. Segment(G, E) → e_1
  41. Segment(N, I) → f_1
  42. Segment(M, J) → g_1
  43. Segment(O, L) → h_1
  44. Segment(H, F) → i_1
  45. Segment(P, K) → j_1
  46. Prism(poly2, (0.6 * a_2)) → b, A_1, edge1, edge2, edge3, edge4, edge5, edge7, edge8, edge6, B_1, C_1, D_1, face1_b, face3_b, face4_b, face2_b, face5_b
  47. Prism(poly3, (0.6 * a_3)) → c, E_1, edge9, edge10, edge11, edge12, edge13, edge15, edge16, edge14, F_1, G_1, H_1, face1_c, face3_c, face4_c, face2_c, face5_c
  48. Prism(poly4, (0.6 * a_4)) → d, K_1, edge17, edge18, edge19, edge20, edge21, edge23, edge24, edge22, L_1, M_1, N_{17}, face1_d, face2_d, face4_d, face3_d, face5_d
  49. Translate(N_5, u) → N_6
  50. Translate(N_6, u) → N_7
  51. Translate(N_7, u) → N_8
  52. Translate(N_1, v') → N_2
  53. Translate(N_2, v') → N_3
  54. Translate(N_3, v') → N_4
  55. Translate(N_9, v) → N_{10}
  56. Translate(N_{10}, v) → N_{11}
  57. Translate(N_{16}, u) → N_{15}
  58. Translate(N_{15}, u) → N_{14}
  59. Translate(N_{14}, u) → N_{13}
  60. Translate(N_{11}, v) → N_{12}
  61. Line(O_1, h_1) → k_1
  62. Prism(poly5, (0.6 * a_5)) → e, P_1, edge25, edge26, edge27, edge28, edge29, edge31, edge32, edge30, Q_1, R_1, S_1, face4_e, face2_e, face3_e, face1_e, face5_e
  63. Prism(poly6, (0.6 * a_6)) → f, T_1, edge33, edge34, edge35, edge36, edge37, edge39, edge40, edge38, U_1, V_1, W_1, face4_f, face2_f, face3_f, face1_f, face5_f
  64. Prism(poly7, (0.6 * a_7)) → g, Z_1, edge41, edge42, edge43, edge44, edge45, edge47, edge48, edge46, A_2, B_2, C_2, face1_g, face3_g, face4_g, face2_g, face5_g
  65. Prism(poly9, (0.6 * a_9)) → i, D_2, edge49, edge50, edge51, edge52, edge53, edge55, edge56, edge54, E_2, F_2, G_2, face1_i, face3_i, face4_i, face2_i, face5_i
  66. Prism(poly8, (0.6 * a_8)) → h, H_2, edge57, edge58, edge59, edge60, edge61, edge63, edge64, edge62, I_2, J_2, K_2, face1_h, face3_h, face4_h, face2_h, face5_h
  67. Prism(poly10, (0.6 * a_{10})) → j, L_2, edge65, edge66, edge67, edge68, edge69, edge71, edge72, edge70, M_2, O_2, P_2, face1_j, face3, face4, face2_j, face5_j
  68. Prism(poly11, (0.6 * a_{11})) → k, Q_2, edge73, edge74, edge75, edge76, edge77, edge79, edge80, edge78, R_2, S_2, T_2, face4_k, face2_k, face3_k, face1_k, face5_k
  69. Prism(poly12, (0.6 * a_{12})) → l, U_2, edge81, edge82, edge83, edge84, edge85, edge87, edge88, edge86, V_2, W_2, Z_2, face1, face1_l, face2_l, face2, face5_l
  70. Prism(poly13, (0.6 * a_{13})) → m, A_3, edge89, edge90, edge91, edge92, edge93, edge95, edge96, edge94, B_3, C_3, D_3, face2_m, face3_m, face4_m, face1_m, face5_m
  71. Prism(poly14, (0.6 * a_{14})) → n, E_3, edge97, edge98, edge99, edge100, edge101, edge103, edge104, edge102, F_3, G_3, H_3, face1_n, face3_n, face4_n, face2_n, face5_n
  72. Prism(poly15, (0.6 * a_{15})) → o, I_3, edge105, edge106, edge107, edge108, edge109, edge111, edge112, edge110, J_3, K_3, L_3, face4_o, face2_o, face3_o, face1_o, face5_o
  73. Prism(poly16, (0.6 * a_{16})) → p, M_3, edge113, edge114, edge115, edge116, edge117, edge119, edge120, edge118, O_3, P_3, Q_3, face1_p, face3_p, face4_p, face2_p, face5_p

AI Drawing Prompt Reference

Draw a parallelogram frame with four points A, B, C, and D, then construct four midpoints E, F, G, and H inside the frame. Connect these midpoints to form a new parallelogram frame. Use vector and translation commands to shift the original and new frames to the right three times and up three times, creating a series of parallelograms. Finally, use the prism command to build a series of prisms based on each frame, extending 0.6 times the edge length upwards.
The prompt above was compiled from the original drawing commands and is for reference only.