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Flatland View of Polygons

Flatland View of Polygons
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2015-02-05 15:30
PolygonComplex NumberMatrix
This example demonstrates the perspective of polygons in a flatland. Key mathematical concepts include polygons, orthocenter, root, matrices, and complex numbers. It is constructed using GeoGebra commands such as Point, Polygon, Segment, Line, etc. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(yAxis) → E
  2. Point(yAxis) → D
  3. Polygon(D, E, 5) → poly2, P_S, e, f, g, h, F, G, H
  4. Segment(H, F) → k
  5. Line(J, F) → p
  6. Line(J, H) → n
  7. LineBisector(P_S) → j
  8. OrthogonalLine(G, j) → r
  9. Intersect(p, r) → N
  10. Intersect(n, r) → M
  11. Segment(M, N) → L_P
  12. Point(yAxis) → B
  13. Point(yAxis) → A
  14. Polygon(A, B, 3) → poly1, T_S, b, c, C
  15. LineBisector(T_S) → i
  16. Line(A, I) → l
  17. Line(B, I) → m
  18. OrthogonalLine(C, i) → q
  19. Intersect(l, q) → K
  20. Intersect(m, q) → L
  21. Segment(C, I) → D_T
  22. Segment(G, J) → D_P
  23. Segment(K, L) → L_T
  24. Segment(O, P) → a
  25. Segment(Q, R) → d
  26. Segment(A, I) → s
  27. Segment(I, B) → t
  28. Segment(H, J) → a_1
  29. Segment(J, F) → b_1
  30. Point(yAxis) → U
  31. Point(yAxis) → W
  32. Polygon(W, Z, 4) → poly3, c_1, d_1, e_1, f_1, A_1, B_1
  33. Line(W, A_1) → g_1
  34. Segment(B_1, C_1) → h_1
  35. Segment(Z, C_1) → i_1
  36. OrthogonalLine(A_1, g_1) → j_1
  37. Intersect(j_1, h_1) → D_1
  38. Intersect(j_1, i_1) → E_1
  39. Segment(D_1, E_1) → S_T
  40. Segment(A_1, C_1) → D_S
  41. Polygon(F_1, G_1, 6) → poly4, k_1, K_1, l_1, m_1, n_1, p_1, q_1, H_1, I_1, J_1
  42. Point(yAxis) → M_1
  43. Polygon(L_1, M_1, 7) → poly5, r_1, P_1, Q_1, R_1, s_1, t_1, a_2, b_2, c_2, d_2, N_1, O_1
  44. OrthogonalLine(P_1, r_1) → e_2
  45. Segment(G_1, I_1) → f_2
  46. LineBisector(f_2) → g_2
  47. Segment(I_1, T_1) → h_2
  48. Segment(G_1, T_1) → i_2
  49. OrthogonalLine(H_1, g_2) → j_2
  50. Intersect(j_2, h_2) → U_1
  51. Intersect(j_2, i_2) → V_1
  52. Segment(U_1, V_1) → k_2
  53. Segment(Q_1, S_1) → l_2
  54. Segment(O_1, S_1) → m_2
  55. Segment(R_1, S_1) → n_2
  56. Segment(S_1, N_1) → p_2
  57. Point(yAxis) → Z_1
  58. Polygon(W_1, Z_1, 8) → poly6, q_2, B_2, C_2, D_2, E_2, F_2, r_2, s_2, t_2, a_3, b_3, c_3, d_3, A_2
  59. Line(Z_1, D_2) → e_3
  60. Segment(E_2, G_2) → f_3
  61. Segment(G_2, C_2) → g_3
  62. Segment(B_2, G_2) → h_3
  63. Segment(F_2, G_2) → i_3
  64. Point(yAxis) → I_2
  65. Polygon(H_2, I_2, 9) → poly7, j_3, J_2, K_2, L_2, M_2, N_2, O_2, P_2, k_3, l_3, m_3, n_3, p_3, q_3, r_3, s_3
  66. LineBisector(j_3) → t_3
  67. Segment(N_2, Q_2) → a_4
  68. Segment(Q_2, L_2) → b_4
  69. Segment(K_2, Q_2) → c_4
  70. Segment(Q_2, O_2) → d_4

AI Drawing Prompt Reference

Draw a flatland view of polygons, including three polygons of different sizes. Start by drawing a pentagon, then a triangle, followed by a quadrilateral and a hexagon, and finally a heptagon. Each polygon has its vertices and sides, and some polygons are connected by line segments, forming specific geometric relationships.
The prompt above was compiled from the original drawing commands and is for reference only.