MathPlotAI Logo MathPlotAI

Geometric Construction of Polygons and Incircles

Geometric Construction of Polygons and Incircles
Loading the math board and drawing, please wait…
2018-09-19 22:23
CirclePolygonFunctionGeometric ConstructionGraphing
This example demonstrates how to construct multiple polygons and their inscribed circles using GeoGebra, involving the concept of similar figures. Core mathematical concepts include: properties of inscribed circles in polygons, perpendicular bisectors, midpoints, function graphs, and root operations. Construction points: Use the Polygon command to draw six polygons (poly1-poly6), use Incircle or OrthogonalLine commands to construct inscribed circles for each polygon, use Midpoint command to mark point coordinates, use Intersect command to find intersections, and use Line and OrthogonalLine commands to draw perpendicular lines and translation paths. Additionally, it demonstrates the combination of piecewise function graphs and bar charts. This example is suitable for middle to high school mathematics teaching, helping students understand similar polygons, properties of inscribed circles, and function transformations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Polygon(C, B, 4) → poly2, j, k, l, m, E, F
  5. Polygon(F, E, 4) → poly3, n, p, q, r, G, H
  6. Polygon(H, G, 4) → poly4, s, t, a, b, I, J
  7. Polygon(J, I, 4) → poly5, c, d, e, f_1, K, L
  8. Polygon(L, K, 4) → poly6, g_1, h_1, i_1, j_1, M, N
  9. Polygon(B, A, 4) → poly7, k_1, l_1, m_1, n_1, O, P
  10. Polygon(E, B, 4) → poly8, p_1, q_1, r_1, s_1, Q, R
  11. Polygon(G, E, 4) → poly9, t_1, a_1, b_1, c_1, S, T
  12. Polygon(I, G, 4) → poly10, d_1, e_1, f_2, g_2, U, V
  13. Polygon(K, I, 4) → poly11, h_2, i_2, j_2, k_2, W, Z
  14. Polygon(M, K, 4) → poly12, l_2, m_2, n_2, p_2, A_1, B_1
  15. Polygon(P, O, 4) → poly13, q_2, r_2, s_2, t_2, C_1, D_1
  16. Polygon(R, P, 4) → poly14, a_2, b_2, c_2, d_2, E_1, F_1
  17. Polygon(T, R, 4) → poly15, e_2, f_3, g_3, h_3, G_1, H_1
  18. Polygon(V, T, 4) → poly16, i_3, j_3, k_3, l_3, I_1, J_1
  19. Polygon(Z, V, 4) → poly17, m_3, n_3, p_3, q_3, K_1, L_1
  20. Polygon(B_1, Z, 4) → poly18, r_3, s_3, t_3, a_3, M_1, N_1
  21. Polygon(D_1, C_1, 4) → poly19, b_3, c_3, d_3, e_3, O_1, P_1
  22. Polygon(F_1, D_1, 4) → poly20, f_4, g_4, h_4, i_4, Q_1, R_1
  23. Polygon(H_1, F_1, 4) → poly21, j_4, k_4, l_4, m_4, S_1, T_1
  24. Polygon(J_1, H_1, 4) → poly22, n_4, p_4, q_4, r_4, U_1, V_1
  25. Polygon(L_1, J_1, 4) → poly23, s_4, t_4, a_4, b_4, W_1, Z_1
  26. Polygon(N_1, L_1, 4) → poly24, c_4, d_4, e_4, f_5, A_2, B_2
  27. Midpoint(D, B) → C_2
  28. Midpoint(C, E) → D_2
  29. Midpoint(F, G) → E_2
  30. Midpoint(H, I) → F_2
  31. Midpoint(J, K) → G_2
  32. Midpoint(L, M) → H_2
  33. Midpoint(N, M) → I_2
  34. Line(B_5, A_5) → g_5
  35. Point(g_5) → J_2
  36. Point(g_5) → M_2
  37. Line(B_2, Z_1) → i_5
  38. OrthogonalLine(J_2, g_5) → j_5
  39. OrthogonalLine(M_2, g_5) → k_5
  40. Line(K_2, O_2) → h_5
  41. Intersect(j_5, h_5) → P_2
  42. Intersect(k_5, h_5) → Q_2
  43. Polygon(P_2, Q_2, M_2, J_2) → poly25, p_5, q_5, m_5, j_6
  44. Polygon(J_2, L_2, N_2, M_2) → poly26, j_7, l_5, n_5, m_6
  45. Midpoint(A, P) → L_3
  46. Midpoint(A, L_3) → M_3
  47. Midpoint(O, D_1) → N_3
  48. Midpoint(O, N_3) → O_3
  49. Midpoint(C_1, P_1) → P_3
  50. Midpoint(C_1, P_3) → Q_3
  51. Midpoint(B, R) → R_3
  52. Midpoint(B, R_3) → S_3
  53. Midpoint(P, F_1) → T_3
  54. Midpoint(P, T_3) → U_3
  55. Midpoint(D_1, R_1) → V_3
  56. Midpoint(D_1, V_3) → W_3
  57. Midpoint(E, T) → Z_3
  58. Midpoint(E, Z_3) → A_4
  59. Midpoint(G, V) → B_4
  60. Midpoint(G, B_4) → C_4
  61. Midpoint(R, H_1) → D_4
  62. Midpoint(R, D_4) → E_4
  63. Midpoint(F_1, T_1) → F_4
  64. Midpoint(F_1, F_4) → G_4
  65. Midpoint(H_1, V_1) → H_4
  66. Midpoint(H_1, H_4) → I_4
  67. Midpoint(T, J_1) → J_4
  68. Midpoint(T, J_4) → K_4
  69. Midpoint(I, Z) → L_4
  70. Midpoint(I, L_4) → M_4
  71. Midpoint(V, L_1) → N_4
  72. Midpoint(V, N_4) → O_4
  73. Midpoint(J_1, Z_1) → P_4
  74. Midpoint(J_1, P_4) → Q_4
  75. Midpoint(K, B_1) → R_4
  76. Midpoint(K, R_4) → S_4
  77. Midpoint(Z, N_1) → T_4
  78. Midpoint(Z, T_4) → U_4
  79. Midpoint(L_1, B_2) → V_4
  80. Midpoint(L_1, V_4) → W_4

AI Drawing Prompt Reference

On a coordinate plane, starting from the origin, construct a series of nested squares, each rotated and scaled relative to the previous one, forming a spiral-like pattern. Inside each square, draw its incircle and mark the midpoints of its sides. Additionally, add a helper line, take two points on it, and draw perpendiculars to this line, intersecting another line to form two quadrilaterals. Finally, mark several midpoints and connect some points to create additional geometric structures, illustrating the relationships among polygons, incircles, and perpendicular lines.
The prompt above was compiled from the original drawing commands and is for reference only.