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Element B: Composite Geometric Construction with Rotation and Isosceles Triangle

Element B: Composite Geometric Construction with Rotation and Isosceles Triangle
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2020-05-14 00:28
TrianglePolygonIntegralTransformationGeometric Construction
① This example demonstrates a composite geometric figure involving rotation, isosceles triangles, logarithms, congruence, and integral concepts, dynamically shown in GeoGebra. ② Core mathematical concepts include rotation, isosceles triangles, logarithms, congruence, and integral calculus, integrating geometry and algebra. ③ Construction highlights: Based on the construction summary, commands such as Polygon, Segment, Line, CircleArc, Point, and Intersect are used to create multiple quadrilaterals (vierhoek1, vierhoek2, vierhoek3) and numerous auxiliary points (A, B, C, D, E, F, etc.) and segments (a, b, c, d, e, f, etc.), building a complex figure through rotation and congruence relations. ④ Suitable for high school or early college students to explore geometric transformations, congruence properties, logarithmic graphs, and integral area problems, also useful as a dynamic geometry teaching example.

GeoGebra Commands & Parameters

  1. Polygon(A, C, D, B) → vierhoek1, a, c, d, b
  2. Polygon(E, P, Q, F) → vierhoek2, e, p, q, f
  3. Polygon(P, N, O, Q) → vierhoek3, p_1, n, o, q_1
  4. Segment(E, A) → g
  5. Segment(G, C) → h
  6. Segment(H, D) → i
  7. Line(L, M) → j
  8. CircleArc(L, N, G) → k
  9. CircleArc(M, O, H) → r
  10. Segment(G, H) → l
  11. Point(k) → R
  12. Point(k) → S
  13. Point(k) → T
  14. Point(k) → U
  15. Point(k) → G_1
  16. Point(k) → H_1
  17. Point(k) → I_1
  18. Point(k) → J_1
  19. Line(R, l) → m
  20. Line(S, l) → s
  21. Line(T, j) → t
  22. Line(U, j) → f_1
  23. Line(J_1, j) → g_1
  24. Line(I_1, j) → h_1
  25. Line(H_1, j) → i_1
  26. Line(G_1, j) → j_1
  27. Intersect(j_1, r) → V,
  28. Intersect(i_1, r) → W,
  29. Intersect(h_1, r) → Z,
  30. Intersect(g_1, r) → A_1,
  31. Intersect(f_1, r) → B_1,
  32. Intersect(t, r) → C_1,
  33. Intersect(s, r) → D_1,
  34. Intersect(m, r) → E_1,
  35. Polygon(G, H, E_1, R) → vierhoek4, g_2, h_2, e_1, r_1
  36. Polygon(S, R, E_1, D_1) → vierhoek5, s_1, r_2, k_1, d_1
  37. Polygon(T, S, D_1, C_1) → vierhoek6, t_1, s_2, l_1, c_1
  38. Polygon(U, T, C_1, B_1) → vierhoek7, u, t_2, m_1, b_1
  39. Polygon(J_1, U, B_1, A_1) → vierhoek8, n_1, u_1, a_1, f_2
  40. Polygon(I_1, J_1, A_1, Z) → vierhoek9, i_2, j_2, k_2, z_1
  41. Polygon(H_1, I_1, Z, W) → vierhoek10, l_2, m_2, z_2, w
  42. Polygon(G_1, H_1, W, V) → vierhoek11, n_2, p_2, w_1, v
  43. Polygon(N, G_1, V, O) → vierhoek12, n_3, q_2, v_1, o_1
  44. Line(N, e) → a_2
  45. Line(G_1, e) → b_2
  46. Line(H_1, e) → c_2
  47. Line(I_1, e) → d_2
  48. Line(J_1, e) → e_2
  49. Line(U, e) → f_3
  50. Line(T, e) → g_3
  51. Line(S, e) → h_3
  52. Line(R, e) → i_3
  53. Line(G, e) → j_3
  54. Intersect(a_2, g) → F_1
  55. Intersect(g, c_2) → L_1
  56. Intersect(d_2, g) → M_1
  57. Intersect(g, e_2) → N_1
  58. Intersect(g, f_3) → O_1
  59. Intersect(g, g_3) → P_1
  60. Intersect(g, h_3) → Q_1
  61. Intersect(g, i_3) → R_1
  62. Intersect(g, j_3) → S_1
  63. Polygon(E, F_1, N, P) → vierhoek13, e_3, k_3, n_4, p_3
  64. Line(G_1, p_3) → l_3
  65. Intersect(l_3, g) → K_1
  66. Polygon(F_1, K_1, G_1, N) → vierhoek14, m_3, q_3, r_3, n_5
  67. Polygon(K_1, L_1, H_1, G_1) → vierhoek15, s_3, t_3, a_3, b_3
  68. Polygon(L_1, M_1, I_1, H_1) → vierhoek16, c_3, d_3, f_4, g_4
  69. Polygon(M_1, N_1, J_1, I_1) → vierhoek17, h_4, i_4, j_4, k_4
  70. Polygon(N_1, O_1, U, J_1) → vierhoek18, l_4, m_4, u_2, p_4
  71. Polygon(O_1, P_1, T, U) → vierhoek19, q_4, r_4, t_4, u_3
  72. Polygon(P_1, Q_1, S, T) → vierhoek20, s_4, a_4, s_5, t_5
  73. Polygon(Q_1, R_1, R, S) → vierhoek21, b_4, c_4, r_5, s_6
  74. Polygon(R_1, S_1, G, R) → vierhoek22, d_4, e_4, g_5, r_6
  75. Polygon(S_1, A, C, G) → vierhoek23, f_5, a_5, c_5, g_6
  76. Segment(F, B) → h_5
  77. Line(O, q) → i_5
  78. Line(V, q) → j_5
  79. Line(W, q) → k_5
  80. Line(Z, q) → l_5
  81. Line(A_1, q) → m_5
  82. Line(B_1, q) → p_5
  83. Line(C_1, q) → q_5
  84. Line(D_1, q) → b_5
  85. Line(E_1, q) → d_5
  86. Line(H, q) → e_5
  87. Intersect(h_5, i_5) → T_1
  88. Intersect(j_5, h_5) → U_1
  89. Intersect(k_5, h_5) → V_1
  90. Intersect(l_5, h_5) → W_1
  91. Intersect(m_5, h_5) → Z_1
  92. Intersect(h_5, p_5) → A_2
  93. Intersect(h_5, q_5) → B_2
  94. Intersect(h_5, b_5) → C_2
  95. Intersect(d_5, h_5) → D_2
  96. Intersect(h_5, e_5) → E_2
  97. Polygon(Q, O, T_1, F) → vierhoek24, q_6, o_2, f_6, f_7
  98. Polygon(O, V) → veelhoek1, o_3, v_2
  99. Polygon(O, V, U_1, T_1) → vierhoek25, o_4, v_3, h_6, i_6
  100. Polygon(V, W, V_1, U_1) → vierhoek26, v_4, w_2, j_6, k_6
  101. Polygon(W, Z, W_1, V_1) → vierhoek27, w_3, z_3, l_6, m_6
  102. Polygon(Z, A_1, Z_1, W_1) → vierhoek28, z_4, n_6, p_6, t_6
  103. Polygon(A_1, B_1, A_2, Z_1) → vierhoek29, a_6, b_6, c_6, d_6
  104. Polygon(B_1, C_1, B_2, A_2) → vierhoek30, e_6, g_7, h_7, i_7
  105. Polygon(C_1, D_1, C_2, B_2) → vierhoek31, j_7, k_7, l_7, m_7
  106. Polygon(D_1, E_1, D_2, C_2) → vierhoek32, n_7, p_7, q_7, r_7
  107. Polygon(E_1, H, E_2, D_2) → vierhoek33, s_7, h_8, t_7, a_7
  108. Polygon(G, C, D, H) → vierhoek34, g_8, c_7, d_7, h_9
  109. Polygon(D, B, E_2, H) → vierhoek35, d_8, b_7, e_7, h_{10}
  110. Polygon(B, A, E, F) → vierhoek36, b_8, a_8, e_8, f_8
  111. Segment(P, Q) → i_8
  112. Segment(P, E) → j_8
  113. Segment(N, O) → k_8
  114. Segment(C, D) → l_8

AI Drawing Prompt Reference

Draw a complex geometric figure involving multiple quadrilaterals and triangles, constructed through rotation and congruence. The figure should include isosceles triangles, logarithmic graphs, and integral areas, showcasing the integration of geometry and algebra. Start by creating a basic framework of quadrilaterals, then generate auxiliary shapes using rotations and intersection points, ultimately forming a complex structure with interconnected quadrilaterals and triangles.
The prompt above was compiled from the original drawing commands and is for reference only.