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Nigde - Ak madrassa: Geometric Construction and Function Analysis

Nigde - Ak madrassa: Geometric Construction and Function Analysis
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2020-08-18 14:04
FunctionCoordinate GeometryGeometric Construction
In collections Fatin Uluengin - muqarnas
This example demonstrates the analysis of function graphs through geometric construction. Key mathematical concepts include trigonometry, coordinate geometry, and geometric construction. The construction involves using GeoGebra commands like Intersect, Polygon, and Rotate to build triangles, circles, and loci. Suitable for high school students or college freshmen learning the application of geometry and functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. ConstructionStep() → stap
  3. Polygon(E, B, C, D) → vierhoek1, e, b, c, d
  4. Segment(E, C) → f
  5. Segment(D, B) → g
  6. Intersect(d, yAxis) → F
  7. Intersect(b, yAxis) → G
  8. Segment(F, G) → h
  9. Intersect(e, xAxis) → H
  10. Intersect(c, xAxis) → I
  11. Segment(H, I) → i
  12. Rotate(I, 22.5°) → I'
  13. Ray(A, I') → j
  14. Intersect(c, j) → J
  15. Segment(A, J) → k
  16. Sequence(Segment[Rotate[A, (nn * 90°)], Rotate[J, (nn * 90°)]], nn, 1, 3) → l1
  17. Mirror(A, xAxis) → A'
  18. Mirror(J, xAxis) → J'
  19. Segment(A', J') → k'
  20. Sequence(Segment[Rotate[A', (nn * 90°)], Rotate[J', (nn * 90°)]], nn, 1, 3) → l2
  21. Rotate(J, 90°) → J'_1
  22. Mirror(J'_1, yAxis) → K
  23. Mirror(J, yAxis) → J'_2
  24. Mirror(J', yAxis) → J''
  25. Mirror(J'_1, xAxis) → L
  26. Mirror(K, xAxis) → K'
  27. Segment(J'_1, L) → l
  28. Segment(K, K') → m
  29. Segment(J'_2, J) → n
  30. Segment(J'', J') → p
  31. Segment(J'', K) → q
  32. Segment(L, J) → r
  33. Segment(J'_1, J') → s
  34. Segment(J'_2, K') → t
  35. Intersect(h, q) → M
  36. Intersect(n, q) → N
  37. Intersect(f, n) → O
  38. Intersect(h, r) → P
  39. Intersect(p, t) → Q
  40. Intersect(g, l) → R
  41. Polygon(R, L, P, Q) → vierhoek2, r_1, l_1, p_1, q_1
  42. Sequence(Polygon[Rotate[R, (nn * 45°)], Rotate[L, (nn * 45°)], Rotate[P, (nn * 45°)], Rotate[Q, (nn * 45°)]], nn, 1, 7) → l3
  43. Segment(J'', L) → a
  44. Line(B, C) → f_1
  45. Line(J'', J) → g_1
  46. Intersect(f_1, g_1) → S
  47. Line(S, yAxis) → h_1
  48. Polygon(B, S, 4) → veelhoek1, i_1, j_1, k_1, m_1, T, U
  49. Line(J'_1, J'_2) → n_1
  50. Line(J, K) → s_1
  51. Line(B, E) → t_1
  52. Intersect(s_1, t_1) → V
  53. Line(C, D) → a_1
  54. Mirror(S, yAxis) → S'
  55. Mirror(T, yAxis) → T'
  56. Polygon(T, T', 4) → veelhoek2, b_1, c_1, d_1, e_1, W, Z
  57. Mirror(S, xAxis) → S'_1
  58. Intersect(n_1, a_1) → A_1
  59. Intersect(g_1, c_1) → B_1
  60. Intersect(a_1, b_1) → C_1
  61. Polygon(S'_1, E, 4) → veelhoek3, f_2, g_2, h_2, i_2, D_1, E_1
  62. Polygon(D, B_1, 4) → veelhoek4, j_2, k_2, l_2, m_2, F_1, G_1
  63. Polygon(C_1, T', 4) → veelhoek5, n_2, p_2, q_2, r_2, H_1, I_1
  64. Segment(S, B_1) → s_2
  65. Segment(S'_1, S') → t_2
  66. Segment(S'_1, C_1) → a_2
  67. Segment(C_1, V) → b_2
  68. Segment(S, A_1) → c_2
  69. Segment(A_1, U) → d_2
  70. Segment(U, B_1) → e_2
  71. Intersect(e_1, xAxis) → J_1
  72. Intersect(c_1, xAxis) → K_1
  73. Segment(J_1, K_1) → f_3
  74. Intersect(d_1, yAxis) → L_1
  75. Intersect(b_1, yAxis) → M_1
  76. Segment(L_1, M_1) → g_3
  77. Segment(V, S') → h_3
  78. Intersect(a_2, c_2) → N_1
  79. Line(N_1, g_3) → i_3
  80. Intersect(i_3, s_2) → O_1
  81. Intersect(i_3, t_2) → P_1
  82. Polygon(P_1, O_1, 8) → veelhoek6, j_3, R_1, S_1, T_1, U_1, V_1, k_3, l_3, m_3, n_3, p_3, q_3, r_3, Q_1
  83. Segment(Z, T') → s_3
  84. Segment(W, T) → t_3
  85. Segment(S, U) → a_3
  86. Intersect(t_3, a_3) → W_1
  87. Rotate(W_1, (-(60°)), B) → Z_1
  88. Rotate(W_1, 60°, B) → A_2
  89. CircleArc(B, Z_1, A_2) → c_3
  90. Intersect(c_3, s_2, 1) → B_2
  91. Intersect(c_3, d_2, 1) → C_2
  92. Rotate(B, (-(120°)), B_2) → B'
  93. CircleArc(B_2, B', B) → d_3
  94. Rotate(B, 120°, C_2) → B'_1
  95. CircleArc(C_2, B, B'_1) → e_3
  96. Intersect(j_1, e_1) → D_2
  97. Intersect(j_1, e_1) → E_2
  98. Intersect(d_3, Segment[S, T]) → F_2,
  99. Intersect(k_1, b_1) → G_2
  100. Intersect(k_1, b_1) → H_2
  101. Intersect(b_1, n_2) → I_2
  102. Intersect(e_3, Segment[T', T]) → J_2,
  103. Segment(F_2, B) → b_3
  104. Segment(F_2, C_2) → f_4
  105. Segment(B, J_2) → g_4
  106. Segment(J_2, B_2) → h_4
  107. Segment(B_2, C_2) → i_4
  108. Sequence(Rotate[l4, (nn * 90°)], nn, 1, 3) → l5
  109. Line(N_1, s_2) → j_4
  110. Line(B_2, g_3) → k_4
  111. Line(C_2, q_2) → l_4
  112. Line(C_2, b_1) → m_4
  113. Point(m_4) → K_2
  114. Intersect(a_2, e_2) → L_2
  115. Mirror(K_2, g_3) → M_2
  116. Polygon(L_2, K_2, M_1, M_2) → vierhoek3, n_4, p_4, q_4, r_4
  117. Line(C_2, p_4) → s_4
  118. Intersect(s_4, b_1) → N_2
  119. Mirror(N_2, g_3) → O_2
  120. Segment(C_2, N_2) → t_4
  121. Mirror(C_2, g_3) → P_2
  122. Segment(C_2, K_2) → a_4
  123. Segment(M_2, P_2) → b_4
  124. Segment(P_2, O_2) → c_4
  125. Segment(L_2, K') → d_4
  126. Segment(Q_1, U) → e_4
  127. Rotate(C_2, (-(90°))) → R_2
  128. Rotate(N_2, (-(90°))) → S_2
  129. Segment(R_2, S_2) → f_5
  130. Rotate(U, (-(90°))) → U'
  131. Rotate(K_2, (-(90°))) → T_2
  132. Rotate(M_2, (-(90°))) → U_2
  133. Segment(J_1, T_2) → g_5
  134. Segment(J_1, U_2) → h_5
  135. Segment(T_2, N_1) → i_5
  136. Segment(U_2, N_1) → j_5
  137. Segment(R_2, T_2) → k_5
  138. Segment(U_2, B_2) → l_5
  139. Segment(L, L_2) → m_5
  140. Mirror(K_2, f_3) → V_2
  141. Mirror(M_2, f_3) → W_2
  142. Intersect(c_2, h_3) → Z_2
  143. Polygon(L_1, V_2, Z_2, W_2) → vierhoek4, n_5, v_2, z_2, w_2
  144. Point(b_2) → A_3
  145. Segment(A_3, V_2) → p_5
  146. Point(l5) → B_3
  147. Segment(W_2, B_3) → q_5
  148. Segment(B_3, U_1) → r_5
  149. Segment(J'_1, Z_2) → s_5
  150. Segment(Z_2, K) → t_5
  151. Segment(K, D) → a_5
  152. Segment(E, J'_1) → b_5
  153. Segment(V, V_1) → c_5
  154. Segment(B_3, A_1) → d_5
  155. Intersect(q_5, d_5) → C_3
  156. Segment(U_1, C_3) → e_5
  157. Mirror(T_2, yAxis) → D_3
  158. Mirror(U_2, yAxis) → E_3
  159. Mirror(N_1, yAxis) → F_3
  160. Segment(D_3, K_1) → f_6
  161. Segment(D_3, F_3) → g_6
  162. Segment(F_3, E_3) → h_6
  163. Segment(E_3, K_1) → i_6
  164. Mirror(R_2, yAxis) → G_3
  165. Mirror(B_2, yAxis) → H_3
  166. Segment(G_3, D_3) → j_6
  167. Segment(E_3, H_3) → k_6
  168. Segment(S'_1, J'_2) → l_6
  169. Segment(S, J'') → m_6
  170. Segment(J', S') → n_6
  171. Segment(J, B_1) → p_6
  172. Segment(R_1, P_2) → q_6
  173. Segment(P_2, C_1) → r_6
  174. Segment(D, J) → s_6
  175. Segment(N_1, J'_2) → t_6
  176. Segment(N_1, J'') → a_6
  177. Segment(J'_2, E) → b_6
  178. Segment(J, F_3) → c_6
  179. Segment(F_3, J') → d_6
  180. Segment(S_1, S') → e_6
  181. Segment(J', C) → f_7
  182. Segment(J'', B) → g_7
  183. Segment(S, O_1) → h_7
  184. Segment(S'_1, P_1) → i_7

AI Drawing Prompt Reference

This is a geometric construction example based on coordinate geometry. The figure consists of the intersection of the coordinate axes, a quadrilateral formed by the axes and segments, triangles generated through rotation and reflection, and trajectories formed by these shapes. The construction order is to first determine the intersection of the axes, then build the quadrilateral, followed by generating other shapes via rotation and reflection, and finally forming polygons and trajectories. Suitable for students learning geometry and functions.
The prompt above was compiled from the original drawing commands and is for reference only.