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Nigde - Ak madrassa：几何作图与函数图像分析

Nigde - Ak madrassa：几何作图与函数图像分析
几何画板及绘图内容加载中，请稍等……
2020-08-18 14:04
函数解析几何几何作图
所属专题 Fatin Uluengin - muqarnas
该范例演示了通过几何作图方法分析函数图像的特性。核心数学概念包括三角函数、解析几何和几何作图。作图要点涉及使用Intersect、Polygon、Rotate等GeoGebra命令构建三角形、圆和轨迹。适合高中生或大学低年级学生用于学习几何与函数结合的应用。

GeoGebra 命令及参数

  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 绘图提示语参考

这是一个基于坐标几何的图形构造示例。图形由坐标轴交点、由坐标轴和线段构成的四边形、通过旋转和反射生成的三角形、以及由这些图形构成的轨迹组成。构造顺序是先确定坐标轴交点，然后构建四边形，接着通过旋转和反射生成其他图形，最后形成多边形和轨迹。适合学习几何与函数的学生使用。
以上提示语为根据原始绘图命令整理而来，仅供参考。