六边形相位演示

六边形相位演示
几何画板及绘图内容加载中,请稍等……
2023-01-09 22:38
①本范例演示六边形的几何构造与相关属性;②涉及核心概念包括角度、多边形、正弦函数、积分等;③构造过程中运用了画圆、射线、交点、线段、扇形、向量、平移、缩放、条件判断、多边形、点、中点、旋转、直线、圆弧等 GeoGebra 命令;④适合高中数学教学,用于理解多边形性质与函数图像关系。

GeoGebra 命令及参数

  1. Circle(C, 1.5) → h
  2. Ray(C, D) → c
  3. Intersect(h, c, 1) → P
  4. Ray(A, B) → a
  5. Ray(B, C) → b
  6. Ray(E, A) → e
  7. Circle(A, 1.5) → f
  8. Circle(B, 1.5) → g
  9. Circle(D, 1.5) → k
  10. Circle(E, 1.5) → p
  11. Segment(C, A) → i
  12. Segment(C, E) → j
  13. Intersect(f, a, 1) → F
  14. Intersect(f, i, 1) → G
  15. Intersect(f, e, 1) → H
  16. Intersect(f, e, 2) → I
  17. Intersect(p, e) → J,
  18. Intersect(p, j) → K,
  19. Intersect(k, c, 2) → O
  20. Intersect(h, j, 1) → Q
  21. Intersect(h, i, 1) → R
  22. Intersect(h, b, 1) → S
  23. Intersect(g, a, 2) → T
  24. Intersect(g, b, 1) → U
  25. Intersect(g, a, 1) → V
  26. CircleSector(A, F, G) → q
  27. CircleSector(A, G, H) → r
  28. CircleSector(B, U, V) → s
  29. CircleSector(C, Q, R) → c_1
  30. CircleSector(C, R, S) → d_1
  31. Intersect(k, c, 1) → W
  32. CircleSector(E, J, K) → h_1
  33. CircleSector(A, I, F) → p_1
  34. CircleSector(B, T, U) → q_1
  35. Intersect(h, b, 2) → Z
  36. CircleSector(C, Z, P) → r_1
  37. Vector(A, B) → u
  38. Vector(C, B) → v
  39. Vector(E, D) → w
  40. Vector(C, D) → u_1
  41. Vector(C, E) → v_1
  42. Vector(A, E) → w_1
  43. Translate(d_1, v) → s_1
  44. Dilate(C, If[1 < l ≤ 2, 2 - l, 0], E) → C'_1
  45. Dilate(C, If[2 < l ≤ 3, 3 - l, 0], D) → C'_2
  46. Dilate(E, If[2 < l ≤ 3, 3 - l, 0], D) → E'
  47. Vector(A, B) → a_1
  48. Vector(E, E') → j_1
  49. Vector(C, C'_2) → l_1
  50. Vector(C, C'_1) → m_1
  51. Translate(r, w_1) → r'_2
  52. Translate(c_1, v_1) → f_2
  53. Translate(c_1, m_1) → g_2
  54. Translate(q, a_1) → r'
  55. Vector(D, C) → u_2
  56. Vector(E, C) → v_2
  57. Vector(A, C) → w_2
  58. Vector(B, C) → l_2
  59. Dilate(B, If[0 < o < 1, 1 - o, 0], C) → B'
  60. Dilate(A, If[1 < o < 2, 2 - o, 0], C) → A'_2
  61. Dilate(E, If[2 < o < 3, 3 - o, 0], C) → E'_1
  62. Dilate(D, If[3 < o < 4, 4 - o, 0], C) → D'
  63. Vector(B, B') → m_2
  64. Vector(A, A'_2) → n_2
  65. Vector(E, E'_1) → s_2
  66. Vector(D, D') → t_2
  67. Translate(q_1, m_2) → c_3
  68. Translate(q_1, l_2) → d_3
  69. Translate(p_1, w_2) → e_3
  70. If(1 < o < 2, Translate[p_1, n_2]) → h_3
  71. Ray(D, A_1) → a_3
  72. Ray(A_1, E) → b_3
  73. Circle(A_1, 1.5) → q_3
  74. Intersect(q_3, b_3, 1) → N
  75. Intersect(q_3, a_3, 2) → B_1
  76. Intersect(k, c, 2) → C_1
  77. Intersect(k, a_3, 1) → D_1
  78. Intersect(k, c, 1) → E_1
  79. Intersect(p, b_3, 1) → F_1
  80. Dilate(C, If[2 < l < 3, 3 - l, 0], A_1) → C'_3
  81. Vector(E, A_1) → f_1
  82. Vector(C, A_1) → g_1
  83. Vector(C, C'_3) → b_2
  84. Intersect(q_3, a_3, 1) → I_1
  85. CircleSector(D, D_1, E_1) → k_3
  86. Vector(C, D) → j_2
  87. Vector(A_1, D) → u_3
  88. Intersect(p, b_3, 2) → J_1
  89. Polygon(A, B, C) → poly1, c_4, a_4, b_4
  90. Polygon(A, C, E) → poly2, e_4, a_5, c_5
  91. Polygon(E, C, A_1) → poly3, a_6, e_5, c_6
  92. Polygon(A_1, C, D) → poly4, d_4, a_7, c_7
  93. Polygon(A, B, C, D, A_1, E) → poly5, a_8, b_5, c_8, d_5, a_9, e_6
  94. Intersect(e, e_6) → K_1
  95. Intersect(p, e, 1) → L_1
  96. CircleSector(E, J_1, L_1) → f_4
  97. CircleSector(A_1, B_1, N) → g_4
  98. CircleSector(D, C_1, D_1) → h_4
  99. Vector(E, C) → j_3
  100. Vector(A_1, C) → l_3
  101. Vector(D, C) → m_3
  102. Translate(f_4, j_3) → k_4
  103. Translate(g_4, l_3) → p_4
  104. Translate(h_4, m_3) → q_4
  105. Dilate(E, If[2 < o < 3, 3 - o, 0], C) → E'_3
  106. Dilate(A_1, If[3 < o < 4, 4 - o, 0], C) → M_7
  107. Dilate(D, If[4 < o < 5, 5 - o, 0], C) → D'_1
  108. Vector(E, E'_3) → n_3
  109. Vector(A_1, M_7) → u_4
  110. Vector(D, D'_1) → v_4
  111. If(2 < o < 3, Translate[f_4, n_3]) → r_4
  112. If(3 < o < 4, Translate[g_4, u_4]) → s_4
  113. If(4 < o < 5, Translate[h_4, v_4]) → t_4
  114. Ray(C, A_1) → l_4
  115. Ray(C, E) → m_4
  116. Point(l_4) → N_1
  117. Point(m_4) → O_1
  118. Segment(D, C) → n_4
  119. Segment(C, B) → f_5
  120. Segment(B, A) → g_5
  121. Segment(A, E) → h_5
  122. Segment(E, A_1) → i_5
  123. Segment(A_1, D) → j_5
  124. Midpoint(f_5) → M_2
  125. Midpoint(g_5) → M_1
  126. Rotate(d_1, If[0 < l ≤ 1, ((-l) * 180°), -180°], M_2) → d
  127. Rotate(C, If[0 < l ≤ 1, ((-l) * 180°), -180°], M_2) → C'
  128. Segment(M_2, C') → t
  129. Rotate(q, If[0 < l ≤ 1, (l * 180°), 180°], M_1) → q'
  130. Rotate(A, If[0 < l ≤ 1, (l * 180°), 180°], M_1) → A'
  131. Segment(M_1, A') → e_1
  132. Rotate(R, 180°, M_2) → R'
  133. Line(B, R') → k_1
  134. Ray(E, O_1) → i_1
  135. Midpoint(h_5) → M_6
  136. Rotate(r, If[1 < l ≤ 2, ((-(l - 1)) * 180°), -180°], M_6) → r'_1
  137. Rotate(A, If[1 < l ≤ 2, ((-(l - 1)) * 180°), -180°], M_6) → A'_1
  138. Segment(M_6, A'_1) → n_1
  139. CircleSector(E, K, F_1) → c_2
  140. Midpoint(i_5) → M_5
  141. Rotate(E, If[2 < l ≤ 3, ((-(l - 2)) * 180°), -180°], M_5) → E'_2
  142. Segment(M_5, E'_2) → a_2
  143. Rotate(c_2, If[2 < l ≤ 3, ((-(l - 2)) * 180°), -180°], M_5) → d_2
  144. Segment(A_1, C) → e_2
  145. Intersect(h, e_2, 1) → U_1
  146. CircleSector(C, U_1, Q) → h_2
  147. CircleSector(C, P, U_1) → k_2
  148. Vector(C, C'_3) → t_1
  149. Translate(h_2, t_1) → p_2
  150. Intersect(q_3, e_2, 1) → R_1
  151. CircleSector(A_1, N, R_1) → q_2
  152. CircleSector(A_1, R_1, I_1) → r_2
  153. Vector(C, A_1) → i_2
  154. Translate(U_1, i_2) → S_1
  155. Ray(A_1, S_1) → f_3
  156. Midpoint(j_5) → M_4
  157. Midpoint(n_4) → M_3
  158. Rotate(k_2, If[3 < l ≤ 4, ((l - 3) * 180°), 180°], M_3) → g_3
  159. Rotate(C, If[3 < l ≤ 4, ((l - 3) * 180°), 180°], M_3) → C'_4
  160. Rotate(U_1, 180°, M_3) → W_1
  161. Segment(M_3, C'_4) → i_3
  162. Rotate(r_2, If[3 < l ≤ 4, ((-(l - 3)) * 180°), -180°], M_4) → p_3
  163. Rotate(A_1, If[3 < l ≤ 4, ((-(l - 3)) * 180°), -180°], M_4) → Z_1
  164. Segment(M_4, Z_1) → r_3
  165. Line(D, W_1) → s_3
  166. CircleArc(C, R, S) → t_3
  167. CircleArc(A, F, G) → k_5
  168. CircleArc(C, Q, R) → p_5
  169. CircleArc(A, G, H) → q_5
  170. CircleArc(C, U_1, Q) → r_5
  171. CircleArc(E, K, F_1) → s_5
  172. CircleArc(C, P, U_1) → t_5
  173. CircleArc(A_1, R_1, I_1) → d_6

AI 绘图提示语参考

请绘制一个正六边形,包含六个等边三角形和六个圆弧。构造顺序是从中心开始,依次画出六个圆,然后连接圆的交点,形成六边形。确保图形对称,线条清晰,适用于数学教育。
以上提示语为根据原始绘图命令整理而来,仅供参考。