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正方形减去风筝等于什么？

正方形减去风筝等于什么？
几何画板及绘图内容加载中，请稍等……
2017-05-02 01:00
多边形变换几何作图
这个范例演示了一个正方形减去一个风筝后的结果。涉及的核心数学概念包括几何变换和多边形。通过使用GeoGebra命令如Ray, Segment, Circle, Intersect, Rotate, Dilate等，可以动态地修改图形。适合初中及以上学生学习几何变换和多边形相关知识。

GeoGebra 命令及参数

  1. Ray(A, B_2) → m_2
  2. Segment(A, B_2) → g
  3. Circle(B_2, g) → q_2
  4. Intersect(q_2, m_2, 2) → J_1
  5. Segment(B_2, J_1) → n_2
  6. Rotate(A, If[1 < e ≤ 2, ((-(e - 1)) * π / 2), -1.5707963267948966], B_2) → A'_1
  7. Dilate(A, If[0 < e ≤ 1, 1 - e, 0], B_2) → A'
  8. Rotate(A', If[1 < e ≤ 2, ((-(e - 1)) * π / 2), -1.5707963267948966], B_2) → A''
  9. Polygon(A, B_2, 4) → poly1, a, b, c, d, C, D
  10. Midpoint(A, C) → V
  11. CircleArc(V, C, D) → g_2
  12. Point(g_2) → B
  13. Segment(C, B) → j_1
  14. Segment(A, B) → n
  15. Rotate(A'', If[2 < e ≤ 3, ((-(e - 2)) * π / 2), -1.5707963267948966], C) → A'''
  16. Rotate(A'_1, If[2 < e ≤ 3, ((-(e - 2)) * π / 2), -1.5707963267948966], C) → R
  17. Segment(R, A''') → f''
  18. Intersect(n, f'') → Z
  19. Segment(B, Z) → l_1
  20. Segment(A, A') → f
  21. Segment(A'_1, A'') → f'
  22. Segment(B_2, C) → h
  23. Segment(C, D) → i
  24. Circle(B_2, (0.1 * Distance[A, B_2])) → p
  25. Segment(D, A) → j
  26. Circle(C, Radius[p]) → k
  27. Circle(A, (0.1 * j)) → q
  28. Circle(D, (0.1 * j)) → r
  29. Segment(A, C) → l
  30. Segment(D, B_2) → m
  31. Intersect(r, j, 1) → F
  32. Intersect(r, m, 1) → G
  33. Intersect(r, i, 1) → H
  34. Intersect(k, i, 1) → I
  35. Intersect(k, l, 1) → J
  36. Intersect(k, h, 1) → K
  37. Intersect(p, h, 1) → L
  38. Intersect(p, m, 1) → M
  39. Intersect(p, g, 1) → N
  40. Intersect(q, g, 1) → O
  41. Intersect(q, l, 1) → P
  42. Intersect(q, j, 1) → Q
  43. CircleSector(B_2, L, N) → s
  44. Rotate(R, If[3 < e ≤ 4, ((-(e - 3)) * π / 2), -1.5707963267948966], D) → R'
  45. Rotate(A''', If[3 < e ≤ 4, ((-(e - 3)) * π / 2), -1.5707963267948966], D) → S
  46. Segment(R', S) → f'''
  47. Dilate(B_2, If[4 < e ≤ 5, 5 - e, 0], C) → B'
  48. Vector(B_2, B') → u
  49. Translate(s, u) → s'
  50. Rotate(s', If[5 < e ≤ 6, ((e - 5) * π / 2), 1.5707963267948966], C) → s''
  51. Dilate(C, If[6 < e ≤ 7, 7 - e, 0], D) → C'
  52. Vector(C, C') → v
  53. Translate(s'', v) → s'''
  54. Rotate(s''', If[7 < e ≤ 8, ((e - 7) * π / 2), 1.5707963267948966], D) → t
  55. Dilate(D, If[8 < e ≤ 9, 9 - e, 0], A) → D'
  56. Vector(D, D') → w
  57. Translate(t, w) → t'
  58. Rotate(t', If[9 < e ≤ 10, ((e - 9) * π / 2), 1.5707963267948966], A) → t''
  59. Dilate(B_2, If[18 < e ≤ 19, 19 - e, 0], C) → B'_1
  60. Dilate(B_2, If[18 < e ≤ 19, 19 - e, 0], A) → B'_2
  61. Dilate(B_2, If[18 < e ≤ 19, 19 - e, 0], D) → B'_3
  62. Vector(B_2, B'_1) → v_1
  63. Vector(B_2, B'_3) → w_1
  64. Vector(B_2, B'_2) → i_1
  65. Circle(A, n - j_1) → h_2
  66. Dilate(B, If[10 < e ≤ 11, 11 - e, 0], C) → W'
  67. Dilate(B_2, If[13 < e ≤ 14, 14 - e, 0], B) → B'_4
  68. Vector(B_2, B'_4) → u_1
  69. Translate(s, u_1) → s'_1
  70. Line(B, f') → a_1
  71. Point(a_1) → U
  72. Angle(U, B, C) → α
  73. Rotate(B, If[14 < e ≤ 15, ((-(e - 14)) * π / 2), ((-π)) / 2], B) → W'_2
  74. Rotate(W', If[14 < e ≤ 15, ((-(e - 14)) * π / 2), ((-π)) / 2], B) → W''
  75. Line(A, B_2) → h_1
  76. Angle(B, A, D) → β
  77. Dilate(D, If[19 < e ≤ 20, 20 - e, 0], B) → D'_1
  78. Mirror(C, D) → C'_1
  79. Rotate(C, ((-π)) / 3, B_2) → C'_2
  80. Segment(B_2, C'_2) → f_1
  81. Segment(C, C'_2) → g_1
  82. Intersect(k, g_1, 1) → E
  83. Intersect(k, h) → T,
  84. CircleSector(C, T, E) → d_1
  85. Rotate(D, 15°, C) → D'_2
  86. Angle(D, C, D'_2) → γ
  87. Ray(C, D'_2) → k_1
  88. Rotate(C, (-(15°)), D) → C'_3
  89. Angle(C'_3, D, C) → δ
  90. Ray(D, C'_3) → m_1
  91. Intersect(k_1, m_1) → W
  92. Rotate(B_2, If[10 < e ≤ 11, (((-π)) / 3 * (e - 10)), ((-π)) / 3], B_2) → A_1
  93. Rotate(C, If[10 < e ≤ 11, (((-π)) / 3 * (e - 10)), ((-π)) / 3], B_2) → C'_4
  94. Rotate(B_2, If[11 < e ≤ 12, (π / 3 * (e - 11)), π / 3], C) → B_1
  95. Rotate(C, If[11 < e ≤ 12, (π / 3 * (e - 11)), π / 3], C) → C'_5
  96. Rotate(E, If[12 < e ≤ 13, (((-π)) / 6 * (e - 12)), ((-π)) / 6], C) → E'
  97. Polygon(C, W, D) → poly2, d_2, c_2, w_2
  98. Polygon(A, W, D) → poly3, d_3, a_2, w_3
  99. Polygon(B_2, W, C) → poly4, c_3, b_2, w_4
  100. Polygon(A, B_2, W) → poly5, w_5, a_3, b_1
  101. Rotate(T, 15°, C) → T'
  102. Angle(T, C, T') → ε
  103. Ray(C, T') → q_1
  104. Dilate(C, If[21 < e ≤ 22, 22 - e, 0], D) → C'_8
  105. Vector(C, C'_8) → u_2
  106. Dilate(D, If[23 < e ≤ 24, 24 - e, 0], W) → D'_3
  107. Dilate(C, If[23 < e ≤ 24, 24 - e, 0], W) → C'_9
  108. Dilate(B_2, If[25 < e ≤ 26, 26 - e, 0], W) → G_1
  109. Dilate(A, If[25 < e ≤ 26, 26 - e, 0], W) → A'_2
  110. Segment(A, A'_2) → j_2
  111. Segment(B_2, G_1) → l_2
  112. Rotate(B_2, If[26.75 < e ≤ 27.75, (π / 2 * (e - 26.75)), π / 2], B_2) → H_1
  113. Rotate(C'_2, If[26.75 < e ≤ 27.75, (π / 2 * (e - 26.75)), π / 2], B_2) → I_1
  114. Rotate(C, If[26.75 < e ≤ 27.75, (π / 2 * (e - 26.75)), π / 2], B_2) → C'_{10}
  115. Polygon(H_1, I_1, C'_{10}) → poly6', c'_{10}, h_3, i_3
  116. Polygon(A, B_2, C, D) → poly7, a_4, b_4, c_4, d_4
  117. Segment(B_2, C) → j_3
  118. Point(j_3) → V_1
  119. Ray(D, V_1) → k_3
  120. Ray(A, B_2) → n_3
  121. Intersect(k_3, n_3) → W_1
  122. Angle(V_1, D, C) → κ
  123. Angle(C, V_1, D) → θ
  124. Segment(V_1, C) → p_3
  125. Rotate(V_1, (2 * θ), V_1) → Z_1
  126. Rotate(C, (2 * θ), V_1) → C'_7
  127. Segment(Z_1, C'_7) → q_3
  128. Ray(D, C'_7) → r_3
  129. Intersect(r_3, n_3) → A_2
  130. Segment(A, A_2) → s_3
  131. Segment(A_2, W_1) → t_3
  132. Polygon(C'_7, V_1, C, D) → poly8, c'_7, v_3, c_5, d_5
  133. Polygon(D, A, B_2, V_1, C'_7) → poly9, d_6, a_5, b_5, v_4, c'_1
  134. Dilate(C, If[10 < e ≤ 11, 11 - e, 0], V_1) → C'_{11}
  135. Segment(C, C'_{11}) → n_1
  136. Dilate(A, If[14 < e ≤ 15, 15 - e, 0], A_2) → A'_4
  137. Segment(A, A'_4) → p_1
  138. Rotate(C, If[11 < e ≤ 12, (((e - 11) * 2) * θ), (2 * θ)], V_1) → C'_{12}
  139. Rotate(C'_{11}, If[11 < e ≤ 12, (((e - 11) * 2) * θ), (2 * θ)], V_1) → U_1
  140. Segment(C'_{12}, U_1) → r_1
  141. Rotate(R, If[12 < e ≤ 13, (((-(e - 12)) * 2) * κ), (-2 * κ)], D) → R'_1
  142. Rotate(A''', If[12 < e ≤ 13, (((-(e - 12)) * 2) * κ), (-2 * κ)], D) → C_2
  143. Segment(R'_1, C_2) → f'''_1
  144. Polygon(D, C, V_1, C'_7) → poly10, d_7, c_6, v_5, c'_2
  145. Dilate(C'_{12}, If[13 < e ≤ 14, 14 - e, 0], A_2) → D_2
  146. Segment(C'_{12}, D_2) → s_1
  147. Dilate(D, If[15 < e ≤ 16, 16 - e, 0], V_1) → D'_4
  148. Segment(D, D'_4) → t_1
  149. Dilate(V_1, If[16 < e ≤ 17, 17 - e, 0], W_1) → C_1
  150. Segment(V_1, C_1) → c_1
  151. Line(A, B_2) → e_1
  152. Circle(A_2, p_1) → e_2
  153. Intersect(e_2, e_1, 2) → D_1
  154. Dilate(A_2, If[15 < e ≤ 16, 16 - e, 0], D_1) → E_1
  155. Segment(A_2, E_1) → f_2
  156. Dilate(D_1, If[16 < e ≤ 17, 17 - e, 0], W_1) → F_1
  157. Segment(D_1, F_1) → i_2
  158. Rotate(A, If[17 < e ≤ 18, ((-(e - 17)) * π), (-π)], A_2) → A'_3
  159. Rotate(A'_4, If[17 < e ≤ 18, ((-(e - 17)) * π), (-π)], A_2) → K_1
  160. Segment(A'_3, K_1) → k_2
  161. Dilate(V_1, If[18 < e ≤ 19, 19 - e, 0], D_1) → L_1
  162. Vector(V_1, L_1) → v_2
  163. Translate(C, v_2) → C'_6
  164. Translate(C'_{11}, v_2) → M_1
  165. Segment(C'_6, M_1) → p_2
  166. Rotate(C'_6, If[19 < e ≤ 20, ((-(e - 19)) * π / 2), ((-π)) / 2], D_1) → N_1
  167. Rotate(M_1, If[19 < e ≤ 20, ((-(e - 19)) * π / 2), ((-π)) / 2], D_1) → O_1
  168. Segment(N_1, O_1) → r_2

AI 绘图提示语参考

画一个正方形和一个风筝形，展示从正方形中减去风筝形的几何结果。首先绘制正方形的边和顶点，然后绘制风筝形的对角线并确定顶点。接着，通过旋转和缩放操作对风筝形进行几何变换，并将其从正方形中减去。最后，添加一些辅助线和圆弧来强调几何变换和关键点，完成整个图形的绘制。
以上提示语为根据原始绘图命令整理而来，仅供参考。