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动态几何图形演示 by Tim Brzezinski (14)

动态几何图形演示 by Tim Brzezinski (14)
几何画板及绘图内容加载中，请稍等……
2017-12-17 09:25
立体几何变换几何作图
①本范例动态演示多边形构造及相关几何变换；②涉及核心概念：面积、质心、相似变换、四边形、极限、立体图形、随机实验、直线；③作图要点：运用Polygon, Midpoint, Segment, Intersect, Angle, Circle, Min, Dilate, Rotate, Vector, Translate, CircleSector等命令；④适合高中及以上学生及数学爱好者用于探索几何变换与极限现象。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → q1, a, b, c, d
  2. Midpoint(c) → E
  3. Midpoint(b) → F
  4. Midpoint(a) → G
  5. Midpoint(d) → H
  6. Segment(A, C) → f
  7. Segment(D, B) → g
  8. Segment(C, H) → h
  9. Segment(A, E) → i
  10. Intersect(i, h) → I
  11. Segment(B, E) → j
  12. Segment(D, F) → k
  13. Intersect(k, j) → J
  14. Segment(C, G) → l
  15. Segment(A, F) → m
  16. Intersect(m, l) → K
  17. Segment(B, H) → n
  18. Segment(D, G) → p
  19. Intersect(p, n) → L
  20. Polygon(I, J, K, L) → q2, i_1, j_1, k_1, l_1
  21. Angle(q2) → α, β, γ, δ
  22. Angle(q1) → ε, ζ, η, θ
  23. Circle(A, a / 3) → e
  24. Intersect(e, a, 1) → M
  25. Circle(M, a / 3) → q
  26. Intersect(q, a, 2) → N
  27. Circle(B, b / 3) → r
  28. Intersect(r, b, 1) → O
  29. Circle(O, b / 3) → s
  30. Intersect(s, b, 2) → P
  31. Circle(C, c / 3) → t
  32. Intersect(t, c, 1) → Q
  33. Circle(Q, c / 3) → c_1
  34. Intersect(c_1, c, 2) → R
  35. Circle(D, d / 3) → d_1
  36. Intersect(d_1, d, 1) → S
  37. Circle(S, d / 3) → e_1
  38. Intersect(e_1, d, 2) → T
  39. Min({l_1, i_1, j_1, k_1}) → o
  40. Circle(L, (0.35 * o)) → g_1
  41. Circle(K, (0.35 * o)) → p_1
  42. Circle(J, (0.35 * o)) → h_1
  43. Circle(I, (0.35 * o)) → f_1
  44. Segment(A, D) → m_1
  45. Segment(D, C) → n_1
  46. Segment(C, B) → q_1
  47. Segment(B, A) → r_1
  48. Segment(L, K) → s_1
  49. Segment(K, J) → t_1
  50. Segment(J, I) → a_1
  51. Segment(I, L) → b_1
  52. Intersect(f_1, b_1, 1) → U
  53. Intersect(g_1, s_1, 1) → V
  54. Intersect(p_1, t_1, 1) → W
  55. Intersect(h_1, a_1) → Z,
  56. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], H) → A'
  57. Dilate(D, If[0 < u ≤ 1, 1 - u, 0], E) → D'
  58. Segment(A, A') → f_2
  59. Segment(D, D') → g_2
  60. Rotate(A, If[1 < u ≤ 2, ((u - 1) * π), π], H) → A'_1
  61. Rotate(A', If[1 < u ≤ 2, ((u - 1) * π), π], H) → A''
  62. Segment(A'_1, A'') → h_2
  63. Rotate(D, If[1 < u ≤ 2, ((u - 1) * π), π], E) → D'_1
  64. Rotate(D', If[1 < u ≤ 2, ((u - 1) * π), π], E) → D''
  65. Segment(D'_1, D'') → i_2
  66. Dilate(A, If[2 < u ≤ 3, 3 - u, 0], E) → A'_2
  67. Dilate(C, If[2 < u ≤ 3, 3 - u, 0], H) → C'
  68. Segment(A, A'_2) → j_2
  69. Segment(C, C') → k_2
  70. Dilate(D, If[6 < u ≤ 7, 7 - u, 0], F) → D'_2
  71. Dilate(B, If[6 < u ≤ 7, 7 - u, 0], E) → B'
  72. Segment(D, D'_2) → l_2
  73. Segment(B, B') → m_2
  74. Dilate(C, If[4 < u ≤ 5, 5 - u, 0], F) → C'_1
  75. Dilate(B, If[4 < u ≤ 5, 5 - u, 0], G) → B'_1
  76. Segment(C, C'_1) → n_2
  77. Segment(B, B'_1) → p_2
  78. Rotate(B, If[5 < u ≤ 6, ((u - 5) * π), π], G) → B'_2
  79. Rotate(B'_1, If[5 < u ≤ 6, ((u - 5) * π), π], G) → A_1
  80. Segment(B'_2, A_1) → q_2
  81. Rotate(C, If[5 < u ≤ 6, ((u - 5) * π), π], F) → C'_2
  82. Rotate(C'_1, If[5 < u ≤ 6, ((u - 5) * π), π], F) → B_1
  83. Segment(C'_2, B_1) → r_2
  84. Dilate(C, If[8 < u ≤ 9, 9 - u, 0], G) → F'
  85. Dilate(A, If[8 < u ≤ 9, 9 - u, 0], F) → A'_3
  86. Segment(C, F') → s_2
  87. Segment(A, A'_3) → t_2
  88. Dilate(B, If[10 < u ≤ 11, 11 - u, 0], H) → B'_3
  89. Dilate(D, If[10 < u ≤ 11, 11 - u, 0], G) → D'_3
  90. Segment(D, D'_3) → a_2
  91. Segment(B, B'_3) → b_2
  92. Dilate(I, If[12 < u ≤ 13, 13 - u, 0], J) → I'
  93. Segment(I, I') → c_2
  94. Dilate(I, If[13 < u ≤ 14, 14 - u, 0], N) → I'_1
  95. Vector(I, I'_1) → v
  96. Translate(I, v) → I'_2
  97. Translate(I', v) → I''
  98. Segment(I'_2, I'') → d_2
  99. Dilate(I, If[14 < u ≤ 15, 15 - u, 0], M) → I'_3
  100. Vector(I, I'_3) → w
  101. Translate(I, w) → I'_4
  102. Translate(I', w) → I''_1
  103. Segment(I'_4, I''_1) → e_2
  104. Dilate(I, If[15 < u ≤ 16, 16 - u, 0], A) → I'_5
  105. Vector(I, I'_5) → u_1
  106. Translate(I, u_1) → I'_6
  107. Translate(I', u_1) → I''_2
  108. Segment(I'_6, I''_2) → f_3
  109. Dilate(J, If[16 < u ≤ 17, 17 - u, 0], K) → J'
  110. Segment(J, J') → g_3
  111. Dilate(J, If[17 < u ≤ 18, 18 - u, 0], D) → J'_1
  112. Dilate(J, If[18 < u ≤ 19, 19 - u, 0], S) → J'_2
  113. Dilate(J, If[19 < u ≤ 20, 20 - u, 0], T) → J'_3
  114. Vector(J, J'_1) → v_1
  115. Vector(J, J'_2) → w_1
  116. Vector(J, J'_3) → u_2
  117. Translate(J, v_1) → J'_4
  118. Translate(J', v_1) → J''
  119. Segment(J'_4, J'') → h_3
  120. Translate(J, w_1) → J'_5
  121. Translate(J', w_1) → J''_1
  122. Segment(J'_5, J''_1) → i_3
  123. Translate(J, u_2) → J'_6
  124. Translate(J', u_2) → J''_2
  125. Segment(J'_6, J''_2) → j_3
  126. Dilate(K, If[20 < u ≤ 21, 21 - u, 0], L) → K'
  127. Segment(K, K') → k_3
  128. Dilate(L, If[21 < u ≤ 22, 22 - u, 0], D) → L'
  129. Dilate(L, If[22 < u ≤ 23, 23 - u, 0], R) → L'_1
  130. Dilate(L, If[23 < u ≤ 24, 24 - u, 0], Q) → L'_2
  131. Dilate(K, If[21 < u ≤ 22, 22 - u, 0], C) → K'_1
  132. Vector(K, K'_1) → v_2
  133. Translate(K, v_2) → K'_2
  134. Translate(K', v_2) → K''
  135. Segment(K'_2, K'') → l_3
  136. Dilate(K, If[22 < u ≤ 23, 23 - u, 0], Q) → K'_3
  137. Vector(K, K'_3) → w_2
  138. Translate(K, w_2) → K'_4
  139. Translate(K', w_2) → K''_1
  140. Segment(K'_4, K''_1) → m_3
  141. Dilate(K, If[23 < u ≤ 24, 24 - u, 0], R) → L'_3
  142. Vector(K, L'_3) → u_3
  143. Translate(K, u_3) → K'_5
  144. Translate(K', u_3) → K''_2
  145. Segment(K'_5, K''_2) → n_3
  146. Dilate(L, If[24 < u ≤ 25, 25 - u, 0], I) → L'_4
  147. Segment(L, L'_4) → p_3
  148. Dilate(L, If[25 < u ≤ 26, 26 - u, 0], B) → L'_5
  149. Dilate(L, If[26 < u ≤ 27, 27 - u, 0], O) → L'_6
  150. Dilate(L, If[27 < u ≤ 28, 28 - u, 0], P) → L'_7
  151. Vector(L, L'_5) → v_3
  152. Vector(L, L'_6) → w_3
  153. Vector(L, L'_7) → a_3
  154. Translate(L, v_3) → L'_8
  155. Translate(L'_4, v_3) → C_1
  156. Segment(L'_8, C_1) → q_3
  157. Translate(L, w_3) → L'_9
  158. Translate(L'_4, w_3) → D_1
  159. Segment(L'_9, D_1) → r_3
  160. Translate(L, a_3) → L'_{10}
  161. Translate(L'_4, a_3) → E_1
  162. Segment(L'_{10}, E_1) → s_3
  163. Rotate(V, If[30 < u ≤ 31, ((u - 30) * δ), δ], L) → V'
  164. CircleSector(L, V, V') → c_3
  165. Rotate(W, If[31 < u ≤ 32, ((u - 31) * γ), γ], K) → W'
  166. CircleSector(K, W, W') → d_3
  167. Rotate(Z, If[32 < u ≤ 33, ((u - 32) * β), β], J) → Z'
  168. CircleSector(J, Z, Z') → e_3
  169. Dilate(L, If[33 < u ≤ 34, 34 - u, 0], C) → L'_{11}
  170. Vector(L, L'_{11}) → b_3
  171. Translate(c_3, b_3) → t_3
  172. Rotate(t_3, If[34 < u ≤ 35, ((u - 34) * π), π], C) → c_4
  173. Dilate(K, If[35 < u ≤ 36, 36 - u, 0], D) → K'_6
  174. Vector(K, K'_6) → u_4
  175. Translate(d_3, u_4) → d_4
  176. Rotate(d_4, If[36 < u ≤ 37, ((u - 36) * π), π], D) → e_4
  177. Dilate(J, If[37 < u ≤ 38, 38 - u, 0], A) → J'_7
  178. Vector(J, J'_7) → v_4
  179. Translate(e_3, v_4) → f_4
  180. Rotate(f_4, If[38 < u ≤ 39, ((u - 38) * π), π], A) → g_4

AI 绘图提示语参考

画一个动态的几何图形，展示多边形构造和相关的几何变换。首先绘制一个四边形，然后找到各边的中点并连接，形成内部的小四边形。接着计算对角线的中点，并连接这些点形成新的图形。再以四边形顶点为中心，绘制不同大小的圆，并找到这些圆与四边形边的交点。最后，以交点为圆心绘制小圆，并连接特定点形成线段，展示面积、质心、缩放、旋转等几何概念。
以上提示语为根据原始绘图命令整理而来，仅供参考。