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正方形变换演示

正方形变换演示
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2016-12-22 22:06
向量变换几何作图
所属专题 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2
这个范例演示了正方形的动态变换。核心数学概念包括几何变换、向量和轨迹。通过使用Dilate、Polygon、Rotate等命令，用户可以动态修改正方形的大小和位置。适合初中及以上学生学习几何变换和向量。

GeoGebra 命令及参数

  1. Dilate(A, If[0 < e ≤ 1, 1 - e, 0], D) → A'
  2. Segment(A, A') → f
  3. Midpoint(f) → V
  4. OrthogonalLine(V, f) → j_2
  5. CircleArc(V, D, A) → k_2
  6. Intersect(k_2, j_2) → C_1,
  7. CircleArc(V, C_1, A) → q_2
  8. Polygon(A, D, 4) → poly1, a, b, c, d, C_2, D_2
  9. Rotate(A, If[1 < e ≤ 2, ((-(e - 1)) * π / 2), -1.5707963267948966], D) → C
  10. Rotate(A', If[1 < e ≤ 2, ((-(e - 1)) * π / 2), -1.5707963267948966], D) → A''
  11. Segment(C, A'') → f'
  12. Segment(A, D) → g
  13. Segment(D, C_2) → h
  14. Segment(C_2, D_2) → i
  15. Segment(D_2, A) → j
  16. Circle(C_2, (0.1 * j)) → k
  17. Circle(D, (0.1 * j)) → p
  18. Circle(A, (0.1 * j)) → q
  19. Circle(D_2, (0.1 * j)) → r
  20. Segment(A, C_2) → l
  21. Segment(D_2, D) → m
  22. Intersect(l, m) → E_1
  23. Intersect(r, j, 1) → F_1
  24. Intersect(r, m, 1) → G_1
  25. Intersect(r, i, 1) → H_1
  26. Intersect(k, i, 1) → I
  27. Intersect(k, l, 1) → J
  28. Intersect(k, h, 1) → K
  29. Intersect(p, h, 1) → L
  30. Intersect(p, m, 1) → M_1
  31. Intersect(p, g, 1) → N_1
  32. Intersect(q, g, 1) → O
  33. Intersect(q, l, 1) → P
  34. Intersect(q, j, 1) → Q
  35. Rotate(C, If[2 < e ≤ 3, ((-(e - 2)) * π / 2), -1.5707963267948966], C_2) → R
  36. Rotate(A'', If[2 < e ≤ 3, ((-(e - 2)) * π / 2), -1.5707963267948966], C_2) → A'''
  37. Segment(R, A''') → f''
  38. CircleSector(D, L, N_1) → s
  39. Rotate(R, If[3 < e ≤ 4, ((-(e - 3)) * π / 2), -1.5707963267948966], D_2) → R'
  40. Rotate(A''', If[3 < e ≤ 4, ((-(e - 3)) * π / 2), -1.5707963267948966], D_2) → S
  41. Segment(R', S) → f'''
  42. Dilate(D, If[4 < e ≤ 5, 5 - e, 0], C_2) → B'
  43. Vector(D, B') → u
  44. Translate(s, u) → s'
  45. Rotate(s', If[5 < e ≤ 6, ((e - 5) * π / 2), 1.5707963267948966], C_2) → s''
  46. Dilate(C_2, If[6 < e ≤ 7, 7 - e, 0], D_2) → C'
  47. Vector(C_2, C') → v
  48. Translate(s'', v) → s'''
  49. Rotate(s''', If[7 < e ≤ 8, ((e - 7) * π / 2), 1.5707963267948966], D_2) → t
  50. Dilate(D_2, If[8 < e ≤ 9, 9 - e, 0], A) → D'
  51. Vector(D_2, D') → w
  52. Translate(t, w) → t'
  53. Rotate(t', If[9 < e ≤ 10, ((e - 9) * π / 2), 1.5707963267948966], A) → t''
  54. Dilate(A, If[10 < e ≤ 11, 11 - e, 0], E_1) → A'_2
  55. Dilate(E_1, If[11 < e ≤ 12, 12 - e, 0], C_2) → E'
  56. Dilate(D_2, If[12 < e ≤ 13, 13 - e, 0], E_1) → D'_1
  57. Dilate(E_1, If[13 < e ≤ 14, 14 - e, 0], D) → E'_1
  58. Dilate(D_2, If[17 < e ≤ 18, 18 - e, 0], E_1) → D'_2
  59. Vector(D_2, D'_2) → u_1
  60. Rotate(E_1, If[15 < e ≤ 16, ((e - 15) * π / 2), 1.5707963267948966], E_1) → E'_2
  61. Rotate(E'_1, If[14 < e ≤ 15, ((e - 14) * π / 2), 1.5708], E_1) → T
  62. Rotate(E'_2, If[16 < e ≤ 17, ((e - 16) * π / 2), 1.5707963267948966], E_1) → U
  63. Rotate(T, If[15 < e ≤ 16, ((e - 15) * π / 2), 1.5708], E_1) → T'
  64. Rotate(U, If[17 < e ≤ 18, ((e - 17) * π / 2), 1.5707963267948966], E_1) → U'
  65. Rotate(T', If[16 < e ≤ 17, ((e - 16) * π / 2), 1.5708], E_1) → T''
  66. Dilate(D, If[18 < e ≤ 19, 19 - e, 0], C_2) → B'_1
  67. Dilate(D, If[18 < e ≤ 19, 19 - e, 0], A) → B'_2
  68. Dilate(D, If[18 < e ≤ 19, 19 - e, 0], D_2) → B'_3
  69. Vector(D, B'_1) → v_1
  70. Vector(D, B'_3) → w_1
  71. Vector(D, B'_2) → i_1
  72. Circle(V, A) → g_2
  73. Midpoint(f') → W
  74. Circle(W, D) → h_2
  75. CircleArc(W, C, D) → p_2
  76. Point(q_2) → E
  77. Segment(A, E) → j_1
  78. Segment(E, D) → l_1
  79. OrthogonalLine(C, l_1) → m_1
  80. Intersect(l_1, m_1) → F
  81. Ray(C, E) → n_1
  82. Ray(D, A) → i_2
  83. Intersect(n_1, i_2) → H
  84. Ray(A, F) → l_2
  85. Intersect(f', l_2) → G
  86. Segment(H, G) → n
  87. Intersect(j_1, n) → M
  88. Intersect(l_1, n) → N
  89. Intersect(l_1, n) → A_1
  90. Distance(G, N) → distanceGN
  91. Distance(M, H) → distanceMH
  92. Angle(C, F, E) → α
  93. Angle(A, E, D) → β
  94. Segment(C, F) → m_2
  95. Distance(H, M) → distanceHM
  96. Intersect(n, m_2) → Z
  97. Distance(Z, G) → distanceZG
  98. Dilate(C, If[10 < e ≤ 11, 11 - e, 0], H) → B_1
  99. Segment(C, B_1) → a_1
  100. Segment(C, E) → b_1
  101. Segment(C, H) → n_2
  102. Dilate(A, If[10 < e ≤ 11, 11 - e, 0], H) → A'_3
  103. Segment(A, A'_3) → r_2
  104. Dilate(C, If[12 < e ≤ 13, 13 - e, 0], F) → D_1
  105. Segment(C, D_1) → f_1
  106. Dilate(A, If[11 < e ≤ 12, 12 - e, 0], E) → A'_4
  107. Dilate(D, If[11 < e ≤ 12, 12 - e, 0], E) → B'_4
  108. Segment(A, M) → g_1
  109. Segment(D, B'_4) → c_1
  110. Segment(A, A'_4) → e_1
  111. Intersect(f'', f''') → I_1
  112. Dilate(I_1, If[13 < e ≤ 14, 14 - e, 0], E) → J_1
  113. Vector(I_1, J_1) → d_1
  114. Translate(t, d_1) → t'_1
  115. Line(I_1, c_1) → h_1
  116. Point(h_1) → K_1
  117. Line(I_1, e_1) → p_1
  118. Point(p_1) → L_1
  119. Angle(L_1, I_1, A) → δ
  120. Rotate(t'_1, If[13 < e ≤ 14, ((-(e - 13)) * δ), (-δ)], J_1) → k_1
  121. Dilate(C, If[14 < e ≤ 15, 15 - e, 0], F) → O_1
  122. Ray(F, C) → q_1
  123. Point(q_1) → P_1
  124. Angle(D, C, P_1) → γ
  125. Vector(C, O_1) → r_1
  126. Translate(s'', r_1) → s'''_1
  127. Rotate(s'''_1, If[14 < e ≤ 15, ((e - 14) * γ), γ], O_1) → s_1
  128. Dilate(H, If[15 < e ≤ 16, 16 - e, 0], M) → H'
  129. Dilate(M, If[16 < e ≤ 17, 17 - e, 0], N) → M'
  130. Dilate(N, If[17 < e ≤ 18, 18 - e, 0], Z) → N'
  131. Dilate(Z, If[18 < e ≤ 19, 19 - e, 0], G) → Z'
  132. Segment(H, H') → t_1
  133. Segment(M, M') → f_2
  134. Segment(N, N') → s_2
  135. Segment(Z, Z') → t_2
  136. Rotate(H, If[19 < e ≤ 20, ((-(e - 19)) * π / 2), ((-π)) / 2], M) → H'_1
  137. Rotate(H', If[19 < e ≤ 20, ((-(e - 19)) * π / 2), ((-π)) / 2], M) → H''
  138. Segment(H'_1, H'') → a_2
  139. Dilate(M, If[20 < e ≤ 21, 21 - e, 0], Z) → M'_1
  140. Vector(M, M'_1) → u_2
  141. Translate(H'_1, u_2) → Q_1
  142. Translate(H'', u_2) → H'''
  143. Segment(Q_1, H''') → b_2
  144. Rotate(Q_1, If[21 < e ≤ 22, ((-(e - 21)) * π / 2), ((-π)) / 2], Z) → R_1
  145. Rotate(H''', If[21 < e ≤ 22, ((-(e - 21)) * π / 2), ((-π)) / 2], Z) → S_1
  146. Segment(R_1, S_1) → c_2
  147. Polygon(A, E, D) → poly2, b_3, a_3, e_2
  148. Polygon(D, F, C) → poly3, c_3, b_4, f_3
  149. Polygon(A, E, F, C, I_1) → poly4, a_4, e_3, f_4, c_4, i_3

AI 绘图提示语参考

画一个动态变换的方形，展示其通过缩放和旋转产生的轨迹。方形初始位于中心，通过向量控制其大小和位置变化。绘制方形缩放和旋转的路径，以及方形顶点到中心的连线，并标示关键交点和辅助圆弧，最终呈现一个包含多个几何元素的动态变换图形。
以上提示语为根据原始绘图命令整理而来，仅供参考。