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瓷砖图案

瓷砖图案
几何画板及绘图内容加载中，请稍等……
2020-06-21 00:05
多边形变换几何作图
这个范例展示了如何使用GeoGebra构造瓷砖图案。它涉及了几何变换和多边形的概念。通过使用Rotate、Intersect、Polygon等命令，可以创建复杂的图案。适合初中及以上学生学习几何作图。

GeoGebra 命令及参数

  1. Rotate(A, (-(90°)), B) → AB
  2. Rotate(B, 90°, A) → BA
  3. Rotate(B, 135°, A) → BAR
  4. Rotate(B, (-(135°)), A) → ABA
  5. Intersect(Ray[ABA, Rotate[A, 45°, ABA]], Ray[B, Rotate[A, (-(45°)), B]]) → ABAB
  6. Intersect(Ray[A, Rotate[B, 45°, A]], Ray[B, Rotate[A, (-(45°)), B]]) → ABH
  7. Intersect(Ray[A, Rotate[B, 67.5°, A]], Ray[B, Rotate[A, (-(67.5°)), B]]) → ABHR
  8. Intersect(Ray[B, Rotate[A, (-(22.5°)), B]], Ray[BA, Rotate[A, 22.5°, BA]]) → ABL
  9. Rotate(A, (-(45°)), B) → ABR
  10. Intersect(OrthogonalLine[BAR, Line[A, B]], OrthogonalLine[B, Line[A, BAR]]) → ABT
  11. Rotate(B, 135°, A) → BBA
  12. Intersect(Ray[B, Rotate[A, (-(67.5°)), B]], Ray[BBA, Rotate[A, 67.5°, BBA]]) → BAJ
  13. Intersect(OrthogonalLine[BAR, Line[A, BAR]], OrthogonalLine[B, Line[A, B]]) → BARB
  14. Intersect(OrthogonalLine[B, Line[A, B]], OrthogonalLine[BBA, Line[BBA, A]]) → BBAB
  15. Polygon(A, B, AB, BA) → Square1, sq12, sq14, sq13, sq11
  16. Segment(A, AB) → sq1pijl1
  17. Segment(B, AB) → sq1pijl2
  18. Segment(BA, AB) → sq1pijl3
  19. Segment(A, B) → sq1vet1
  20. Segment(A, BA) → sq1vet2
  21. Dilate(A, 0.75, Centroid[Square1]) → A'
  22. Dilate(B, 0.75, Centroid[Square1]) → B'
  23. Dilate(AB, 0.75, Centroid[Square1]) → AB'
  24. Dilate(BA, 0.75, Centroid[Square1]) → BA'
  25. Polygon(Dilate[A, 0.75, Centroid[Square1]], Dilate[B, 0.75, Centroid[Square1]], Dilate[AB, 0.75, Centroid[Square1]], Dilate[BA, 0.75, Centroid[Square1]]) → Square1', f, g, i, j
  26. Polygon(A, B, ABR, BAR) → Rhombus2, rh24, rh23, rh22, rh21
  27. Dilate(A, 0.75, Centroid[Rhombus2]) → A'_1
  28. Dilate(B, 0.75, Centroid[Rhombus2]) → B'_1
  29. Dilate(ABR, 0.75, Centroid[Rhombus2]) → ABR'
  30. Dilate(BAR, 0.75, Centroid[Rhombus2]) → BAR'
  31. Polygon(A'_1, B'_1, ABR', BAR') → Rhombus2', a'_1, b'_1, abr', bar'
  32. Segment(A, ABR) → rh2pijl1
  33. Segment(B, ABR) → rh2pijl2
  34. Segment(BAR, ABR) → rh2pijl3
  35. Segment(A, B) → rh2vet1
  36. Segment(BAR, A) → rh2vet2
  37. Polygon(A, B, BBAB, BBA) → Almond3, alm34, alm33, alm32, alm31
  38. Dilate(A, 0.75, Centroid[Almond3]) → A'_2
  39. Dilate(B, 0.75, Centroid[Almond3]) → B'_2
  40. Dilate(BBAB, 0.75, Centroid[Almond3]) → BBAB'
  41. Dilate(BBA, 0.75, Centroid[Almond3]) → BBA'
  42. Polygon(Dilate[A, 0.75, Centroid[Almond3]], Dilate[B, 0.75, Centroid[Almond3]], Dilate[BBAB, 0.75, Centroid[Almond3]], Dilate[BBA, 0.75, Centroid[Almond3]]) → Almond3', k, l, m, n
  43. Segment(A, BBAB) → alm3pijl1
  44. Segment(B, BBAB) → alm3pijl2
  45. Segment(A, B) → alm3vet1
  46. Segment(A, BBA) → alm3vet2
  47. Segment(BBA, BBAB) → alm3pijl3
  48. Polygon(A, B, BAJ, BBA) → Jug4, jug44, jug43, jug42, jug41
  49. Segment(A, BAJ) → jug4pijl1
  50. Segment(BBA, BAJ) → jug4pijl2
  51. Segment(B, BAJ) → jug4pijl3
  52. Segment(A, B) → jugvet1
  53. Segment(BBA, A) → jugvet2
  54. Dilate(A, 0.75, Centroid[Jug4]) → A'_3
  55. Dilate(B, 0.75, Centroid[Jug4]) → B'_3
  56. Dilate(BAJ, 0.75, Centroid[Jug4]) → BAJ'
  57. Dilate(BBA, 0.75, Centroid[Jug4]) → BBA'_1
  58. Polygon(A'_3, B'_3, BAJ', BBA'_1) → Jug4', a'_3, b'_3, baj', bba'_1
  59. Polygon(A, B, ABH) → HSquare5, hsq53, hsq52, hsq51
  60. Dilate(A, 0.75, Centroid[HSquare5]) → A'_4
  61. Dilate(B, 0.75, Centroid[HSquare5]) → B'_4
  62. Dilate(ABH, 0.75, Centroid[HSquare5]) → ABH'
  63. Polygon(A'_4, B'_4, ABH') → HSquare5', abh', a'_4, b'_4
  64. Segment(Midpoint[A, B], ABH) → hsq5pijl1
  65. Segment(A, ABH) → hsq5pijl2
  66. Segment(B, ABH) → hsq5pijl3
  67. Segment(A, B) → hsq5vet1
  68. Polygon(A, B, ABHR) → HRhombus6, hrh63, hrh62, hrh61
  69. Segment(Midpoint[A, B], ABHR) → hrh6pijl1
  70. Segment(A, ABHR) → hrh6pijl2
  71. Segment(B, ABHR) → hrh6pijl3
  72. Segment(A, B) → hrh6vet1
  73. Dilate(A, 0.75, Centroid[HRhombus6]) → A'_5
  74. Dilate(B, 0.75, Centroid[HRhombus6]) → B'_5
  75. Dilate(ABHR, 0.75, Centroid[HRhombus6]) → ABHR'
  76. Polygon(A'_5, B'_5, ABHR') → HRhombus6', abhr', a'_5, b'_5
  77. Segment(A, BA) → sq7pijl2
  78. Segment(A, B) → sq7pijl3
  79. Segment(A, B) → rh8pijl2
  80. Segment(A, BAR) → rh8pijl3
  81. Polygon(A, B, ABT, BAR) → SmBiped9, smb94, smb93, smb92, smb91
  82. Polygon(A, B, ABL, BA) → LBiped10, lb104, lb103, lb102, lb101
  83. Segment(A, ABL) → lbp10pijl1
  84. Segment(A, B) → lbp10pijl2
  85. Segment(A, BA) → lbp10pijl3
  86. Polygon(A, B, BA) → HSquare11, hsq113, hsq112, hsq111
  87. Dilate(A, 0.75, Centroid[HSquare11]) → A'_6
  88. Dilate(B, 0.75, Centroid[HSquare11]) → B'_6
  89. Dilate(BA, 0.75, Centroid[HSquare11]) → BA'_1
  90. Polygon(A'_6, B'_6, BA'_1) → HSquare11', ba'_1, a'_6, b'_6
  91. Segment(A, Midpoint[BA, B]) → hsq11pijl1
  92. Segment(A, BA) → hsq11pijl2
  93. Segment(A, B) → hsq11pijl3
  94. Polygon(A, B, BAR) → HRhombus12, hrh123, hrh122, hrh121
  95. Dilate(A, 0.75, Centroid[HRhombus12]) → A'_7
  96. Dilate(B, 0.75, Centroid[HRhombus12]) → B'_7
  97. Dilate(BAR, 0.75, Centroid[HRhombus12]) → BAR'_1
  98. Polygon(A'_7, B'_7, BAR'_1) → HRhombus12', bar'_1, a'_7, b'_7
  99. Segment(A, Midpoint[BAR, B]) → hrh12pijl1
  100. Segment(A, BAR) → hrh12pijl2
  101. Segment(A, B) → hrh12pijl3
  102. Polygon(ABA, A, B, ABAB) → SmBiped13, smbp134, smbp133, smbp132, smbp131
  103. Dilate(ABA, 0.75, Centroid[SmBiped13]) → ABA'
  104. Dilate(A, 0.75, Centroid[SmBiped13]) → A'_8
  105. Dilate(B, 0.75, Centroid[SmBiped13]) → B'_8
  106. Dilate(ABAB, 0.75, Centroid[SmBiped13]) → ABAB'
  107. Polygon(Dilate[ABA, 0.75, Centroid[SmBiped13]], Dilate[A, 0.75, Centroid[SmBiped13]], Dilate[B, 0.75, Centroid[SmBiped13]], Dilate[ABAB, 0.75, Centroid[SmBiped13]]) → SmBiped13', p, q, r, s
  108. Segment(A, ABAB) → smbp13pijl1
  109. Segment(ABA, ABAB) → smbp13pijl2
  110. Segment(B, ABAB) → smb13pijl3
  111. Segment(ABA, A) → smbp13vet1
  112. Segment(A, B) → smbp13vet2
  113. Polygon(A, B, BARB, BAR) → Almond14, alm144, alm143, alm142, alm141
  114. Segment(A, BARB) → alm14pijl1
  115. Segment(A, B) → alm14pijl2
  116. Segment(A, BAR) → alm14pijl3
  117. Dilate(A, 0.75, Centroid[SmBiped9]) → A'_9
  118. Dilate(B, 0.75, Centroid[SmBiped9]) → B'_9
  119. Dilate(ABT, 0.75, Centroid[SmBiped9]) → ABT'
  120. Dilate(BAR, 0.75, Centroid[SmBiped9]) → BAR'_2
  121. Polygon(A'_9, B'_9, ABT', BAR'_2) → SmBiped9', a'_9, b'_9, abt', bar'_2
  122. Segment(A, ABT) → smb9pijl1
  123. Segment(A, B) → smb9pijl2
  124. Segment(A, BAR) → smb9pijl3
  125. Dilate(A, 0.75, Centroid[LBiped10]) → A'_{10}
  126. Dilate(B, 0.75, Centroid[LBiped10]) → B'_{10}
  127. Dilate(ABL, 0.75, Centroid[LBiped10]) → ABL'
  128. Dilate(BA, 0.75, Centroid[LBiped10]) → BA'_2
  129. Polygon(A'_{10}, B'_{10}, ABL', BA'_2) → LBiped10', a'_{10}, b'_{10}, abl', ba'_2
  130. Dilate(A, 0.75, Centroid[Almond14]) → A'_{11}
  131. Dilate(B, 0.75, Centroid[Almond14]) → B'_{11}
  132. Dilate(BARB, 0.75, Centroid[Almond14]) → BARB'
  133. Dilate(BAR, 0.75, Centroid[Almond14]) → BAR'_3
  134. Polygon(A'_{11}, B'_{11}, BARB', BAR'_3) → Almond14', a'_{11}, b'_{11}, barb', bar'_3
  135. Intersect(Line[C, Line[D, E]], Line[E, Line[D, C]]) → CE
  136. Intersect(Line[C, Rotate[D, 45°, Line[C, C + (0, 0, 1)]]], Line[E, Rotate[D, (-(45°)), Line[E, E + (0, 0, 1)]]]) → CESB
  137. Intersect(Line[C, Rotate[D, 22.5°, Line[C, C + (0, 0, 1)]]], Line[E, Rotate[D, (-(22.5°)), Line[E, E + (0, 0, 1)]]]) → CELB
  138. Intersect(Line[C, Rotate[D, 90°, Line[C, C + (0, 0, 1)]]], Line[E, Rotate[D, (-(90°)), Line[E, E + (0, 0, 1)]]]) → CEA
  139. Polygon(D, E, EE, DD) → achter1, d, e, ee, dd
  140. Polygon(C, CC, DD, D) → achter2, c, cc, t, d_1
  141. Polygon(EE, EC, DD) → ESquare1boven1, a, b, ec
  142. Polygon(CC, EC, DD) → ESquare1boven2, f_1, g_1, h_1
  143. Polygon(EE, ECA, DD) → EAlmond3boven1, i_1, j_1, eca
  144. Polygon(CC, ECA, DD) → EAlmond3boven2, k_1, l_1, m_1
  145. Polygon(EE, ECJ, DD) → EJug4boven1, n_1, p_1, ecj
  146. Polygon(CC, ECJ, DD) → EJug4boven2, q_1, r_1, s_1
  147. Polygon(CC, DD, CDHS) → EHSquare5boven, cdhs, t_1, a_1
  148. Polygon(CC, DD, CDHR) → EHRhombus6boven, cdhr, b_1, c_1
  149. Polygon(EE, ECSB, DD) → ESmBiped13boven1, e_1, f_2, ecsb
  150. Polygon(DD, ECSB, CC) → ESmBiped13boven2, g_2, h_2, i_2
  151. Polygon(DU, E, CESB) → ESmBiped9boven1, cesb, du, e_2
  152. Polygon(DU, CESB, C) → ESmBiped9boven2, c_2, j_2, k_2
  153. Polygon(DU, E, CE) → ESquare7boven1, ce, l_2, e_3
  154. Polygon(DU, CE, C) → ESquare7boven2, c_3, m_2, n_2
  155. Polygon(DU, E, CELB) → ELBiped10boven1, celb, p_2, e_4
  156. Polygon(DU, CELB, C) → ELBiped10boven2, c_4, q_2, r_2
  157. Polygon(C, DU, E) → EHSquare11boven, e_5, c_5, s_2
  158. Polygon(DU, E, CEA) → EAmond14onder1, cea, t_2, e_6
  159. Polygon(DU, CEA, C) → EAmond14onder2, c_6, a_2, b_2