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Equilateral Triangles and Rotations

Equilateral Triangles and Rotations
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2016-04-15 05:32
TriangleCirclePolygonTransformationGeometric Construction
This example demonstrates the geometric transformation of equilateral triangles under rotation, involving core math concepts like rotation, properties of equilateral triangles, geometric transformations, probability & statistics, Pythagorean theorem, and circumcircle. It uses commands such as Rotate, Polygon, and Mirror in GeoGebra for construction, making it suitable for high school mathematics teaching or geometric transformation studies to understand the patterns and properties of rotational transformations.

GeoGebra Commands & Parameters

  1. Rotate(B1, 60°, A1) → C1
  2. Rotate(C1, (-a), B1) → D1
  3. Rotate(C1, -60° - a, B1) → E1
  4. Polygon({A1, B1, C1}) → F1
  5. Polygon({B1, D1, E1}) → G1
  6. Rotate(B1, a, E1) → A2
  7. Rotate(B1, 60° + a, E1) → B2
  8. Rotate(B2, 60°, A2) → C2
  9. Rotate(C2, (-a), B2) → D2
  10. Rotate(C2, -60° - a, B2) → E2
  11. Polygon({A2, B2, C2}) → F2
  12. Polygon({B2, D2, E2}) → G2
  13. Rotate(B2, a, E2) → A3
  14. Rotate(B2, 60° + a, E2) → B3
  15. Rotate(B3, 60°, A3) → C3
  16. Rotate(C3, (-a), B3) → D3
  17. Rotate(C3, -60° - a, B3) → E3
  18. Polygon({A3, B3, C3}) → F3
  19. Polygon({B3, D3, E3}) → G3
  20. Rotate(F1, 60°) → J1
  21. Rotate(G1, 60°) → K1
  22. Rotate(F2, 60°) → J2
  23. Rotate(G2, 60°) → K2
  24. Rotate(F3, 60°) → J3
  25. Rotate(G3, 60°) → K3
  26. Rotate(F1, 120°) → L1
  27. Rotate(G1, 120°) → M1
  28. Rotate(F1, 180°) → N1
  29. Rotate(G1, 180°) → O1
  30. Rotate(F1, 240°) → P1
  31. Rotate(G1, 240°) → Q1
  32. Rotate(F1, 300°) → R1
  33. Rotate(G1, 300°) → S1
  34. Rotate(F2, 120°) → L2
  35. Rotate(G2, 120°) → M2
  36. Rotate(F2, 180°) → N2
  37. Rotate(G2, 180°) → O2
  38. Rotate(F2, 240°) → P2
  39. Rotate(G2, 240°) → Q2
  40. Rotate(F2, 300°) → R2
  41. Rotate(G2, 300°) → S2
  42. Rotate(F3, 120°) → L3
  43. Rotate(G3, 120°) → M3
  44. Rotate(F3, 180°) → N3
  45. Rotate(G3, 180°) → O3
  46. Rotate(F3, 240°) → P3
  47. Rotate(G3, 240°) → Q3
  48. Rotate(F3, 300°) → R3
  49. Rotate(G3, 300°) → S3
  50. Rotate(B3, a, E3) → A4
  51. Rotate(B3, 60° + a, E3) → B4
  52. Rotate(B4, 60°, A4) → C4
  53. Rotate(C4, (-a), B4) → D4
  54. Rotate(C4, -60° - a, B4) → E4
  55. Polygon({A4, B4, C4}) → F4
  56. Polygon({B4, D4, E4}) → G4
  57. Rotate(F4, 60°) → J4
  58. Rotate(G4, 60°) → K4
  59. Rotate(F4, 120°) → L4
  60. Rotate(G4, 120°) → M4
  61. Rotate(F4, 180°) → N4
  62. Rotate(G4, 180°) → O4
  63. Rotate(F4, 240°) → P4
  64. Rotate(G4, 240°) → Q4
  65. Rotate(F4, 300°) → R4
  66. Rotate(G4, 300°) → S4
  67. Mirror(G1, Line[E1, D1]) → H1
  68. Mirror(G2, Line[E2, D2]) → H2
  69. Mirror(G3, Line[E3, D3]) → H3
  70. Mirror(G4, Line[E4, D4]) → H4
  71. Mirror(F3, Line[A3, B3]) → I3
  72. Mirror(F4, Line[A4, B4]) → I4
  73. Rotate(H1, 60°) → T1
  74. Rotate(H1, 120°) → U1
  75. Rotate(H1, 180°) → V1
  76. Rotate(H1, 240°) → W1
  77. Rotate(H1, 300°) → X1
  78. Rotate(H2, 60°) → T2
  79. Rotate(H2, 120°) → U2
  80. Rotate(H2, 180°) → V2
  81. Rotate(H2, 240°) → W2
  82. Rotate(H2, 300°) → X2
  83. Rotate(H3, 60°) → T3
  84. Rotate(H3, 120°) → U3
  85. Rotate(H3, 180°) → V3
  86. Rotate(H3, 240°) → W3
  87. Rotate(H3, 300°) → X3
  88. Rotate(H4, 60°) → T4
  89. Rotate(H4, 120°) → U4
  90. Rotate(H4, 180°) → V4
  91. Rotate(H4, 240°) → W4
  92. Rotate(H4, 300°) → X4
  93. Rotate(I3, 60°) → Y3
  94. Rotate(I3, 120°) → Z3
  95. Rotate(I3, 180°) → AA3
  96. Rotate(I3, 240°) → AB3
  97. Rotate(I3, 300°) → AC3
  98. Rotate(I4, 60°) → Y4
  99. Rotate(I4, 120°) → Z4
  100. Rotate(I4, 180°) → AA4
  101. Rotate(I4, 240°) → AB4
  102. Rotate(I4, 300°) → AC4
  103. Rotate(I3, -60°, A3) → I13
  104. Rotate(I13, 60°) → J13
  105. Rotate(I13, 120°) → K13
  106. Rotate(I13, 180°) → L13
  107. Rotate(I13, 2400°) → M13
  108. Rotate(I13, 300°) → N13
  109. Rotate(I4, -60°, A4) → I14
  110. Rotate(I14, 60°) → J14
  111. Rotate(I14, 120°) → K14
  112. Rotate(I14, 180°) → L14
  113. Rotate(I14, 2400°) → M14
  114. Rotate(I14, 300°) → N14
  115. Rotate(H3, 60°, D3) → I15
  116. Rotate(H4, 60°, D4) → I16
  117. Rotate(I15, 60°) → J15
  118. Rotate(I15, 120°) → K15
  119. Rotate(I15, 180°) → L15
  120. Rotate(I15, 2400°) → M15
  121. Rotate(I15, 300°) → N15
  122. Rotate(I16, 60°) → J16
  123. Rotate(I16, 120°) → K16
  124. Rotate(I16, 180°) → L16
  125. Rotate(I16, 2400°) → M16
  126. Rotate(I16, 300°) → N16