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Short Sunderland Geometric Model: Rotation, Symmetry, and Transformations

Short Sunderland Geometric Model: Rotation, Symmetry, and Transformations
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2012-07-02 01:45
CirclePolygonVectorTransformationGeometric Construction
This example uses GeoGebra geometry to build a working model of the Short Sunderland flying boat, demonstrating how points, segments, polygons, circles, and transformations can create a dynamic mechanical illustration. The main mathematical ideas are rotation, reflection, symmetry, translation, vectors, and geometric construction, with supporting use of circumcircle arcs and line bisectors. The construction begins with Point, Segment, and Polygon to define objects such as A, B, C, D, E, F, G, H, I, J, K, L, M, poly1, and poly2. Circle, CircumcircleArc, and LineBisector establish curved and symmetric reference elements, while Mirror, Rotate, Vector, Translate, and Propellor generate transformed parts such as C', D', E', poly1', e', c', d', H', L', K', g', and the propeller motion. The source theme also references limits, random variables, expected value, and statistics, but the visible construction is primarily geometric. It is suitable for secondary geometry, dynamic modeling, transformation lessons, and interactive demonstrations of how GeoGebra commands combine into a working figure.

GeoGebra Commands & Parameters

  1. Polygon(C, D, E) → poly1, e, c, d
  2. Segment(F, G) → a
  3. Mirror(C, a) → C'
  4. Mirror(D, a) → D'
  5. Mirror(E, a) → E'
  6. Polygon(C', D', E') → poly1', e', c', d'
  7. Point(a) → I
  8. Polygon(F, H, C, E, I, E', C', J) → poly2, f, h, c_1, e_1, i, e'_1, c'_1, j
  9. Point(a) → K
  10. CircumcircleArc(H, L, K) → g
  11. Mirror(H, a) → H'
  12. Mirror(L, a) → L'
  13. Mirror(K, a) → K'
  14. CircumcircleArc(H', L', K') → g'
  15. Polygon(M, N, O, P) → poly3, m, n, o, p
  16. CircumcircleArc(P, Q, O) → k
  17. Mirror(M, a) → M'
  18. Mirror(N, a) → N'
  19. Mirror(O, a) → O'
  20. Mirror(P, a) → P'
  21. Polygon(M', N', O', P') → poly3', m', n', o', p'
  22. Mirror(P, a) → P'_1
  23. Mirror(Q, a) → Q'
  24. Mirror(O, a) → O'_1
  25. CircumcircleArc(P'_1, Q', O'_1) → k'
  26. Point(e) → R
  27. Point(k) → S
  28. Segment(R, S) → b
  29. Segment(U, V) → l
  30. Segment(W, Z) → q
  31. Mirror(F, l) → F'
  32. Mirror(R, a) → R'
  33. Mirror(S, a) → S'
  34. Segment(R', S') → b'
  35. Mirror(U, a) → U'
  36. Mirror(V, a) → V'
  37. Segment(U', V') → l'
  38. Mirror(W, a) → W'
  39. Mirror(Z, a) → Z'
  40. Segment(W', Z') → q'
  41. Circle(A_1, B_1) → r
  42. Point(r) → C_1
  43. Segment(A_1, C_1) → s
  44. LineBisector(s) → t
  45. Point(t) → D_1
  46. CircumcircleArc(C_1, D_1, A_1) → d_1
  47. Mirror(C_1, s) → E_1
  48. Mirror(D_1, s) → F_1
  49. Mirror(A_1, s) → G_1
  50. CircumcircleArc(E_1, F_1, G_1) → f_1
  51. Rotate(A_1, 240*°, A_1) → H_1
  52. Rotate(C_1, 240*°, A_1) → I_1
  53. Segment(H_1, I_1) → s'
  54. Rotate(H_1, 240*°, A_1) → J_1
  55. Rotate(I_1, 240*°, A_1) → K_1
  56. Segment(J_1, K_1) → s''
  57. Rotate(C_1, 240*°, A_1) → L_1
  58. Rotate(D_1, 240*°, A_1) → M_1
  59. Rotate(A_1, 240*°, A_1) → N_1
  60. CircumcircleArc(L_1, M_1, N_1) → g_1
  61. Rotate(E_1, 240*°, A_1) → O_1
  62. Rotate(F_1, 240*°, A_1) → P_1
  63. Rotate(G_1, 240*°, A_1) → Q_1
  64. CircumcircleArc(O_1, P_1, Q_1) → h_1
  65. Rotate(O_1, 240*°, A_1) → R_1
  66. Rotate(P_1, 240*°, A_1) → S_1
  67. Rotate(Q_1, 240*°, A_1) → T_1
  68. CircumcircleArc(R_1, S_1, T_1) → k_1
  69. Rotate(L_1, 240*°, A_1) → U_1
  70. Rotate(M_1, 240*°, A_1) → V_1
  71. Rotate(N_1, 240*°, A_1) → W_1
  72. CircumcircleArc(U_1, V_1, W_1) → p_1
  73. Vector(A_1, T) → u
  74. Translate(B_1, u) → Z_1
  75. Translate(C_1, u) → A_2
  76. Translate(D_1, u) → B_2
  77. Propellor(T, Z_1, A_2, B_2) → q_1, r_1, s_1, t_1, c_2, d_2
  78. Mirror(A_1, a) → C_2
  79. Mirror(T, a) → T'
  80. Vector(A_1, C_2) → v
  81. Vector(C_2, T') → w
  82. Translate(B_1, v) → D_2
  83. Translate(C_1, v) → E_2
  84. Translate(D_1, v) → F_2
  85. Translate(C_1, v) → G_2
  86. Translate(D_1, v) → H_2
  87. Translate(A_1, v) → I_2
  88. CircumcircleArc(G_2, H_2, I_2) → e_2
  89. Translate(E_1, v) → J_2
  90. Translate(F_1, v) → K_2
  91. Translate(G_1, v) → L_2
  92. CircumcircleArc(J_2, K_2, L_2) → f_2
  93. Translate(R_1, v) → M_2
  94. Translate(S_1, v) → N_2
  95. Translate(T_1, v) → O_2
  96. CircumcircleArc(M_2, N_2, O_2) → g_2
  97. Translate(U_1, v) → P_2
  98. Translate(V_1, v) → Q_2
  99. Translate(W_1, v) → R_2
  100. CircumcircleArc(P_2, Q_2, R_2) → h_2
  101. Translate(L_1, v) → S_2
  102. Translate(M_1, v) → T_2
  103. Translate(N_1, v) → U_2
  104. CircumcircleArc(S_2, T_2, U_2) → k_2
  105. Translate(O_1, v) → V_2
  106. Translate(P_1, v) → W_2
  107. Translate(Q_1, v) → Z_2
  108. CircumcircleArc(V_2, W_2, Z_2) → p_2
  109. Translate(G_2, w) → A_3
  110. Translate(H_2, w) → B_3
  111. Translate(I_2, w) → C_3
  112. CircumcircleArc(A_3, B_3, C_3) → q_2
  113. Translate(J_2, w) → D_3
  114. Translate(K_2, w) → E_3
  115. Translate(L_2, w) → F_3
  116. CircumcircleArc(D_3, E_3, F_3) → r_2
  117. Translate(P_2, w) → G_3
  118. Translate(Q_2, w) → H_3
  119. Translate(R_2, w) → I_3
  120. CircumcircleArc(G_3, H_3, I_3) → s_2
  121. Translate(M_2, w) → J_3
  122. Translate(N_2, w) → K_3
  123. Translate(O_2, w) → L_3
  124. CircumcircleArc(J_3, K_3, L_3) → t_2
  125. Translate(S_2, w) → M_3
  126. Translate(T_2, w) → N_3
  127. Translate(U_2, w) → O_3
  128. CircumcircleArc(M_3, N_3, O_3) → c_3
  129. Translate(V_2, w) → P_3
  130. Translate(W_2, w) → Q_3
  131. Translate(Z_2, w) → R_3
  132. CircumcircleArc(P_3, Q_3, R_3) → d_3

AI Drawing Prompt Reference

Draw a Short Sunderland flying boat geometric model. Start by drawing polygon CDE, then draw segment FG. Mirror C, D, E about FG to get C', D', E', and draw polygon C'D'E'. Next, draw segment FI and mirror H, L, K about FI to get H', L', K', and draw arc HKL and arc H'K'L'. Continue by drawing polygon MNO, then mirror M, N, O, P about MN to get M', N', O', P', and draw arc PQO and arc P'Q'O'. Draw segment RS and mirror F, R, S about RS to get F', R', S', then draw segment UV and segment WZ, mirror U, V about UV to get U', V', and mirror W, Z about WZ to get W', Z'. Finally, draw circle A1B1 and mirror C1, D1 about A1B1 to get E1, F1.
The prompt above was compiled from the original drawing commands and is for reference only.