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Sun Microsystems Logo Geometric Construction

Sun Microsystems Logo Geometric Construction
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2019-06-27 05:13
AngleVectorFunctionTransformationGeometric Construction
This example demonstrates how to accurately draw the geometric shape of the Sun Microsystems logo using GeoGebra geometric construction tools. The core mathematical concepts involved include angles, geometric constructions, geometric transformations, vector operations, and function graphs. Key construction steps are derived from the command summary, utilizing commands and objects such as Line (straight line), LineBisector (angle bisector), Vector (vector), OrthogonalVector (orthogonal vector), Intersect (intersection), OrthogonalLine (perpendicular line), Rotate (rotation), Mirror (reflection), Midpoint (midpoint), Polygon (polygon), and CircleArc (arc). This is suitable for high school mathematics teaching, demonstrating the construction process and mathematical applications of complex geometric shapes.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. LineBisector(A, B) → g
  3. Vector(A, B) → u
  4. OrthogonalVector(u) → v
  5. Intersect(g, f) → C
  6. LineBisector(A, C) → h
  7. OrthogonalLine(A, f) → i
  8. Rotate(B, 90°, C) → B'
  9. Rotate(B, (-(90°)), C) → B'_1
  10. OrthogonalLine(B', h) → j
  11. Intersect(i, j) → E
  12. Mirror(E, f) → E'
  13. Mirror(E', g) → E''
  14. Mirror(E, g) → E'_1
  15. Mirror(j, f) → j'
  16. Midpoint(C, A) → F
  17. Midpoint(F, A) → G
  18. Midpoint(D, H) → I
  19. Mirror(J, I) → J'
  20. OrthogonalLine(G, f) → k
  21. Intersect(j', k) → K
  22. Line(J', i) → l
  23. Mirror(l, k) → l'
  24. Line(D, i) → m
  25. Mirror(L, k) → L'
  26. Line(L, j') → n
  27. Intersect(n, l) → M
  28. Polygon(D, J', M, L) → q1, d, p, m_1, l_1
  29. CircleArc(N, L, L') → c
  30. Mirror(D, k) → D'
  31. Mirror(J', k) → J''
  32. Mirror(M, k) → M'
  33. Mirror(L, k) → L'_1
  34. Polygon(D', J'', M', L'_1) → q1', d', j'', m', l'_1
  35. Mirror(D, C) → D'_1
  36. Mirror(J', C) → J''_1
  37. Mirror(M, C) → M'_1
  38. Mirror(L, C) → L'_2
  39. Polygon(D'_1, J''_1, M'_1, L'_2) → q1'_1, d'_1, j''_1, m'_1, l'_2
  40. Mirror(D', C) → D''
  41. Mirror(J'', C) → J'''
  42. Mirror(M', C) → M''
  43. Mirror(L'_1, C) → O
  44. Polygon(D'', J''', M'', O) → q1'', d'', j''', m'', o_1
  45. Mirror(c, C) → c'
  46. Midpoint(I, K) → P
  47. OrthogonalLine(P, g) → q
  48. Intersect(q, h) → Q
  49. Mirror(D', Q) → D''_1
  50. Mirror(J'', Q) → J'''_1
  51. Mirror(M', Q) → M''_1
  52. Mirror(L'_1, Q) → R
  53. Polygon(D''_1, J'''_1, M''_1, R) → q1''_1, d''_1, j'''_1, m''_1, r
  54. Mirror(D, Q) → D'_2
  55. Mirror(J', Q) → J''_2
  56. Mirror(M, Q) → M'_2
  57. Mirror(L, Q) → L'_3
  58. Polygon(D'_2, J''_2, M'_2, L'_3) → q1'_2, d'_2, j''_2, m'_2, l'_3
  59. Mirror(c, Q) → c'_1
  60. Mirror(D''_1, C) → S
  61. Mirror(J'''_1, C) → T
  62. Mirror(M''_1, C) → U
  63. Mirror(R, C) → R'
  64. Polygon(S, T, U, R') → q2, s, t, u_1, r'
  65. Mirror(D'_2, C) → V
  66. Mirror(J''_2, C) → W
  67. Mirror(M'_2, C) → Z
  68. Mirror(L'_3, C) → A_1
  69. Polygon(V, W, Z, A_1) → q3, v_1, w, z_1, a_1
  70. Mirror(c'_1, C) → e
  71. Rotate(D'_1, 90°, B) → B_1
  72. Rotate(J''_1, 90°, B) → C_1
  73. Rotate(M'_1, 90°, B) → D_1
  74. Rotate(L'_2, 90°, B) → E_1
  75. Polygon(B_1, C_1, D_1, E_1) → q4, b_1, c_1, d_1, e_1
  76. Rotate(D'', 90°, B) → D'''
  77. Rotate(J''', 90°, B) → F_1
  78. Rotate(M'', 90°, B) → M'''
  79. Rotate(O, 90°, B) → O'
  80. Polygon(D''', F_1, M''', O') → q1''', d''', f_1, m''', o'
  81. Rotate(c', 90°, B) → c''
  82. Rotate(D, 90°, A) → D'_3
  83. Rotate(J', 90°, A) → J''_3
  84. Rotate(M, 90°, A) → M'_3
  85. Rotate(L, 90°, A) → L'_4
  86. Polygon(D'_3, J''_3, M'_3, L'_4) → q1'_3, d'_3, j''_3, m'_3, l'_4
  87. Rotate(D', 90°, A) → D''_2
  88. Rotate(J'', 90°, A) → J'''_2
  89. Rotate(M', 90°, A) → M''_2
  90. Rotate(L'_1, 90°, A) → G_1
  91. Polygon(D''_2, J'''_2, M''_2, G_1) → q1''_2, d''_2, j'''_2, m''_2, g_1
  92. Rotate(c, 90°, A) → c'_2
  93. Rotate(V, (-(90°)), B') → V'
  94. Rotate(W, (-(90°)), B') → W'
  95. Rotate(Z, (-(90°)), B') → Z'
  96. Rotate(A_1, (-(90°)), B') → H_1
  97. Polygon(V', W', Z', H_1) → q3', v', w', z', h_1
  98. Rotate(S, (-(90°)), B') → S'
  99. Rotate(T, (-(90°)), B') → T'
  100. Rotate(U, (-(90°)), B') → U'
  101. Rotate(R', (-(90°)), B') → R''
  102. Polygon(S', T', U', R'') → q2', s', t', u', r''
  103. Rotate(e, (-(90°)), B') → e'
  104. Rotate(D'_2, (-(90°)), B'_1) → I_1
  105. Rotate(J''_2, (-(90°)), B'_1) → J_1
  106. Rotate(M'_2, (-(90°)), B'_1) → K_1
  107. Rotate(L'_3, (-(90°)), B'_1) → L_1
  108. Polygon(I_1, J_1, K_1, L_1) → q5, i_1, j_1, k_1, a
  109. Rotate(D''_1, (-(90°)), B'_1) → M_1
  110. Rotate(J'''_1, (-(90°)), B'_1) → N_1
  111. Rotate(M''_1, (-(90°)), B'_1) → O_1
  112. Rotate(R, (-(90°)), B'_1) → R'_1
  113. Polygon(M_1, N_1, O_1, R'_1) → q6, b, n_1, p_1, r'_1
  114. Rotate(c'_1, (-(90°)), B'_1) → q_1

AI Drawing Prompt Reference

Draw a complex geometric logo composed of symmetric elements. Start with a horizontal baseline and its perpendicular bisector, intersecting at a central point. Rotate one endpoint of the baseline by 90 degrees and -90 degrees around the center to create two vertical lines. Use angle bisectors and perpendicular lines to construct multiple symmetric points, then connect these points to form three identical quadrilaterals positioned above, below, and on both sides of the center. Outside the shape, draw a circular arc centered at a point, and mirror it about the center to get another arc. The overall figure has rotational symmetry, combining straight lines, perpendiculars, angle bisectors, polygons, and arcs, resembling the Sun Microsystems logo.
The prompt above was compiled from the original drawing commands and is for reference only.