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Geometric Construction of the KALVIN JONSHON Logo

Geometric Construction of the KALVIN JONSHON Logo
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2020-06-20 22:53
CirclePolygonVectorTransformationGeometric Construction
① This example demonstrates how to construct a planar logo named 'KALVIN JONSHON' using GeoGebra's geometric tools, combining lines, circles, polygons, vectors, and quadratic functions. ② Core mathematical concepts include two-dimensional vectors, angles, circles, quadrilaterals, quadratic functions, rotation, piecewise functions, area, and plane figures, showcasing the integration of geometry and algebra in graphic design. ③ Construction highlights: from the summary, commands such as LineBisector, Line, OrthogonalLine, Vector, OrthogonalVector, Intersect, Mirror, and Polygon are used, along with numerous objects like e_2, e_1, B, A, m, s, b, u, v, F, f, A_1, l, I, f', D, i, E, G, H, k, K, t, r, j, g, C, plus text objects and auxiliary points, to precisely build the logo's outline and internal structure. ④ Suitable for high school or early college mathematics and geometry drawing courses, as well as teaching the mathematical principles behind graphic design, helping students understand the practical application of geometric transformations, vector operations, and function graphs in creative work.

GeoGebra Commands & Parameters

  1. LineBisector(A, B) → m
  2. Line(A, B) → s
  3. OrthogonalLine(A, s) → b
  4. Vector(A, B) → u
  5. OrthogonalVector(u) → v
  6. OrthogonalLine(F, b) → f
  7. LineBisector(A_1, A) → l
  8. Intersect(m, l) → I
  9. Mirror(f, l) → f'
  10. OrthogonalLine(D, s) → i
  11. Intersect(i, f') → E
  12. OrthogonalLine(H, i) → k
  13. OrthogonalLine(G, b) → t
  14. OrthogonalLine(A_1, b) → r
  15. OrthogonalLine(K, l) → j
  16. OrthogonalLine(B, u, xOyPlane) → g
  17. Intersect(g, r) → C
  18. Mirror(f, l) → f'_1
  19. Mirror(F, l) → F'
  20. Polygon(A_1, C, B, A) → c4, a_1, c_3, b_2, a_2
  21. Intersect(m, f') → J
  22. Intersect(m, k) → M
  23. LineBisector(A, B) → n
  24. Mirror(i, n) → i'
  25. Intersect(n, f) → O
  26. Line(R, k) → h
  27. Line(S, h) → p
  28. Line(T, h) → q
  29. Line(L, q) → a
  30. Line(U, a) → c
  31. Intersect(j, c) → N
  32. OrthogonalLine(P, r) → d
  33. Line(Q, d) → e
  34. Line(V, e) → f_1
  35. Line(W, f_1) → g_1
  36. Line(O, N) → h_1
  37. Line(E, h_1) → i_1
  38. Line(E, N) → j_1
  39. Line(G, i_1) → k_1
  40. Line(H, i_1) → l_1
  41. Line(R, i_1) → m_1
  42. Line(S, i_1) → n_1
  43. Line(T, n_1) → p_1
  44. Line(L, i_1) → q_1
  45. Line(U, i_1) → r_1
  46. Intersect(j_1, k_1) → Z
  47. Intersect(j_1, l_1) → B_1
  48. Intersect(j_1, m_1) → C_1
  49. Intersect(j_1, n_1) → D_1
  50. Intersect(j_1, p_1) → E_1
  51. Intersect(j_1, q_1) → F_1
  52. Intersect(j_1, r_1) → G_1
  53. Intersect(n, n_1) → L_1
  54. Intersect(n, p_1) → M_1
  55. Intersect(n, q_1) → N_1
  56. Intersect(n, r_1) → O_1
  57. Line(P_1, n) → s_1
  58. Intersect(s_1, i_1) → H_1
  59. Intersect(s_1, k_1) → I_1
  60. Intersect(s_1, l_1) → J_1
  61. Intersect(s_1, m_1) → K_1
  62. Polygon(E, H_1, I_1, Z) → c1, e_3, t_1, b_1, z_1
  63. Intersect(d, l_1) → Q_1
  64. Intersect(d, m_1) → R_1
  65. Intersect(d, n_1) → S_1
  66. Intersect(d, p_1) → T_1
  67. Intersect(d, q_1) → U_1
  68. Intersect(d, r_1) → V_1
  69. Polygon(Q_1, R_1, C_1, B_1) → c2, c_1, d_1, f_2, g_2
  70. Polygon(S_1, D_1, E_1, T_1) → c3, h_2, i_2, j_2, k_2
  71. Polygon(V_1, U_1, F_1, G_1) → c5, v_1, u_1, l_2, m_2
  72. Intersect(e, r_1) → W_1
  73. Intersect(e, q_1) → Z_1
  74. Polygon(Z_1, N_1, O_1, W_1) → c6, n_2, p_2, o_1, w_1
  75. Intersect(g_1, l_1) → A_2
  76. Intersect(g_1, m_1) → B_2
  77. Polygon(A_2, J_1, K_1, B_2) → c7, q_2, r_2, s_2, t_2
  78. Intersect(k_1, e) → C_2
  79. Intersect(f_1, k_1) → D_2
  80. Intersect(p_1, e) → E_2
  81. Intersect(n_1, f_1) → F_2
  82. Polygon(E_2, M_1, L_1, F_2, D_2, C_2) → polígono1, c_2, d_2, f_3, g_3, h_3, i_3
  83. Mirror(E, n) → E'
  84. Mirror(H_1, n) → G_2
  85. Mirror(I_1, n) → H_2
  86. Mirror(Z, n) → Z'
  87. Polygon(E', G_2, H_2, Z') → c1', e', j_3, k_3, z'
  88. Mirror(Q_1, n) → I_2
  89. Mirror(R_1, n) → J_2
  90. Mirror(C_1, n) → K_2
  91. Mirror(B_1, n) → L_2
  92. Polygon(I_2, J_2, K_2, L_2) → c2', l_3, m_3, n_3, p_3
  93. Mirror(S_1, n) → M_2
  94. Mirror(D_1, n) → N_2
  95. Mirror(E_1, n) → O_2
  96. Mirror(T_1, n) → P_2
  97. Polygon(M_2, N_2, O_2, P_2) → c3', q_3, r_3, o_2, s_3
  98. Mirror(V_1, n) → Q_2
  99. Mirror(U_1, n) → R_2
  100. Mirror(F_1, n) → S_2
  101. Mirror(G_1, n) → T_2
  102. Polygon(Q_2, R_2, S_2, T_2) → c5', t_3, b_3, d_3, f_4
  103. Mirror(Z_1, n) → U_2
  104. Mirror(N_1, n) → V_2
  105. Mirror(O_1, n) → W_2
  106. Mirror(W_1, n) → Z_2
  107. Polygon(U_2, V_2, W_2, Z_2) → c6', u_2, v_2, w_2, z_2
  108. Mirror(A_2, n) → A_3
  109. Mirror(J_1, n) → B_3
  110. Mirror(K_1, n) → C_3
  111. Mirror(B_2, n) → D_3
  112. Polygon(A_3, B_3, C_3, D_3) → c7', g_4, h_4, i_4, j_4
  113. Mirror(E_2, n) → E_3
  114. Mirror(M_1, n) → F_3
  115. Mirror(L_1, n) → G_3
  116. Mirror(F_2, n) → H_3
  117. Mirror(D_2, n) → I_3
  118. Mirror(C_2, n) → J_3
  119. OrthogonalLine(A_3, f'_1) → k_4
  120. Mirror(p_1, n) → l_4
  121. Mirror(n_1, n) → m_4
  122. Intersect(k_4, m_4) → K_3
  123. Intersect(k_4, l_4) → L_3
  124. Polygon(G_3, K_3, L_3, F_3) → c8, n_4, p_4, q_4, r_4
  125. OrthogonalLine(I_3, k) → s_4
  126. Mirror(q_1, n) → t_4
  127. Intersect(s_4, t_4) → M_3
  128. Polygon(I_3, J_3, U_2, M_3) → c9, a_4, b_4, c_4, d_4