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MAHOU Logo

MAHOU Logo
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2020-10-18 04:06
CircleVectorTransformation
This GeoGebra example demonstrates the geometric construction of a MAHOU logo. Key mathematical concepts include vectors, angles, circles, and transformations. Using commands like Vector, OrthogonalVector, LineBisector, etc., the essential elements of the logo are constructed. Suitable for high school students or math enthusiasts learning geometric construction and transformations.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. OrthogonalVector(u) → v
  3. LineBisector(A_1, A) → l
  4. Line(A, B) → s
  5. OrthogonalLine(D, s) → i
  6. OrthogonalLine(A, s) → b
  7. OrthogonalLine(I, b) → h
  8. OrthogonalLine(F, b) → f
  9. Mirror(f, l) → f'
  10. Intersect(i, f') → E
  11. Mirror(f, l) → f'_1
  12. OrthogonalLine(Q, f'_1) → n
  13. Intersect(n, h) → Z
  14. Translate(Z, Vector[(0.232 * u)]) → Z'
  15. Translate(Z', Vector[(0.24 * u)]) → Z''_2
  16. OrthogonalLine(L, f'_1) → k
  17. OrthogonalLine(R, b) → q
  18. Intersect(k, q) → S
  19. LineBisector(M, S) → t
  20. Intersect(t, i) → T
  21. LineBisector(A, B) → m
  22. OrthogonalLine(B, u, xOyPlane) → g
  23. Mirror(i, m) → i'
  24. Intersect(m, f) → G
  25. Intersect(i', f') → P
  26. OrthogonalLine(A_1, b) → r
  27. Intersect(m, l) → K
  28. Intersect(i, l) → J
  29. Intersect(g, r) → C
  30. Mirror(F, l) → F'
  31. Polygon(A_1, C, B, A) → c4, a_1, c_3, b_2, a_2
  32. Intersect(i', f) → J_1
  33. Mirror(E, l) → E'
  34. OrthogonalLine(H, b) → j
  35. OrthogonalLine(M, b) → p
  36. CircleArc(T, S, M) → c
  37. Intersect(k, h) → W
  38. Polygon(W, Z, V, O, N, M, S) → poly1, w, z_1, v_1, o, n_1, m_1, s_1
  39. LineBisector(O, V) → a
  40. Intersect(a, p) → U
  41. Intersect(m, a) → B_1
  42. Vector(U, B_1) → e
  43. CircleArc(C_1, V, O) → d
  44. Translate(W, Vector[(0.232 * u)]) → W'
  45. Translate(V, Vector[(0.232 * u)]) → V'
  46. Translate(O, Vector[(0.232 * u)]) → O'
  47. Translate(N, Vector[(0.232 * u)]) → N'
  48. Translate(M, Vector[(0.232 * u)]) → M'
  49. Translate(S, Vector[(0.232 * u)]) → S'
  50. Polygon(Translate[W, Vector[(0.24 * u)]], Translate[Z, Vector[(0.24 * u)]], Translate[V, Vector[(0.24 * u)]], Translate[O, Vector[(0.24 * u)]], Translate[N, Vector[(0.24 * u)]], Translate[M, Vector[(0.24 * u)]], Translate[S, Vector[(0.24 * u)]]) → poly1', j_2, k_2, l_2, m_2, n_2, p_2, q_2
  51. Translate(d, Vector[(0.234 * u)]) → d'
  52. Translate(c, Vector[(0.23 * u)]) → c'
  53. Translate(W', Vector[(0.24 * u)]) → W''_2
  54. Translate(V', Vector[(0.24 * u)]) → V''_2
  55. Translate(O', Vector[(0.24 * u)]) → O''_2
  56. Translate(N', Vector[(0.24 * u)]) → N''_2
  57. Translate(M', Vector[(0.24 * u)]) → M''
  58. Translate(S', Vector[(0.24 * u)]) → S''
  59. Polygon(W''_2, Z''_2, V''_2, O''_2, N''_2, M'', S'') → poly1'', w''_2, z''_2, v''_2, o''_2, n''_2, m'', s''
  60. Translate(d', Vector[(0.24 * u)]) → d''
  61. Translate(c', Vector[(0.24 * u)]) → c''
  62. Polygon(G_1, F_1, E_1, D_1) → q1, g_1, f_1, h_1, d_1
  63. LineBisector(F_1, E_1) → i_1
  64. Intersect(i_1, g_1) → I_1
  65. LineBisector(N_1, D_1) → j_1
  66. Intersect(j_1, l) → H_1
  67. Polygon(F_1, W''_2, E_1) → t1, l_1, p_1, q_1
  68. Line(E_1, D_1) → r_1
  69. Line(V''_2, Z''_2) → t_1
  70. Intersect(r_1, t_1) → K_1
  71. Polygon(Z''_2, K_1, E_1) → t2, b_1, f_2, g_2
  72. Intersect(i_1, j) → L_1
  73. Vector(I_1, L_1) → u_1
  74. CircleArc(M_1, F_1, E_1) → c_1
  75. Intersect(j_1, f) → O_1
  76. Vector(H_1, O_1) → w_1
  77. CircleSector(P_1, N_1, D_1) → k_1
  78. Intersect(n, q) → Q_1
  79. LineBisector(F, H) → r_2
  80. Circle(R_1, S_1) → c_2
  81. Rotate(S_1, 72°, R_1) → T_1
  82. Angle(S_1, R_1, T_1) → α
  83. Rotate(T_1, 72°, R_1) → U_1
  84. Angle(T_1, R_1, U_1) → β
  85. Rotate(U_1, 72°, R_1) → W_1
  86. Angle(U_1, R_1, W_1) → γ
  87. Rotate(W_1, 72°, R_1) → Z_1
  88. Angle(W_1, R_1, Z_1) → δ
  89. Polygon(Z_1, T_1, W_1, S_1, U_1) → poly2, s_2, t_2, d_2, f_3, g_3
  90. Intersect(s_2, poly2) → A_2, B_2, C_2, D_2
  91. Intersect(t_2, poly2) → E_2, F_2, G_2, H_2
  92. Intersect(g_3, poly2) → I_2, J_2, K_2, L_2
  93. Polygon(B_2, C_2, F_2, G_2, K_2) → poly3, h_3, i_3, j_3, k_3, l_3
  94. Translate(Z_1, Vector[(0.18 * u)]) → M_2
  95. Translate(T_1, Vector[(0.18 * u)]) → N_2
  96. Translate(W_1, Vector[(0.18 * u)]) → O_2
  97. Translate(S_1, Vector[(0.18 * u)]) → P_2
  98. Translate(U_1, Vector[(0.18 * u)]) → Q_2
  99. Translate(Z_1, Vector[(0.2 * u)]) → R_2
  100. Translate(T_1, Vector[(0.2 * u)]) → S_2
  101. Translate(W_1, Vector[(0.2 * u)]) → T_2
  102. Translate(S_1, Vector[(0.2 * u)]) → U_2
  103. Translate(U_1, Vector[(0.2 * u)]) → V_2
  104. Polygon(Translate[Z_1, Vector[(0.18 * u)]], Translate[T_1, Vector[(0.18 * u)]], Translate[W_1, Vector[(0.18 * u)]], Translate[S_1, Vector[(0.18 * u)]], Translate[U_1, Vector[(0.18 * u)]]) → poly2', m_3, n_3, p_3, q_3, i_5
  105. Translate(B_2, Vector[(0.2 * u)]) → W_2
  106. Translate(C_2, Vector[(0.2 * u)]) → Z_2
  107. Translate(F_2, Vector[(0.2 * u)]) → A_3
  108. Translate(G_2, Vector[(0.2 * u)]) → B_3
  109. Translate(K_2, Vector[(0.2 * u)]) → C_3
  110. Polygon(Translate[B_2, Vector[(0.18 * u)]], Translate[C_2, Vector[(0.18 * u)]], Translate[F_2, Vector[(0.18 * u)]], Translate[G_2, Vector[(0.18 * u)]], Translate[K_2, Vector[(0.18 * u)]]) → poly3', r_3, s_3, b_3, j_5, k_5
  111. Translate(R_2, Vector[(0.2 * u)]) → D_3
  112. Translate(S_2, Vector[(0.2 * u)]) → E_3
  113. Translate(T_2, Vector[(0.2 * u)]) → F_3
  114. Translate(U_2, Vector[(0.2 * u)]) → G_3
  115. Translate(V_2, Vector[(0.2 * u)]) → H_3
  116. Translate(poly2', Vector[(0.18 * u)]) → poly2''
  117. Translate(W_2, Vector[(0.2 * u)]) → I_3
  118. Translate(Z_2, Vector[(0.2 * u)]) → J_3
  119. Translate(A_3, Vector[(0.2 * u)]) → K_3
  120. Translate(B_3, Vector[(0.2 * u)]) → L_3
  121. Translate(C_3, Vector[(0.2 * u)]) → M_3
  122. Translate(poly3', Vector[(0.18 * u)]) → poly3''
  123. Translate(D_3, Vector[(0.2 * u)]) → N_3
  124. Translate(E_3, Vector[(0.2 * u)]) → O_3
  125. Translate(F_3, Vector[(0.2 * u)]) → P_3
  126. Translate(G_3, Vector[(0.2 * u)]) → Q_3
  127. Translate(H_3, Vector[(0.2 * u)]) → R_3
  128. Translate(poly2'', Vector[(0.18 * u)]) → poly2'''
  129. Translate(I_3, Vector[(0.2 * u)]) → S_3
  130. Translate(J_3, Vector[(0.2 * u)]) → T_3
  131. Translate(K_3, Vector[(0.2 * u)]) → U_3
  132. Translate(L_3, Vector[(0.2 * u)]) → V_3
  133. Translate(M_3, Vector[(0.2 * u)]) → W_3
  134. Translate(poly3'', Vector[(0.18 * u)]) → poly3'''
  135. Translate(O_3, Vector[(0.18 * u)]) → A_4
  136. Translate(P_3, Vector[(0.18 * u)]) → B_4
  137. Translate(Q_3, Vector[(0.18 * u)]) → C_4
  138. Translate(R_3, Vector[(0.18 * u)]) → D_4
  139. Translate(poly2''', Vector[(0.18 * u)]) → poly4
  140. Translate(S_3, Vector[(0.18 * u)]) → E_4
  141. Translate(T_3, Vector[(0.18 * u)]) → F_4
  142. Translate(U_3, Vector[(0.18 * u)]) → G_4
  143. Translate(V_3, Vector[(0.18 * u)]) → H_4
  144. Translate(W_3, Vector[(0.18 * u)]) → I_4
  145. Translate(poly3''', Vector[(0.18 * u)]) → poly5
  146. LineBisector(V, O) → t_3
  147. Intersect(n, q) → J_4
  148. Polygon(V, U, J_4) → t4, j_4, v_2, u_2

AI Drawing Prompt Reference

Draw a logo composed of geometric transformations. Start with a base segment and its perpendicular direction. Construct the perpendicular bisector of the segment and lines perpendicular to the base through its endpoints. Use reflection and translation to generate parallel lines on both sides, then find intersections to define key points. Connect these points to form two polygons: a quadrilateral and a heptagon. Finally, draw two circular arcs centered at certain points, tangent to or intersecting the polygon edges. The overall shape shows symmetry and rotation, reflecting the beauty of vectors and circles.
The prompt above was compiled from the original drawing commands and is for reference only.