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Logo Sena Eco-Plastics Math Example

Logo Sena Eco-Plastics Math Example
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2019-09-06 15:31
CircleVectorCoordinate GeometryGeometric Construction
This example demonstrates how to use GeoGebra to construct geometric figures related to the Logo Sena and eco-plastics theme. It involves core mathematical concepts such as angles, area, circle, circumcircle, geometry, mathematics, division, 2D vectors, differential calculus, statistical characteristics, and percentages. The construction utilizes commands/objects like Line, OrthogonalLine, Vector, OrthogonalVector, Intersect, LineBisector, Mirror, Circle, Rotate, Angle, Midpoint, Polygon, Semicircle, CurveCartesian, Segment, and CircleSector. It is suitable for high school students and teachers for geometry construction and exploration.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. OrthogonalLine(A, f) → j
  3. Vector(A, B) → u
  4. OrthogonalVector(u) → v
  5. Line(F, f) → i
  6. Intersect(j, i) → B_1
  7. Line(G, f) → h
  8. OrthogonalLine(R_1, h) → k_2
  9. Intersect(k_2, h) → S_1
  10. Line(W_1, h) → m_2
  11. Line(D_3, k_2) → h_4
  12. LineBisector(D_3, C_3) → j_4
  13. Line(C_3, k_2) → g_4
  14. Intersect(g_4, i) → E_3
  15. LineBisector(C_3, E_3) → i_4
  16. Intersect(j_4, i_4) → O_3
  17. Mirror(J_3, i_4) → S_3
  18. Intersect(h_4, m_2) → o
  19. Mirror(H_3, O_3) → P_3
  20. Circle(M, H) → d
  21. Line(E, f) → g
  22. Intersect(j, g) → J
  23. Circle(J, E) → e
  24. Rotate(E, (-(60°)), K) → E'
  25. Line(K, E') → k
  26. Line(M, k) → p
  27. Intersect(d, p) → N, P
  28. LineBisector(H, P) → n
  29. Line(A, k) → l
  30. Intersect(e, l) → T, U
  31. OrthogonalLine(U, f) → q
  32. Intersect(q, n) → Z
  33. Line(L, l) → m
  34. Intersect(e, m) → V, W
  35. OrthogonalLine(W, f) → s
  36. Intersect(s, n) → A_1
  37. Circle(D, C) → c
  38. Angle(E', K, E) → α
  39. Intersect(e, p) → O, Q
  40. Intersect(e, k) → R, S
  41. Midpoint(K, J) → E_1
  42. Line(E_1, j) → a
  43. Intersect(a, m) → D_1
  44. Mirror(D_1, j) → F_1
  45. Polygon(E, K, S, Q, P, H, B) → poly1, e_1, k_1, s_1, q_1, p_1, h_1, b
  46. Polygon(W, U, A, L, G_1, D_1) → poly2, g_1, i_1, j_1, l_1, m_1, n_1
  47. Mirror(W, j) → W'
  48. Mirror(U, j) → U'
  49. Mirror(A, j) → A'
  50. Mirror(L, j) → L'
  51. Mirror(G_1, j) → I
  52. Mirror(D_1, j) → H_1
  53. Polygon(W', U', A', L', I, H_1) → poly2', w', u', a', l', i_2, r_1
  54. Mirror(E, j) → E'_1
  55. Mirror(K, j) → K'
  56. Mirror(S, j) → S'
  57. Mirror(Q, j) → Q'
  58. Mirror(P, j) → P'
  59. Mirror(H, j) → H'
  60. Mirror(B, j) → B'
  61. Polygon(E'_1, K', S', Q', P', H', B') → poly1', e'_1, k', s', q', p', h', b'
  62. Semicircle(H_1, D_1) → t
  63. Polygon(G, I_1, O_1, L_1, M_1, K_1, J_1, N_1, C_1, B_1) → poly3, g_2, h_2, f_1, o_1, t_1, a_1, b_1, c_1, d_1, f_2
  64. OrthogonalLine(P_1, i) → j_2
  65. Intersect(j_2, h) → Q_1
  66. OrthogonalLine(T_1, h) → l_2
  67. Intersect(l_2, i) → U_1
  68. Midpoint(T_1, U_1) → V_1
  69. Mirror(Z_1, V_1) → A_2
  70. Line(Z_1, h) → n_2
  71. Mirror(W_1, V_1) → B_2
  72. Line(A_2, n_2) → p_2
  73. Line(B_2, p_2) → q_2
  74. Intersect(j_2, m_2) → C_2
  75. Intersect(j_2, q_2) → F_2
  76. Polygon(S_1, R_1, C_2, Q_1, P_1, F_2, B_2, A_2, E_2, D_2, Z_1, W_1) → poly4, r_2, w_1, f_3, g_3, s_2, t_2, a_2, b_2, c_2, e_2, d_2, z_1
  77. LineBisector(H_2, I_2) → h_3
  78. Mirror(G_2, h_3) → J_2
  79. Line(H_2, G_2) → i_3
  80. Line(K_2, i_3) → j_3
  81. Intersect(j_3, i) → L_2
  82. Line(M_2, i) → k_3
  83. Line(N_2, k_3) → l_3
  84. Intersect(j_3, k_3) → O_2
  85. Intersect(j_3, l_3) → P_2
  86. Intersect(h_3, h) → Q_2
  87. Polygon(H_2, G_2, L_2, P_2, N_2, M_2, O_2, K_2, Q_2) → poly5, m_3, n_3, p_3, q_3, r_3, s_3, o_2, t_3, a_3
  88. Mirror(H_2, h_3) → R_2
  89. Mirror(G_2, h_3) → S_2
  90. Mirror(L_2, h_3) → T_2
  91. Mirror(P_2, h_3) → U_2
  92. Mirror(N_2, h_3) → V_2
  93. Mirror(M_2, h_3) → W_2
  94. Mirror(O_2, h_3) → Z_2
  95. Mirror(K_2, h_3) → A_3
  96. Mirror(Q_2, h_3) → B_3
  97. Polygon(R_2, S_2, T_2, U_2, V_2, W_2, Z_2, A_3, B_3) → poly5', b_3, c_3, d_3, u_2, v_2, w_2, z_2, e_3, f_4
  98. Mirror(J_3, j_4) → K_3
  99. Mirror(N_3, j_4) → M_3
  100. CurveCartesian(((1 - t)^(3) * J_3) + (((3 * (1 - t)^(2)) * t) * M_3) + (((3 * (1 - t)) * t^(2)) * N_3) + (t^(3) * K_3), t, 0, 1) → u_1
  101. CurveCartesian(((1 - t)^(3) * F_3) + (((3 * (1 - t)^(2)) * t) * I_3) + (((3 * (1 - t)) * t^(2)) * L_3) + (t^(3) * F_4), t, 0, 1) → w
  102. Mirror(w, i_4) → w'_1
  103. Mirror(u_1, i_4) → v_1
  104. Mirror(F_3, i_4) → T_3
  105. Mirror(o, O_3) → Q_3
  106. Mirror(H_3, O_3) → R_3
  107. Mirror(K_3, O_3) → U_3
  108. CurveCartesian(((1 - t)^(4) * H_3) + (((4 * (1 - t)^(3)) * t) * V_3) + (((6 * (1 - t)^(2)) * t^(2)) * W_3) + (((4 * (1 - t)) * t^(3)) * G_3) + (t^(4) * S_3), t, 0, 1) → o_3
  109. Mirror(o_3, O_3) → v_3
  110. Polygon(H_3, K_3, P_3, S_3) → q1, q_4, r_4, s_4, t_4
  111. Mirror(H_3, O_3) → G_4
  112. Mirror(F_4, O_3) → H_4
  113. Mirror(K_3, O_3) → I_4
  114. Polygon(H_3, F_4, K_3) → t1, k_4, l_4, m_4
  115. Mirror(H_3, O_3) → J_4
  116. Mirror(F_4, O_3) → K_4
  117. Mirror(K_3, O_3) → L_4
  118. Polygon(J_4, K_4, L_4) → t1', n_4, p_4, c_4
  119. Segment(K_3, J_3) → a_4
  120. Mirror(K_3, i_4) → A_4
  121. Mirror(J_3, i_4) → B_4
  122. Segment(A_4, B_4) → b_4
  123. Mirror(K_3, b_4) → C_4
  124. Mirror(J_3, b_4) → D_4
  125. Segment(C_4, D_4) → d_4
  126. CircleSector(G_1, D_1, H_1) → e_4

AI Drawing Prompt Reference

Construct a geometric figure with lines, perpendiculars, vectors, circles, polygons, and arcs. Start with a horizontal baseline, draw a perpendicular through a point on it, and create a vector with its orthogonal counterpart. Use intersections of parallel lines and perpendiculars, along with angle bisectors and midpoints, to build symmetric points. Then draw two circles—one centered at a point passing through another, and another centered at an intersection passing through a point—and rotate a segment by 60 degrees. Finally, connect multiple intersection points to form two polygons, and mirror some points to complete the symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.