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PS 2 Logo

PS 2 Logo
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2020-03-13 06:46
TriangleVectorGeometric Construction
This example demonstrates a PS 2 logo composed of an isosceles triangle and a square. Key mathematical concepts include the properties of isosceles triangles and squares. Construction highlights the use of vector, line, mirror, and midpoint commands in GeoGebra. Suitable for middle school and above students for geometric construction.

GeoGebra Commands & Parameters

  1. Line(A, B) → s
  2. OrthogonalLine(A, s) → b
  3. Vector(A, B) → u
  4. OrthogonalVector(u) → v
  5. OrthogonalLine(F, b) → f
  6. OrthogonalLine(A_1, b) → r
  7. OrthogonalLine(I_1, r) → f_1
  8. OrthogonalLine(O_1, s) → g_1
  9. LineBisector(A, B) → m
  10. Intersect(m, f) → E
  11. Mirror(H, m) → H'
  12. OrthogonalLine(H', s) → k
  13. Line(H, I) → j
  14. Line(D_1, j) → q
  15. Intersect(f_1, q) → J_1
  16. Line(J_1, E_1) → m_1
  17. Intersect(g_1, q) → Q_1
  18. Line(Q_1, m_1) → i_2
  19. Line(C_1, j) → n_2
  20. Intersect(n_2, i_2) → W_1
  21. Midpoint(Q_1, W_1) → U_1
  22. OrthogonalLine(U_1, i_2) → m_2
  23. Line(M, j) → g_3
  24. Intersect(m_2, g_3) → V_1
  25. Line(V_1, m_1) → h_3
  26. OrthogonalLine(P_1, s) → j_1
  27. Intersect(j_1, h_3) → R_1
  28. Line(R_1, i_2) → j_2
  29. Midpoint(E_1, B_1) → F_1
  30. Intersect(i_2, k) → S_1
  31. Line(F_1, q) → t
  32. Intersect(t, j_1) → G_1
  33. OrthogonalLine(B, u, xOyPlane) → g
  34. Intersect(g, r) → C
  35. Polygon(A_1, C, B, A) → q1, a_1, c, b_1, a_2
  36. LineBisector(A_1, A) → h
  37. Mirror(f, h) → f'
  38. OrthogonalLine(D, s) → i
  39. Intersect(k, f') → K
  40. Line(K, j) → l
  41. Mirror(k, m) → k'
  42. Intersect(k', l) → L
  43. Line(M, m) → n
  44. Line(N, h) → p
  45. Intersect(p, n) → O
  46. Intersect(n, h) → P
  47. Semicircle(N, O) → d
  48. Intersect(n, l) → R
  49. Polygon(K, L, H, I) → q2, k_1, l_1, h_1, i_1
  50. Polygon(L, R, O, N) → q3, l_2, r_1, o_1, n_1
  51. OrthogonalLine(H_1, r) → e
  52. Polygon(E_1, F_1, G_1) → t1, p_1, e_1, q_1
  53. Intersect(h_3, k) → W
  54. Polygon(D_1, W, R_1) → t2, s_1, d_1, k_2
  55. Polygon(G_1, J_1, Q_1, S_1, F_1) → poly1, t_1, c_1, f_2, g_2, h_2
  56. CurveCartesian(((1 - t)^(5) * R) + (((5 * t) * (1 - t)^(4)) * T_1) + (((10 * (1 - t)^(3)) * t^(2)) * S) + (((10 * (1 - t)^(2)) * t^(3)) * U) + (((5 * (1 - t)) * t^(4)) * V) + (t^(5) * Q), t, 0, 1) → a
  57. Semicircle(V_1, U_1) → c_2
  58. Polygon(R_1, V_1, U_1, Q_1) → q4, p_2, v_1, u_1, q_2
  59. Polygon(R_1, V_1, C_1, D_1) → q5, r_2, s_2, t_2, b_2
  60. Polygon(J_1, Q_1, U_1) → t3, d_2, e_2, f_3
  61. CurveCartesian(((1 - t)^(5) * J_1) + (((5 * t) * (1 - t)^(4)) * Z_1) + (((10 * (1 - t)^(3)) * t^(2)) * K_1) + (((10 * (1 - t)^(2)) * t^(3)) * L_1) + (((5 * (1 - t)) * t^(4)) * M_1) + (t^(5) * C_1), t, 0, 1) → w
  62. Line(H, m_1) → i_3
  63. Intersect(k', q) → N_1
  64. Line(N_1, i_3) → j_3
  65. Intersect(t, l_1) → A_2
  66. Intersect(t, i_3) → B_2
  67. Intersect(t, j_3) → C_2
  68. Line(A_2, i_3) → k_3
  69. Line(D_2, i_3) → l_3
  70. Intersect(q, i_3) → E_2
  71. Intersect(t, l_3) → F_2
  72. Polygon(H, N_1, E_2) → t4, m_3, h_4, n_3
  73. Polygon(B_2, C_2, N_1, E_2) → q6, p_3, q_3, r_3, s_3
  74. Polygon(F_2, A_2, D_2) → t5, t_3, a_3, b_3
  75. Segment(O, Q) → c_3
  76. OrthogonalLine(B_2, i_3) → d_3
  77. Intersect(d_3, l_3) → I_2
  78. Intersect(d_3, j_3) → M_2
  79. Polygon(F_2, I_2, M_2, C_2) → q7, f_4, g_4, i_4, j_4
  80. CurveCartesian(((1 - t)^(5) * A_2) + (((5 * t) * (1 - t)^(4)) * N_2) + (((10 * (1 - t)^(3)) * t^(2)) * H_2) + (((10 * (1 - t)^(2)) * t^(3)) * L_2) + (((5 * (1 - t)) * t^(4)) * J_2) + (t^(5) * B_2), t, 0, 1) → w_1
  81. Segment(F_2, C_2) → k_4
  82. CurveCartesian(((1 - t)^(3) * I_2) + (((3 * (1 - t)^(2)) * t) * Q_2) + (((3 * (1 - t)) * t^(2)) * K_2) + (t^(3) * M_2), t, 0, 1) → o_2
  83. Segment(N, O) → e_3

AI Drawing Prompt Reference

Draw a PS 2 logo consisting of an isosceles triangle and a square. Start by drawing the base AB of the isosceles triangle, then draw the perpendicular bisector m of AB. Next, draw the base BC of the square, and draw a line u perpendicular to BC through B, followed by the perpendicular line v to u. Use these lines to construct the height of the isosceles triangle and the perpendicular bisector of AB, gradually completing the isosceles triangle and square.
The prompt above was compiled from the original drawing commands and is for reference only.