PS 2标志

PS 2标志
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2020-03-13 06:46
该范例演示了一个等腰三角形和正方形组成的PS 2标志。涉及的核心数学概念包括等腰三角形和正方形的性质。作图要点包括使用向量、线段、镜像、中点等GeoGebra命令。适合初中及以上学生学习几何作图。

GeoGebra 命令及参数

  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 绘图提示语参考

绘制一个由等腰三角形和正方形组成的PS 2标志。首先画出等腰三角形的底边AB,然后通过A点和B点画出底边的垂直平分线m。接着画出正方形的底边BC,通过B点画出垂直于底边的线u,再画出u的垂线v。利用这些线构造等腰三角形的高线和底边的垂直平分线,逐步完成等腰三角形和正方形的构造。
以上提示语为根据原始绘图命令整理而来,仅供参考。