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内马尔标志

内马尔标志
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2020-06-04 00:50
多边形向量几何作图
这个范例演示了如何使用向量和几何变换来构造内马尔标志。核心数学概念包括向量、几何变换和多边形。通过使用Vector、OrthogonalVector、Mirror等GeoGebra命令，可以构造出标志的各个部分。适合高中数学教学和学习几何作图。

GeoGebra 命令及参数

  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(F, b) → f
  8. Mirror(f, l) → f'
  9. Intersect(i, f') → E
  10. OrthogonalLine(G, b) → t
  11. OrthogonalLine(H, i) → k
  12. OrthogonalLine(U, k) → q
  13. Intersect(i, l) → P
  14. OrthogonalLine(I, b) → n
  15. OrthogonalLine(A_1, b) → r
  16. OrthogonalLine(K, l) → j
  17. Intersect(j, n) → B_1
  18. OrthogonalLine(V, r) → a
  19. Intersect(a, n) → E_1
  20. OrthogonalLine(Z, i) → h
  21. OrthogonalLine(N, h) → p
  22. Intersect(h, p) → H_1
  23. Intersect(p, n) → C_1
  24. Intersect(t, j) → I_1
  25. Intersect(q, n) → D_1
  26. Intersect(p, t) → F_1
  27. OrthogonalLine(S, l) → m
  28. Intersect(m, f) → M
  29. Intersect(m, l) → L
  30. OrthogonalLine(B, u, xOyPlane) → g
  31. Intersect(g, r) → C
  32. Mirror(f, l) → f'_1
  33. Mirror(F, l) → F'
  34. Polygon(A_1, C, B, A) → c4, a_1, c_3, b_2, a_2
  35. Mirror(t, l) → t'
  36. OrthogonalLine(J, l) → c
  37. OrthogonalLine(Q, l) → d
  38. OrthogonalLine(R, l) → e
  39. Intersect(q, t) → G_1
  40. Polygon(G, K, C_1, B_1, I_1, Z, N, F_1, U, V, E_1, D_1, G_1, H_1) → polígono1, g_1, q_1, r_1, s_1, t_1, b_1, h_1, i_1, j_1, k_1, l_1, m_1, n_1, p_1
  41. OrthogonalLine(T, l) → f_1
  42. Intersect(m, t') → J_1
  43. Mirror(h, l) → h'
  44. Intersect(q, h') → K_1
  45. Intersect(q, t') → L_1
  46. Intersect(f, c) → M_1
  47. Polygon(M_1, J, S, J_1, K_1, L_1, M) → polígono2, c_1, j_2, s_2, d_1, f_2, g_2, m_2
  48. Intersect(d, n) → N_1
  49. Intersect(n, e) → O_1
  50. Intersect(e, h) → P_1
  51. Intersect(f_1, t) → Q_1
  52. Intersect(h, f_1) → R_1
  53. OrthogonalLine(W, l) → i'
  54. Intersect(h, i') → S_1
  55. Intersect(e, t) → T_1
  56. Polygon(N_1, O_1, Q, P_1, Q_1, R_1, S_1, W, T, T_1, R) → polígono3, h_2, r_2, q_2, o_1, i_2, k_2, l_2, n_2, w, t_2, p_2