欧拉公式

欧拉公式
几何画板及绘图内容加载中,请稍等……
2022-05-08 18:52
该范例演示了欧拉公式,涉及复数与指数函数的关系。通过点、圆、向量等对象的构造,展示了欧拉公式在解析几何中的应用。使用了Point、Circle、Vector等GeoGebra命令,适合高中数学教学。

GeoGebra 命令及参数

  1. Point(yAxis) → A
  2. Circle(A, 1) → c
  3. Vector(A, B) → u
  4. Vector(B, C) → v
  5. Circle(C, t02) → d
  6. OrthogonalLine(C, yAxis) → f
  7. Intersect(d, f, 2) → D
  8. Vector(C, D) → w
  9. Circle(D, t03) → e
  10. OrthogonalLine(D, w) → g
  11. Intersect(e, g) → E, F
  12. Vector(D, F) → a
  13. Circle(F, t04) → h
  14. OrthogonalLine(F, yAxis) → i
  15. Intersect(h, i, 1) → G
  16. Vector(F, G) → b
  17. OrthogonalLine(G, b) → j
  18. Circle(G, t05) → k
  19. Intersect(k, j) → H, I
  20. Vector(G, I) → l
  21. Circle(I, t06) → p
  22. OrthogonalLine(I, l) → m
  23. Intersect(p, m, 2) → J
  24. Vector(I, J) → n
  25. Circle(J, t07) → q
  26. OrthogonalLine(J, n) → r
  27. Intersect(q, r, 2) → K
  28. Vector(J, K) → s
  29. Circle(K, t08) → t
  30. OrthogonalLine(K, s) → f_1
  31. Intersect(t, f_1, 2) → L
  32. Vector(K, L) → u_1
  33. Circle(L, t09) → c_1
  34. OrthogonalLine(L, u_1) → g_1
  35. Intersect(c_1, g_1, 2) → M
  36. Vector(L, M) → v_1
  37. Circle(M, t10) → d_1
  38. OrthogonalLine(M, v_1) → h_1
  39. Intersect(d_1, h_1, 2) → N
  40. Vector(M, N) → w_1
  41. Circle(N, t11) → e_1
  42. OrthogonalLine(N, w_1) → i_1
  43. Intersect(e_1, i_1, 2) → O
  44. Vector(N, O) → a_1
  45. Circle(O, t12) → k_1
  46. OrthogonalLine(O, a_1) → j_1
  47. Intersect(k_1, j_1, 2) → P
  48. Vector(O, P) → b_1
  49. Circle(P, t13) → p_1
  50. OrthogonalLine(P, b_1) → l_1
  51. Intersect(p_1, l_1, 2) → Q
  52. Vector(P, Q) → m_1
  53. Circle(Q, t14) → q_1
  54. OrthogonalLine(Q, m_1) → n_1
  55. Intersect(q_1, n_1, 2) → R
  56. Vector(Q, R) → r_1
  57. Circle(R, t15) → s_1
  58. OrthogonalLine(R, r_1) → t_1
  59. Intersect(s_1, t_1, 2) → S
  60. Vector(R, S) → u_2
  61. Circle(S, t16) → c_2
  62. OrthogonalLine(S, u_2) → f_2
  63. Intersect(c_2, f_2, 2) → T
  64. Vector(S, T) → v_2
  65. Circle(T, t17) → d_2
  66. OrthogonalLine(T, v_2) → g_2
  67. Intersect(d_2, g_2, 2) → U
  68. Vector(T, U) → w_2
  69. Circle(U, t18) → e_2
  70. OrthogonalLine(U, w_2) → h_2
  71. Intersect(e_2, h_2, 2) → V
  72. Vector(U, V) → a_2

AI 绘图提示语参考

画一个展示欧拉公式的图形,包含一个点在y轴上,以此点为圆心画一个单位圆,再从圆上点向y轴作向量,接着以向量终点为圆心画圆,交点作向量,重复此过程,展示复数与指数函数的关系,适合高中数学教育。
以上提示语为根据原始绘图命令整理而来,仅供参考。