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周长、面积与体积的比例

周长、面积与体积的比例
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2017-12-18 18:44
复数几何作图
本范例演示了周长、面积与体积之间的比例关系。涉及的核心数学概念包括几何中的周长、面积和体积，以及复数。通过使用GeoGebra命令如Intersect、Point、Vector等，可以动态地展示这些概念。适合高中及以上学生或教师使用。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → C
  3. Point(xAxis) → B
  4. Point(xAxis) → E
  5. Point(xAxis) → F
  6. Vector(A, A) → v_0
  7. Sequence(E + Element[vectors, Element[combo_2, k]] + Element[vectors, Element[combo_2, k + 1]], k, 1, Length[combo_2], 2) → points_2
  8. Sequence(F + Element[vectors, Element[combo_3, k]] + Element[vectors, Element[combo_3, k + 1]], k, 1, Length[combo_3], 2) → points_3
  9. Point(points_2) → H
  10. Segment(E, H) → d_1
  11. Point(points_2) → I
  12. Segment(H, I) → e
  13. Point(points_2) → J
  14. Segment(I, J) → f
  15. Segment(J, E) → g
  16. Point(points_3) → K
  17. Segment(F, K) → h_1
  18. Point(points_3) → L
  19. Segment(K, L) → i
  20. Point(points_3) → M
  21. Segment(L, M) → j
  22. Segment(M, F) → k_1
  23. Point(points_3) → N
  24. Point(points_3) → O
  25. Segment(N, O) → l
  26. Point(points_3) → P
  27. Segment(O, P) → m
  28. Segment(P, G) → n
  29. Segment(G, N) → p
  30. Segment(M, N) → q
  31. Segment(L, G) → r
  32. Segment(F, O) → s
  33. Segment(K, P) → t
  34. Sequence(A + Element[vectors, k], k, 2, 4, 1) → points_1
  35. Point(points_1) → Q
  36. Segment(A, Q) → a
  37. Point(points_1) → R
  38. Segment(A, R) → b
  39. Point(points_1) → S
  40. Segment(A, S) → c
  41. Segment(A, B) → a_0
  42. Segment(A, C) → b_0
  43. Segment(A, D) → c_0
  44. Segment(E, E + (1, 0)) → d_0
  45. Segment(E + (1, 0), E + (1, 0) + (0, 1)) → e_0
  46. Segment(E + (1, 0) + (0, 1), E + (0, 1)) → f_0
  47. Segment(E, E + (0, 1)) → g_0
  48. Segment(F, F + (1, 0)) → h_0
  49. Segment(F + (1, 0), F + (1, 0) + (0, 1)) → i_0
  50. Segment(F + (1, 0) + (0, 1), F + (0, 1)) → j_0
  51. Segment(F, F + (0, 1)) → k_0
  52. Segment(F + (cos(π / 3), sin(π / 3)), F + (cos(π / 3), sin(π / 3)) + (0, 1)) → l_0
  53. Segment(F + (cos(π / 3), sin(π / 3)), F + (cos(π / 3), sin(π / 3)) + (1, 0)) → m_0
  54. Segment(F + (cos(π / 3), sin(π / 3)) + (1, 0), F + (cos(π / 3), sin(π / 3)) + (1, 0) + (0, 1)) → n_0
  55. Segment(F + (cos(π / 3), sin(π / 3)) + (1, 0) + (0, 1), F + (cos(π / 3), sin(π / 3)) + (0, 1)) → p_0
  56. Segment(F + (0, 1), F + (cos(π / 3), sin(π / 3)) + (0, 1)) → q_0
  57. Segment(F + (1, 0) + (0, 1), F + (1, 0) + (0, 1) + (cos(π / 3), sin(π / 3))) → r_0
  58. Segment(F, F + (cos(π / 3), sin(π / 3))) → s_0
  59. Segment(F + (1, 0), F + (1, 0) + (cos(π / 3), sin(π / 3))) → t_0