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正方锥体 by David Boudreaux

正方锥体 by David Boudreaux
几何画板及绘图内容加载中，请稍等……
2016-05-27 02:33
多边形角立体几何几何作图
①本范例演示正方锥体的几何构造与性质；②涉及核心数学概念包括立体几何、多边形、角度、向量等；③作图要点运用了Circle（圆）、Point（点）、Intersect（交点）、Polygon（多边形）、Midpoint（中点）、Line（线）、Angle（角度）、Rotate（旋转）、Segment（线段）等GeoGebra命令；④适合高中及以上学生及数学爱好者用于学习立体几何与几何作图。

GeoGebra 命令及参数

  1. Circle(A, a) → c
  2. Point(c) → B
  3. Circle(B, a) → d
  4. Intersect(c, d) → C, D, ,
  5. Point(d) → E
  6. Circle(E, a) → e
  7. Intersect(e, c) → F, G, ,
  8. Polygon(A, B, E, G) → poly1, a_1, b, e_1, g
  9. Midpoint(g) → H
  10. Midpoint(e_1) → I
  11. Midpoint(b) → J
  12. Midpoint(a_1) → K
  13. Line(K, I) → f
  14. Line(H, J) → h_1
  15. Intersect(h_1, f) → L
  16. Circle(L, a + h) → k
  17. Intersect(k, h_1) → M, N
  18. Intersect(k, f) → O, P
  19. Polygon(B, N, E) → poly2, e_2, b_1, n_1
  20. Polygon(G, P, E) → poly3, e_3, g_1, p
  21. Polygon(A, M, G) → poly4, g_2, a_2, m
  22. Polygon(A, O, B) → poly5, b_2, a_3, o
  23. Line(L, yAxis) → i
  24. Point(i) → Q
  25. Angle(Q, L, M) → α
  26. Angle(Q, L, O) → β
  27. Angle(P, L, Q) → γ
  28. Angle(N, L, Q) → δ
  29. Rotate(M, (-((n * α))), L) → M'
  30. Rotate(O, (-((n * β))), L) → O'
  31. Polygon(A, M', G) → poly6, g_3, a_4, m'
  32. Polygon(O', A, B) → poly7, b_3, o', a_5
  33. Angle(N, B, Q) → ε
  34. Rotate(P, (n * γ), L) → P'
  35. Polygon(G, P', E) → poly8, e_4, g_4, p'
  36. Rotate(N, (n * δ), L) → N'
  37. Polygon(E, N', B) → poly9, b_4, e_5, n'
  38. Polygon(B, E, N') → poly10, n'_1, b_5, e_6
  39. Polygon(R, S, 4) → poly11, j, l, q, r, T, U
  40. Circle(U, V) → s
  41. Circle(T, Distance[U, V]) → t
  42. Intersect(s, t, 1) → W
  43. Segment(U, W) → c_1
  44. Segment(W, T) → d_1
  45. Polygon(U, T, W) → poly12, w, u, t_1
  46. Segment(R, T) → f_1
  47. Midpoint(f_1) → Z
  48. Rotate(U, 90°, Z) → U'
  49. Rotate(T, 90°, Z) → T'
  50. Rotate(W, 90°, Z) → W'
  51. Polygon(U', T', W') → poly12', w', u', t'
  52. Rotate(U, 180°, Z) → U'_1
  53. Rotate(T, 180°, Z) → T'_1
  54. Rotate(W, 180°, Z) → W'_1
  55. Polygon(U'_1, T'_1, W'_1) → poly12'_1, w'_1, u'_1, t'_1
  56. Rotate(U, 270°, Z) → U'_2
  57. Rotate(T, 270°, Z) → T'_2
  58. Rotate(W, 270°, Z) → W'_2
  59. Polygon(U'_2, T'_2, W'_2) → poly12'_2, w'_2, u'_2, t'_2