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三个圆柱的交集

三个圆柱的交集
几何画板及绘图内容加载中，请稍等……
2016-08-05 03:02
解析几何立体几何几何作图
所属专题 intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
①本范例演示三个圆柱体相交形成的几何体及其截面；②涉及核心数学概念包括立体几何、交集计算、曲面面积、坐标几何；③构造要点：使用Cylinder（圆柱）、CurveCartesian（笛卡尔曲线）、Point（点）、Sphere（球体）、PointIn（点在对象上）、Surface（曲面）、Cube（立方体）等命令和对象；④适合高中及以上学生及数学爱好者用于理解空间几何体关系和计算。

GeoGebra 命令及参数

  1. Cylinder(A, B, r) → d, e, f, g
  2. Cylinder(C, D, r) → h, h_2, h_3, h_4
  3. Cylinder(E, F, r) → j, j_2, j_3, j_4
  4. CurveCartesian((cos(t) * r), (cos(t) * r), (sin(t) * r), t, (-π), π) → m
  5. CurveCartesian((cos(t) * r), ((-cos(t)) * r), (sin(t) * r), t, (-π), π) → b
  6. CurveCartesian((sin(t) * r), (cos(t) * r), (cos(t) * r), t, (-π), π) → c
  7. CurveCartesian((sin(t) * r), (cos(t) * r), ((-cos(t)) * r), t, (-π), π) → i
  8. CurveCartesian((cos(t) * r), (sin(t) * r), (cos(t) * r), t, (-π), π) → k
  9. CurveCartesian((cos(t) * r), (sin(t) * r), ((-cos(t)) * r), t, (-π), π) → l
  10. Point(c) → G
  11. Point(b) → H
  12. Point(i) → I
  13. Point(m) → J
  14. Point(k) → K
  15. Point(m) → L
  16. Point(b) → M
  17. Point(k) → N
  18. Sphere(O, J) → n
  19. PointIn(h_4) → Bodh4
  20. Surface((cos(t) * r), ((cos(t) * r) * s), (sin(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → r_1
  21. Surface((cos(t) * r), ((cos(t) * r) * s), ((-sin(t)) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → s
  22. Surface((sin(t) * r), ((s * cos(t)) * r), (cos(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → t
  23. Surface(((-sin(t)) * r), ((s * cos(t)) * r), (cos(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → u
  24. Surface((sin(t) * r), (cos(t) * r), (((-cos(t)) * r) * s), s, -1, 1, t, π / 4, (3 * π / 4)) → v
  25. Surface(((-sin(t)) * r), (cos(t) * r), ((cos(t) * r) * s), s, -1, 1, t, π / 4, (3 * π / 4)) → w
  26. Surface(((cos(t) * r) * s), (cos(t) * r), ((-sin(t)) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → b_1
  27. Surface(((cos(t) * r) * s), (sin(t) * r), (cos(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → c_1
  28. Surface((cos(t) * r), (sin(t) * r), ((cos(t) * r) * s), s, -1, 1, t, π / 4, (3 * π / 4)) → d_1
  29. Surface((cos(t) * r), ((-sin(t)) * r), ((cos(t) * r) * s), s, -1, 1, t, π / 4, (3 * π / 4)) → e_1
  30. Surface(((cos(t) * r) * s), ((-sin(t)) * r), (cos(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → f_1
  31. Surface(((cos(t) * r) * s), (cos(t) * r), (sin(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → a_1
  32. Cube(A_1, B_1, o_1) → p_1, P, stena4, stenaPQUT, stenaRSTU, hrana2, hrana1, hrana4, hranaPQ, hrana3, hranaQU, hranaRU, Q, hranaRS, hrana5, hranaST, hranaPT, hranaTU, R, S, T, U, stena1, stena3, stena2
  33. Cylinder(A, B, r) → q_1, s_1, t_1, u_1
  34. Cylinder(C, D, r) → v_1, c_2, d_2, w_1
  35. Cylinder(E, F, r) → a_2, e_2, f_2, b_2
  36. Surface((cos(t) * r), ((-sin(t)) * r) - g_2, ((cos(t) * r) * s), s, -1, 1, t, π / 4, (3 * π / 4)) → g_1
  37. Surface(((cos(t) * r) * s), ((-sin(t)) * r) - g_2, (cos(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → h_1
  38. Surface((cos(t) * r), ((cos(t) * r) * s), (sin(t) * r) + g_2, s, -1, 1, t, π / 4, (3 * π / 4)) → i_1
  39. Surface((cos(t) * r), ((cos(t) * r) * s), ((-sin(t)) * r) - g_2, s, -1, 1, t, π / 4, (3 * π / 4)) → j_1
  40. Surface((sin(t) * r) + g_2, ((s * cos(t)) * r), (cos(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → k_1
  41. Surface(((-sin(t)) * r) - g_2, ((s * cos(t)) * r), (cos(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → l_1
  42. Surface((sin(t) * r) + g_2, (cos(t) * r), (((-cos(t)) * r) * s), s, -1, 1, t, π / 4, (3 * π / 4)) → m_1
  43. Surface(((-sin(t)) * r) - g_2, (cos(t) * r), ((cos(t) * r) * s), s, -1, 1, t, π / 4, (3 * π / 4)) → n_1
  44. Surface(((cos(t) * r) * s), (cos(t) * r), ((-sin(t)) * r) - g_2, s, -1, 1, t, π / 4, (3 * π / 4)) → o
  45. Surface(((cos(t) * r) * s), (sin(t) * r) + g_2, (cos(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → p
  46. Surface((cos(t) * r), (sin(t) * r) + g_2, ((cos(t) * r) * s), s, -1, 1, t, π / 4, (3 * π / 4)) → q
  47. Surface(((cos(t) * r) * s), (cos(t) * r), (sin(t) * r) + g_2, s, -1, 1, t, π / 4, (3 * π / 4)) → a