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斜切圆柱的展开

斜切圆柱的展开
几何画板及绘图内容加载中，请稍等……
2015-07-22 14:21
立体几何参数方程不等式
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本范例演示了斜切圆柱的展开图形；②涉及的核心数学概念包括立体几何、曲面、不等式、参数方程；③作图要点提炼自构造摘要，使用了Intersect（相交）、Point（点）、Circle（圆）、Cylinder（圆柱）、Translate（平移）、Plane（平面）、IntersectPath（路径相交）、Surface（曲面）、CurveCartesian（笛卡尔曲线）、Segment（线段）、CornerThreeD（三维角点）等GeoGebra命令/对象；④适合高中及以上学段，用于立体几何和微积分教学。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Point(zAxis) → C
  5. Cylinder(A, C, 1) → a, d, e, b
  6. Translate(xOyPlane, Vector[(0, 0, 1.719232508579406)]) → xOyPlane'
  7. Plane((0, 1, z(C) / 2), (0, -1, z(C) / 2), (1, 0, (z(C) / 2 * (1 - t)))) → f
  8. IntersectPath(f, a) → g
  9. Surface((l * (1 - cos((v * φ)))) - 1, (l * sin((v * φ))), ((u * h / 2) * (1 + (t * cos((v * π))))), u, 0, 1, v, -1, 1) → j
  10. Surface(-1, u, ((v * h / 2) * (1 + (t * cos(u)))), u, -3.141592653589793, 3.141592653589793, v, 0, 1) → i
  11. Surface(cos(u), sin(u), h - ((v * h / 2) * (1 + (t * cos(u)))), u, -3.141592653589793, 3.141592653589793, v, 0, 1) → m
  12. CurveCartesian((l * (1 - cos((v * φ)))) - 1, (l * sin((v * φ))), (h / 2 * (1 + (t * cos((v * π))))), v, -1, 1) → k
  13. CurveCartesian(-1, u, (h / 2 * (1 + (t * cos(u)))), u, -3.14159, 3.141592653589793) → n
  14. CurveCartesian((l * (1 - cos((v * φ)))) - 1, (l * sin((v * φ))), 0, v, -1, 1) → o
  15. Segment((-1, -3.141592653589793), (-1, 3.141592653589793)) → p
  16. Segment(D, F) → q
  17. Segment(E, G) → r
  18. Segment((-1, -3.141592653589793, 0), (-1, (-π), (h / 2 * (1 - t)))) → a_1
  19. Segment((-1, 3.141592653589793, 0), (-1, π, (h / 2 * (1 - t)))) → b_1
  20. CurveCartesian(cos(u), sin(u), h, u, 0, 6.283185307179586) → u
  21. CornerThreeD(-1, 11) → C_v