积极 AI Logo 积极 AI

斜截面圆柱展开方程

斜截面圆柱展开方程
几何画板及绘图内容加载中，请稍等……
2017-06-20 07:51
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本范例演示斜截面切割圆柱后的展开图形与方程关系；②涉及核心数学概念包括圆柱几何、斜截面、解析几何、线性回归；③作图要点提炼自构造摘要，使用Intersect, Circle, Cylinder, Segment, Point, Plane, IntersectPath, Corner, CircleArc, OrthogonalLine, Midpoint, Angle, Distance, Polygon等GeoGebra命令与对象；④适合高中及以上数学学习者和几何爱好者用于理解空间几何与解析几何的关联应用。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, B) → c
  3. Cylinder(c, 4) → a, d, b
  4. Segment(B, F) → e
  5. Point(e) → G
  6. Plane(D, E, G) → f
  7. IntersectPath(f, a) → g
  8. Corner(g) → I, J, K, L
  9. Point(c) → C
  10. CircleArc(A, C, B) → h
  11. OrthogonalLine(C, xOyPlane) → i
  12. Intersect(i, g) → H,
  13. Segment(C, H) → j
  14. Segment((0, 0), (h, 0)) → k
  15. Segment(N, M) → l
  16. Midpoint(D, E) → O
  17. Angle(C, A, B) → θ
  18. Distance(F, B) → distanceFB
  19. Segment(O, F) → m
  20. Angle(P, O, F, zAxis) → α
  21. Segment(P, O) → q
  22. Segment(A, C) → r
  23. Segment(A, B) → s
  24. Segment(H, P) → t
  25. Segment(G, F) → p
  26. Segment(G, B) → a_1
  27. CircleArc(O, P, F, zAxis) → c_1
  28. Segment(O, D) → b_1
  29. OrthogonalLine(P, b_1, space) → d_1
  30. Intersect(d_1, Line[O, D]) → Q
  31. Segment(O, Q) → n
  32. Polygon(Q, P, H) → poly1, h_1, q_1, p_1
  33. Polygon(O, F, G) → poly2, g_1, o, f_1
  34. Angle(O, P, Q) → β
  35. Distance(P, H) → PH
  36. Segment(((2 * π), 0), ((2 * π), 1)) → i_1
  37. Segment(((2 * π), 0), ((2 * π), 1)) → j_1