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Plane Section of a Cylinder

Plane Section of a Cylinder
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2014-11-01 02:26
VectorSolid GeometryGeometric Construction
This example demonstrates the plane section of a cylinder and introduces Dandelin spheres. Key mathematical concepts include cylinder, section, rhombus or rectangle, vectors, etc. Using GeoGebra commands such as OrthogonalLine, InfiniteCylinder, Line, Point, etc., the section of a cylinder can be constructed. Suitable for high school geometry and solid geometry courses.

GeoGebra Commands & Parameters

  1. OrthogonalLine(T, xOyPlane) → a
  2. InfiniteCylinder(a, r) → b
  3. Line(B_1, a) → c
  4. Line(C_1, a) → d
  5. Point(c) → A
  6. Point(d) → B
  7. Plane(A, a) → e
  8. Line(A, B) → f
  9. Intersect(a, f) → M
  10. OrthogonalPlane(M, a) → g
  11. OrthogonalPlane(M, f) → h
  12. IntersectPath(h, g) → i
  13. Intersect(i, b) → C, D
  14. OrthogonalLine(M, f, e) → k
  15. Circle(M, r, e) → p
  16. Intersect(k, p) → E, F
  17. Line(F, f) → l
  18. Line(E, f) → m
  19. Intersect(a, l) → M_2
  20. Intersect(a, m) → M_1
  21. OrthogonalLine(M_2, f, e) → n
  22. OrthogonalLine(M_1, f, e) → q
  23. Intersect(f, q) → F_1
  24. Intersect(f, n) → F_2
  25. Plane(f, i) → ε
  26. Ellipse(F_1, F_2, C, ε) → s
  27. OrthogonalLine(M_2, a, e) → t
  28. OrthogonalLine(M_1, a, e) → a_1
  29. Intersect(d, t) → G
  30. Intersect(d, a_1) → H
  31. Circle(a, G) → c_1
  32. Circle(a, H) → d_1
  33. Sphere(M_2, F_2) → kug2
  34. Sphere(M_1, F_1) → kug1
  35. Circle(M_2, F_2, e) → k_2
  36. Circle(M_1, F_1, e) → k_1
  37. Point(s) → P
  38. Line(P, c) → b_1
  39. Intersect(b_1, c_1) → P_2,
  40. Intersect(b_1, d_1) → P_1,
  41. Segment(F_1, P) → l_1
  42. Segment(P, P_1) → f_1
  43. Segment(F_2, P) → l_2
  44. Segment(P, P_2) → h_1
  45. Angle(n, f, e) → α
  46. Angle(f, q, e) → β