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Cross Sections of a Cylinder by nandrews

Cross Sections of a Cylinder by nandrews
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2016-05-10 22:21
TrigonometryCoordinate GeometrySolid GeometryProbability & StatisticsGeometric Construction
This example demonstrates the various cross-section shapes formed by a cylinder as the cutting plane's angle and position are altered, including circles, ellipses, rectangles, and trapezoids. Key mathematical concepts involve solid geometry, coordinate geometry, geometric construction, and probability & statistics. The construction utilizes GeoGebra commands and objects such as Intersect, Point, Circle, Cylinder, OrthogonalLine, Plane, IntersectPath, Corner, and Segment. It is suitable for high school and above students to explore spatial geometry and cross-sectional analysis.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Cylinder(c, 6) → a, d, b
  5. Point(d) → C
  6. OrthogonalLine(C, d) → e
  7. Point(d) → D
  8. OrthogonalLine(D, d) → f
  9. Point(e) → E
  10. Plane(C, D, E) → g
  11. IntersectPath(g, a) → h
  12. Corner(h) → F, G, H, I
  13. Point(h) → J
  14. Point(d) → K
  15. OrthogonalLine(K, d) → i
  16. Intersect(i, c, 1) → L
  17. Segment(K, L) → j
  18. OrthogonalLine(J, j, space) → k
  19. Intersect(k, j) → M
  20. Segment(D, F) → l
  21. OrthogonalLine(M, l, space) → m
  22. Intersect(m, b, 1) → N
  23. Plane(J, M, N) → n
  24. IntersectPath(n, a) → p
  25. Point(d) → O
  26. Point(c) → P
  27. Point(c) → Q
  28. Point(d) → R
  29. OrthogonalLine(R, d) → r
  30. Intersect(r, c, 1) → S
  31. Segment(R, S) → s
  32. Point(s) → T
  33. Point(d) → U
  34. OrthogonalLine(U, d) → t
  35. Intersect(t, c, 1) → V
  36. Segment(U, V) → a_1
  37. Point(a_1) → W
  38. Plane(O, W, T) → u
  39. IntersectPath(u, a) → c_1
  40. Corner(c_1) → Z, A_1, B_1, C_1
  41. Point(s) → D_1
  42. Point(a_1) → E_1
  43. Point(d) → F_1
  44. OrthogonalLine(F_1, d) → b_1
  45. Point(b_1) → G_1
  46. Plane(G_1, D_1, E_1) → w
  47. IntersectPath(w, a) → d_1
  48. Corner(d_1) → H_1, I_1, J_1, K_1