MathPlotAI Logo MathPlotAI

Unfolding of the oblique section of a cylinder

Unfolding of the oblique section of a cylinder
Loading the math board and drawing, please wait…
2020-03-25 16:27
PolygonSolid GeometryGeometric Construction
This example demonstrates the unfolding process of an oblique section of a cylinder, visually showing how the oblique section unfolds into a planar shape. Key mathematical concepts involved include cylinder, polygons, area calculation, rational numbers, straight lines, and incircle. The construction utilizes GeoGebra commands such as Line, OrthogonalPlane, Segment, Rotate, Sequence, Cylinder, Conic, If, Translate, Polygon, and Vector. It is suitable for high school solid geometry teaching, helping students understand the unfolding and reconstruction of spatial geometric bodies and enhancing geometric intuition.

GeoGebra Commands & Parameters

  1. Line(E_1, yAxis) → g_1
  2. OrthogonalPlane(E_1, xAxis) → e
  3. Segment((0, 0, 0), (h, 0, 0)) → f
  4. Rotate(e, α, g_1) → e_1
  5. Sequence((0, ((i * π) * r / 180), 0), i, 0, 359) → L9
  6. Sequence(Rotate[f, i°, Line[M_1, M_2]], i, 0, 359) → L
  7. Sequence(Intersect[e_1, Element[L, i]], i, 1, 360) → L1
  8. Cylinder((0, 0, r), (h, 0, r), r) → b, b_2, b_3, b_4
  9. Conic(Element[L1, 1], Element[L1, 91], Element[L1, 181], Element[L1, 271], Element[L1, 330]) → d
  10. Sequence(Rotate[(0, 0, 0), i°, Line[M_1, M_2]], i, 1, 359) → L2
  11. If(Defined[d], Sequence[Segment[Element[L1, i], Element[L2, i]], i, 1, 359]) → L3
  12. Sequence(Rotate[(h, 0, 0), i°, Line[M_1, M_2]], i, 1, 359) → L4
  13. If(Defined[d], Sequence[Segment[Element[L1, i], Element[L4, i]], i, 1, 359]) → L5
  14. Translate(b_3, Vector[(0, abw, 0)]) → g
  15. Translate(Line[M_1, M_2], Vector[(0, abw, 0)]) → j
  16. Rotate(A, ((((-abw)) / π * 180 / r))°, j) → A'
  17. Cylinder(g, (-h)) → i, k, l
  18. Segment(A', B) → m
  19. Sequence(Element[L9, i] + (x(Element[L1, i]), 0, 0), i, 1, 360) → L14
  20. Sequence(Element[L14, i], i, 1, o) → L17
  21. Sequence(Rotate[E, i°, j], i, 0, 359) → L7
  22. Sequence(Translate[Element[L3, i], Vector[Element[L2, i], Element[L7, i]]], i, 1, 360) → L8
  23. Sequence(Translate[Element[L3, i], Vector[Element[L2, i], Element[L9, i]]], i, 1, 360) → L10
  24. Sequence(Element[L7, i] + (x(Element[L1, i]), 0, 0), i, 1, 360) → L15
  25. Sequence(Element[L15, i], i, o + 1, 360) → L16
  26. Sequence(Element[L8, i], i, o + 1, 359) → L13
  27. If(Defined[d], 1, 0) → def
  28. Polygon((-4, -4, 0), (h + 4, -4, 0), (h + 4, ((2 * π) * r) + 4, 0), (-4, ((2 * π) * r) + 4, 0)) → v2, p, q, s, t
  29. Translate(L7, Vector[E, A']) → L7'
  30. Sequence(Element[L7', i], i, o + 1, 359) → L6
  31. Vector((0, 0, (2 * r) + 1), (a, 0, (2 * r) + 1)) → u
  32. Vector((a, 0, (2 * r) + 1), (0, 0, (2 * r) + 1)) → v
  33. Segment((0, 0, 0), (0, 0, (2 * r) + 1.5)) → c
  34. Segment((a, 0, 0), (a, 0, (2 * r) + 1.5)) → f_1
  35. Sequence(Element[L10, i], i, 1, o - 1) → L12
  36. Segment(D, A) → n
  37. Segment((0, 0, 0), D) → h_1
  38. Sequence(Translate[Element[L3, i], Vector[Element[L2, i], Element[L9, i]]], i, 1, 360) → l1