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Unwrapping a Cylinder Cut by an Oblique Plane by Anthony OR 柯志明 (2)

Unwrapping a Cylinder Cut by an Oblique Plane by Anthony OR 柯志明 (2)
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2015-07-17 16:21
TrigonometrySolid GeometryGeometric Construction
This example demonstrates the trajectory obtained by unwrapping a cylinder cut by an oblique plane. Key mathematical concepts include cylinder, oblique plane, and unwrapped surface. GeoGebra commands used include Intersect, Point, Circle, Cylinder, Translate, Plane, IntersectPath, Line, Segment, and CircleArc. Suitable for high school geometry and solid geometry studies.

GeoGebra Commands & Parameters

  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. Line(F, zAxis) → f_1
  10. Intersect(f_1, g) → D,
  11. Segment(D, F) → h
  12. Segment(E, (x(E), 0)) → i
  13. CircleArc((0, 0), F, (1, 0)) → k
  14. Segment((-3.141592653589793, 0), G) → l