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

Unwrapping a Cylinder Cut by an Oblique Plane by Anthony OR 柯志明
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2015-07-18 12:38
FunctionSolid GeometryGeometric Construction
This example demonstrates how to unfold a cylinder cut by an oblique plane using tracing methods. Key math concepts include cylinder, median line, addition, rhombus, and function graph. Construction highlights the use of GeoGebra commands like Intersect, Point, Circle, Cylinder, Translate, Plane, IntersectPath, Line, Segment, and CircleArc, along with objects such as s, A, B, c, C, a, d, e, b, xOyPlane, t, f, g, F, f_1, D, E, h, i, text1, j, G, k, H, l. Suitable for high school solid geometry and geometric construction learning.

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