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Unwrapping a Cylinder Cut by an Oblique Plane - Equation

Unwrapping a Cylinder Cut by an Oblique Plane - Equation
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2017-06-20 07:51
Coordinate GeometrySolid GeometryGeometric Construction
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
This example demonstrates the unwrapping of a cylinder cut by an oblique plane and its corresponding equations. It involves core mathematical concepts such as cylinder geometry, oblique planes, coordinate geometry, and linear regression. The construction utilizes GeoGebra commands and objects like Intersect, Circle, Cylinder, Segment, Point, Plane, IntersectPath, Corner, CircleArc, OrthogonalLine, Midpoint, Angle, Distance, and Polygon. It is suitable for high school students and geometry enthusiasts exploring the connection between spatial geometry and analytical geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, B) → c
  3. Cylinder(c, 4) → a, d, b
  4. Segment(B, F) → e
  5. Point(e) → G
  6. Plane(D, E, G) → f
  7. IntersectPath(f, a) → g
  8. Corner(g) → I, J, K, L
  9. Point(c) → C
  10. CircleArc(A, C, B) → h
  11. OrthogonalLine(C, xOyPlane) → i
  12. Intersect(i, g) → H,
  13. Segment(C, H) → j
  14. Segment((0, 0), (h, 0)) → k
  15. Segment(N, M) → l
  16. Midpoint(D, E) → O
  17. Angle(C, A, B) → θ
  18. Distance(F, B) → distanceFB
  19. Segment(O, F) → m
  20. Angle(P, O, F, zAxis) → α
  21. Segment(P, O) → q
  22. Segment(A, C) → r
  23. Segment(A, B) → s
  24. Segment(H, P) → t
  25. Segment(G, F) → p
  26. Segment(G, B) → a_1
  27. CircleArc(O, P, F, zAxis) → c_1
  28. Segment(O, D) → b_1
  29. OrthogonalLine(P, b_1, space) → d_1
  30. Intersect(d_1, Line[O, D]) → Q
  31. Segment(O, Q) → n
  32. Polygon(Q, P, H) → poly1, h_1, q_1, p_1
  33. Polygon(O, F, G) → poly2, g_1, o, f_1
  34. Angle(O, P, Q) → β
  35. Distance(P, H) → PH
  36. Segment(((2 * π), 0), ((2 * π), 1)) → i_1
  37. Segment(((2 * π), 0), ((2 * π), 1)) → j_1