Mathematics — Corner Case — The Hallway Problem Feb 2021

A slightly different take on the corner problem
Determine the longest beam that can turn the corner of two halls of given width, x and y.

  • The general solution.
  • The extent of the path of the beam.

In the calculations, I use both L and R to represent the beam length; I use L when finding the maximum length; I use R when the beam length is given.

moment of inertia of a circular cross-section

General solution

Extent of beam path calculations (1)
Extent of beam path (1)
Reference: https://en.wikipedia.org/wiki/Line-line_intersection
Extent of beam path calculations (2)
Extent of beam path (2)
Extent of beam path calculations (3)
Extent of beam path (3)
Extent of beam path calculations (4)
Extent of beam path (4)
Chart showing extent of beam path
Finite width beam (1)
Finite width beam (1)
Finite width beam (2)
Finite width beam (2)
Finite width beam (3)
Finite width beam (3)
Finite width beam (3)

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