Sofa Moving Problem

or If the Movers Had Been Mathematicians

Reflection

Now we can assume that the maximum length of the pole is the minimum segment with ends on the outer walls, which touches the inner corner I.

This sounds a little odd - the maximum length is the minimum segment?

Try to convince yourselves on the dynamic worksheet.

Tips and Tricks.
Move point A and observe the length of the pole p. When A moves towards the corner, the length is decreasing and then, at some point, it starts increasing. At this point the segment is minimum and this is the longest pole (if we fix its length) that can move around the corner without getting stuck.

If you are still not convinced, re-create the situation with some appropriate materials (pencils of different length, cardboard boxes, etc.).

Change the accuracy of the length (Options -> Rounding) to obtain more accurate results.

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