Category: PIVOT!

fuckyeahphysica: If one remembers this partic…

fuckyeahphysica:

If one remembers this particular episode from the popular sitcom ‘Friends’ where Ross is trying to carry a sofa to his apartment, it seems that moving a sofa up the stairs is ridiculously hard.

But life shouldn’t be that hard now should it?

The mathematician Leo Moser posed in 1966 the following curious mathematical problem: what
is the shape of largest area in the plane that can be moved around a
right-angled corner in a two-dimensional hallway of width 1?
This question became known as the moving sofa problem, and is still unsolved fifty years after it was first asked.

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The most common shape to move around a tight right angled corner is a square.

And another common shape that would satisfy this criterion is a semi-circle.

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But
what is the largest area that can be moved around?

Well, it has been
conjectured that the shape with the largest area that one can move around a corner is known as “Gerver’s
sofa”. And it looks like so:

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Wait.. Hang on a second

This
sofa would only be effective for right handed turns. One can clearly
see that if we have to turn left somewhere we would be kind of in a tough
spot.

Prof.Romik from the University of California, Davis has
proposed this shape popularly know as Romik’s ambidextrous sofa that
solves this problem.

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Although Prof.Romik’s sofa may/may not be the not the optimal solution, it is definitely is a breakthrough since this can pave the way for more complex ideas in mathematical analysis and more importantly sofa design.

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Have a good one!