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Tim HuttonTim Hutton - 2014-11-06 08:20:02+0000 - Updated: 2014-11-06 08:20:02+0000
Originally shared by Philip GibbsHaving finished with computing Gerver's Sofa I think it might be interesting to turn to a related problem posed by John H Conway. This is to find a shape that can go round right angle turns in a corridor, like the sofa, but with the advantage that it can turn left or right. This also means that it can use a side road off a T-junction to turn round.

As with the sofa the objective is to find the shape of largest area that can do it, and the picture here shows a numerical solution. I have assumed some symmetry in doing the computation and need to investigate whether that makes any difference. 

The area is about 1.647

Perhaps there will be practical applications for this one day as parking spaces and roads get tighter.Having finished with computing Gerver's Sofa I think it might be interesting to turn to a related problem posed by John H Conway. This is to find a shape that can go round right angle turns in a corridor, like the sofa, but with the advantage that it can turn left or right. This also means that it can use a side road off a T-junction to turn round. As with the sofa the objective is to find the shape of largest area that can do it, and the picture here shows a numerical solution. I have assumed some symmetry in doing the computation and need to investigate whether that makes any difference. The area is about 1.647 Perhaps there will be practical applications for this one day as parking spaces and roads get tighter.

Having finished with computing Gerver's Sofa I think it might be interesting to turn to a related problem posed by John H Conway. This is to find a shape that can go round right angle turns in a corridor, like the sofa, but with the advantage that it can turn left or right. This also means that it can use a side road off a T-junction to turn round. As with the sofa the objective is to find the shape of largest area that can do it, and the picture here shows a numerical solution. I have assumed some symmetry in doing the computation and need to investigate whether that makes any difference. The area is about 1.647 Perhaps there will be practical applications for this one day as parking spaces and roads get tighter.

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+1'd by: JF Peter sen, Roice Nelson, Henry Segerman, Oliver Hamilton

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