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Question: Given a closed curve C, what will be the (bounds on) dimension of the interval it will pass through?

i.e. which are the necessary and sufficient conditions for a planar compact set C to pass through a closed interval in a plane?

The matter has been studied in the 1982 paper by Gilbert Strang, "The width of a chair," in Amer. Math. Monthly; but only ends in certain (interesting) conjectures in case of a non convex C (the problem in case of a convex C does get a definitive answer as its shortest orthogonal chord).

A development over this question would be the still open moving sofa problem (Leo Moser's 1966 problem, "Moving Furniture through a Hallway," Problem 66-11 in SIAM Review).

Does the question have a definitive answer? Any references/latest work done with regards to the question are welcome.

Question: Given a closed curve C, what will be the (bounds on) dimension of the interval it will pass through?

i.e. which are the necessary and sufficient conditions for a planar compact set C to pass through a closed interval in a plane?

The matter has been studied in the 1982 paper by Gilbert Strang, "The width of a chair," in Amer. Math. Monthly; but only ends in certain (interesting) conjectures in case of a non convex C (the problem in case of a convex C does get a definitive answer as its shortest orthogonal chord).

A development over this question would be the still open moving sofa problem (Leo Moser's 1966 problem, "Moving Furniture through a Hallway," Problem 66-11 in SIAM Review).

Does the question have a definitive answer? Any references/latest work done with regards to the question are welcome.

Q Given a closed curve C; what will be the (bounds on ) dimension of the interval it will pass through.

i.e. which are the necessary and sufficient conditions for a planer compact set C to pass through a closed interval in a plane.

The matter has been studied in the 1982 paper by Gilbert Strang, "The width of a chair," in Amer. Math. Monthly; but only ends in certain (interesting) conjectures in case of a non convex C (the problem in case of a covex C does get a definitive answer as its shortest orthogonal chord).

A development over this question would be the still open moving sofa problem (Leo Moser's 1966 problem, "Moving Furniture through a Hallway," Problem 66-11 in SIAM Review.)

Does the question have a definitive answer? Any references/latest work done with regards to the question are welcome.

Question: Given a closed curve C, what will be the (bounds on) dimension of the interval it will pass through?

i.e. which are the necessary and sufficient conditions for a planar compact set C to pass through a closed interval in a plane?

The matter has been studied in the 1982 paper by Gilbert Strang, "The width of a chair," in Amer. Math. Monthly; but only ends in certain (interesting) conjectures in case of a non convex C (the problem in case of a convex C does get a definitive answer as its shortest orthogonal chord).

A development over this question would be the still open moving sofa problem (Leo Moser's 1966 problem, "Moving Furniture through a Hallway," Problem 66-11 in SIAM Review).

Does the question have a definitive answer? Any references/latest work done with regards to the question are welcome.

Q Given a closed curve C; what will be the (bounds on ) dimensions of the interval it will pass through.

i.e. which are the necessary and sufficient conditions for a planer compact set C to pass through a closed interval in a plane.

The matter has been studied in the 1982 paper by Gilbert Strang, "The width of a chair," in Amer. Math. Monthly; but only ends in certain (interesting) conjectures in case of a non convex C (the problem in case of a covex C does get a definitive answer as its shortest orthogonal chord).

A development over this question would be the still open moving sofa problem (Leo Moser's 1966 problem, "Moving Furniture through a Hallway," Problem 66-11 in SIAM Review.)

Does the question have a definitive answer? Any references/latest work done with regards to the question are welcome.

Q Given a closed curve C; what will be the (bounds on ) dimension of the interval it will pass through.

i.e. which are the necessary and sufficient conditions for a planer compact set C to pass through a closed interval in a plane.

The matter has been studied in the 1982 paper by Gilbert Strang, "The width of a chair," in Amer. Math. Monthly; but only ends in certain (interesting) conjectures in case of a non convex C (the problem in case of a covex C does get a definitive answer as its shortest orthogonal chord).

A development over this question would be the still open moving sofa problem (Leo Moser's 1966 problem, "Moving Furniture through a Hallway," Problem 66-11 in SIAM Review.)

Does the question have a definitive answer? Any references/latest work done with regards to the question are welcome.