“Moving Sofa Constant”的概念、定义、习题解题方法及翻译-数学辞典

单词

Moving Sofa Constant

释义

Moving Sofa Constant

N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.

What is the sofa of greatest Area which can be moved around a right-angled hallway of unit width? Hammersley (Croft et al. 1994) showed that

(1)

Gerver (1992) found a sofa with larger Area and provided arguments indicating that it is either optimal or close to it.The boundary of Gerver's sofa is a complicated shape composed of 18 Arcs. Its Area can be given by defining theconstants

, and

by solving

(2)

(3)

(4)

(5)

This gives

			(6)
			(7)
			(8)
			(9)

Now define

(10)

where

			(11)

			(12)

			(13)

Finally, define the functions

			(14)
			(15)
			(16)

The Area of the optimal sofa is given by


	(17)

(Finch).

See also Piano Mover's Problem

References

Croft, H. T.; Falconer, K. J.; and Guy, R. K. Unsolved Problems in Geometry. New York: Springer-Verlag, 1994.

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/sofa/sofa.html

Gerver, J. L. ``On Moving a Sofa Around a Corner.'' Geometriae Dedicata 42, 267-283, 1992.

Stewart, I. Another Fine Math You've Got Me Into.... New York: W. H. Freeman, 1992.

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