

A073008


Decimal expansion of the Traveling Salesman constant.


3



7, 1, 4, 7, 8, 2, 7, 0, 0, 7, 9, 1, 2, 9, 4, 2, 7, 2, 0, 1, 8, 9, 8, 4, 8, 7, 9, 6, 2, 1, 0, 8, 4, 0, 9, 6, 7, 3, 1, 3, 4, 5, 5, 9, 7, 0, 9, 4, 4, 3, 0, 3, 1, 9, 3, 9, 6, 4, 5, 7, 0, 0, 4, 1, 1, 5, 4, 6, 1, 1, 7, 7, 3, 8, 3, 3, 5, 8, 7, 9, 7, 0, 6, 7, 7, 0, 2, 1, 3, 4, 1, 3, 0, 9, 6, 2, 9, 4, 5, 3, 3, 5, 6, 1, 5
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OFFSET

0,1


COMMENTS

In 1959 J. Beardwood, J. H. Halton and J. M. Hammersley showed that the shortest tour through N random uniformly distributed points in a bounded plane region of area A approaches K*sqrt(N*A), where K is the Traveling Salesman constant, as N approaches infinity. They also proved that 5/8 <= K < 0.922.
In 2015 S. Steinerberger slightly improved both bounds.
In 1995 P. Moscato and N. G. Norman proved that a planefilling curve called MNPeano is the shortest tour through the set of points defined by MNPeano and observed that the asymptotic expected length of this curve is given by (4/153)*(1+2*sqrt(2))*sqrt(51)*sqrt(N*A), which is very close to the empirical value of the traveling salesman constant.
(End)


REFERENCES

J. Beardwood, J. H. Halton and J. M. Hammersley, The shortest path through many points, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 55, No. 4, 1959, pp. 299327.


LINKS



FORMULA

Conjectured to be equal to (4/153)*(1+2*sqrt(2))*sqrt(51).


EXAMPLE

0.7147827007912942720189848796210840967313...


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



