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In [[geometry]], '''Robbins' constant''', named after [[David P. Robbins]], is the average distance between two points selected at random within a [[unit cube]]. Robbins' constant can be expressed as <ref>D. Robbins, ''Average distance between two points in a box'', [[American Mathematical Monthly]], 85 (1978) p. 278</ref>
 
:<math>
\frac{4+17\sqrt2-6\sqrt3-7\pi}{105} + \frac{\ln(1+\sqrt2)}{5} + \frac{2\ln(2+\sqrt3)}{5}.
</math>
 
Its numerical value is approximately <ref>[http://www.worldwideschool.org/library/books/sci/math/miscellaneousmathematicalconstants/chap80.html Miscellaneous Mathematical Constants by Simon Plouffe]</ref>
 
:<math>0.66170718226717623515583.</math>
 
==References==
<references/>
 
[[Category:Geometry]]
 
{{geometry-stub}}

Revision as of 11:46, 22 January 2013

In geometry, Robbins' constant, named after David P. Robbins, is the average distance between two points selected at random within a unit cube. Robbins' constant can be expressed as [1]

4+172637π105+ln(1+2)5+2ln(2+3)5.

Its numerical value is approximately [2]

0.66170718226717623515583.

References

  1. D. Robbins, Average distance between two points in a box, American Mathematical Monthly, 85 (1978) p. 278
  2. Miscellaneous Mathematical Constants by Simon Plouffe



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