|
%I #47 Aug 21 2023 10:27:19
%S 3,5,3,5,5,3,3,9,0,5,9,3,2,7,3,7,6,2,2,0,0,4,2,2,1,8,1,0,5,2,4,2,4,5,
%T 1,9,6,4,2,4,1,7,9,6,8,8,4,4,2,3,7,0,1,8,2,9,4,1,6,9,9,3,4,4,9,7,6,8,
%U 3,1,1,9,6,1,5,5,2,6,7,5,9,7,1,2,5,9,6,8,8,3,5,8,1,9,1,0,3,9,3
%N Decimal expansion of 1/sqrt(8).
%C Multiplied by 10, this is the real and the imaginary part of sqrt(25i). - _Alonso del Arte_, Jan 11 2013
%C Radius of the midsphere (tangent to the edges) in a regular tetrahedron with unit edges. - _Stanislav Sykora_, Nov 20 2013
%C The side of the largest cubical present that can be wrapped (with cutting) by a unit square of wrapping paper. See Problem 10716 link. - _Michel Marcus_, Jul 24 2018
%C The ratio between the thickness and diameter of a geometrically fair coin having an equal probability, 1/3, of landing on each of its two faces and on its side after being tossed in the air. The calculation is based on comparing the areal projections of the faces and sides of the coin on a circumscribing sphere. (Mosteller, 1965). See A020760 for a physical solution. - _Amiram Eldar_, Sep 01 2020
%D Frederick Mosteller, Fifty challenging problems of probability, Dover, New York, 1965. See problem 38, pp. 10 and 58-60.
%H Ivan Panchenko, <a href="/A020765/b020765.txt">Table of n, a(n) for n = 0..1000</a>
%H Michael L. Catalano-Johnson, Daniel Loeb and John Beebee, <a href="https://www.jstor.org/stable/2695694">A cubical gift: Problem 10716</a>, The American Mathematical Monthly, Vol. 108, No. 1 (Jan., 2001), pp. 81-82.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetrahedron">Tetrahedron</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Platonic solid">Platonic solid</a>.
%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F A010503 divided by 2.
%F Equals A201488 minus 1/2. Equals 1/(A010487-4) minus 1/4. - _Jon E. Schoenfield_, Jan 09 2017
%e 1/sqrt(8) = 0.353553390593273762200422181052424519642417968844237018294...
%p Digits:=100; evalf(1/sqrt(8)); # _Wesley Ivan Hurt_, Mar 27 2014
%t RealDigits[N[1/Sqrt[8], 200]] (* _Vladimir Joseph Stephan Orlovsky_, May 27 2010 *)
%o (PARI) sqrt(1/8) \\ _Charles R Greathouse IV_, Apr 25 2016
%Y Cf. Midsphere radii in Platonic solids:
%Y A020761 (octahedron),
%Y A010503 (cube),
%Y A019863 (icosahedron),
%Y A239798 (dodecahedron).
%K nonn,cons
%O 0,1
%A _N. J. A. Sloane_
|
