A020765 Decimal expansion of 1/sqrt(8).

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, 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, 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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

Multiplied by 10, this is the real and the imaginary part of sqrt(25i). - Alonso del Arte, Jan 11 2013

Radius of the midsphere (tangent to the edges) in a regular tetrahedron with unit edges. - Stanislav Sykora, Nov 20 2013

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

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

Examples

			1/sqrt(8) = 0.353553390593273762200422181052424519642417968844237018294...
		

References

• Frederick Mosteller, Fifty challenging problems of probability, Dover, New York, 1965. See problem 38, pp. 10 and 58-60.

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Michael L. Catalano-Johnson, Daniel Loeb and John Beebee, A cubical gift: Problem 10716, The American Mathematical Monthly, Vol. 108, No. 1 (Jan., 2001), pp. 81-82.
• Wikipedia, Tetrahedron.
• Wikipedia, Platonic solid.
• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. Midsphere radii in Platonic solids:

A020761 (octahedron),

A010503 (cube),

A019863 (icosahedron),

A239798 (dodecahedron).

Programs

Maple

Digits:=100; evalf(1/sqrt(8)); # Wesley Ivan Hurt, Mar 27 2014

Mathematica

RealDigits[N[1/Sqrt[8], 200]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *)
realDigitsRecip[Sqrt[8]] (* The realDigitsRecip program is at A021200 *) (* Harvey P. Dale, Apr 05 2025 *)

PARI

sqrt(1/8) \\ Charles R Greathouse IV, Apr 25 2016

Formula

A010503 divided by 2.

Equals A201488 minus 1/2. Equals 1/(A010487-4) minus 1/4. - Jon E. Schoenfield, Jan 09 2017

Equals Integral_{x=0..oo} x*exp(-x)*BesselJ(0,x) dx. - Kritsada Moomuang, Jun 03 2025