A240935 Decimal expansion of 3*sqrt(3)/(4*Pi).

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

Offset

0,1

Comments

A triangle of maximal area inside a circle is necessarily an inscribed equilateral triangle. This constant is the ratio of the triangle's area to the circle's area. In general, the ratio of an arbitrary triangle's area to the area of its unique Steiner ellipse, which has the least area of any circumscribed ellipse (an equilateral triangle's Steiner ellipse is a circle).

Also the probability that the distance between 2 randomly selected points within a circle will be larger than the radius. - Amiram Eldar, Mar 03 2019

Links

Table of n, a(n) for n=0..104.

B. F. Finkel, Problem 38, solved by O. W. Anthony, Henry Heaton, and G. B. M. Zerr, The American Mathematical Monthly, Vol. 3, No. 12 (1896), pp. 324-326.

I. Todhunter, A treatise on the Integral Calculus, London and Cambridge: MacMillan and Co., 1868, page 320, Example 7.

Wikipedia, Steiner ellipse

Index entries for transcendental numbers

Formula

3*sqrt(3)/(4*Pi) = 3*A002194/(4*A000796).

Example

0.4134966715663440371334948737347270810480...

Maple

Digits:=100: evalf(3*sqrt(3)/(4*Pi)); # Wesley Ivan Hurt, Aug 03 2014

Mathematica

Flatten[RealDigits[3 Sqrt[3]/(4 Pi), 10, 100, -1]] (* Wesley Ivan Hurt, Aug 03 2014 *)

Prog

(PARI)
default(realprecision, 120);
3*sqrt(3)/(4*Pi)

Crossrefs

Cf. A073010, A060294, A003881, A002194, A000796, A102519.

Sequence in context: A078147 A362331 A058303 * A090724 A343571 A308633

Adjacent sequences: A240932 A240933 A240934 * A240936 A240937 A240938

Keyword

nonn,cons

Author

Rick L. Shepherd, Aug 03 2014

Status

approved