cp's OEIS Frontend

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

%I A240935 #25 May 18 2024 04:34:20
%S A240935 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,
%T A240935 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,
%U A240935 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
%N A240935 Decimal expansion of 3*sqrt(3)/(4*Pi).
%C A240935 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).
%C A240935 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
%H A240935 B. F. Finkel, <a href="https://www.jstor.org/stable/2970989">Problem 38</a>, solved by O. W. Anthony, Henry Heaton, and G. B. M. Zerr, The American Mathematical Monthly, Vol. 3, No. 12 (1896), pp. 324-326.
%H A240935 Paul J. Nahin, <a href="https://doi.org/10.1007/978-3-030-43788-6">Inside interesting integrals</a>, Undergrad. Lecture Notes in Physics, Springer (2020), p.52
%H A240935 I. Todhunter, <a href="https://archive.org/stream/treatiseontheint017146mbp#page/n321/mode/2up">A treatise on the Integral Calculus</a>, London and Cambridge: MacMillan and Co., 1868, page 320, Example 7.
%H A240935 Wikipedia, <a href="http://en.wikipedia.org/wiki/Steiner_ellipse">Steiner ellipse</a>
%H A240935 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A240935 3*sqrt(3)/(4*Pi) = 3*A002194/(4*A000796).
%F A240935 Equals A093604^2. - _Hugo Pfoertner_, May 18 2024
%e A240935 0.4134966715663440371334948737347270810480...
%p A240935 Digits:=100: evalf(3*sqrt(3)/(4*Pi)); # _Wesley Ivan Hurt_, Aug 03 2014
%t A240935 Flatten[RealDigits[3 Sqrt[3]/(4 Pi), 10, 100, -1]] (* _Wesley Ivan Hurt_, Aug 03 2014 *)
%o A240935 (PARI)
%o A240935 default(realprecision, 120);
%o A240935 3*sqrt(3)/(4*Pi)
%Y A240935 Cf. A073010, A060294, A003881, A002194, A000796, A102519, A086089.
%K A240935 nonn,cons
%O A240935 0,1
%A A240935 _Rick L. Shepherd_, Aug 03 2014