cp's OEIS Frontend

A295709 Decimal expansion of the arc length of the loop of the Folium of Descartes, a curve given by x^3 + y^3 = 3axy, with a = 1.

%I A295709 #12 Feb 16 2025 08:33:52
%S A295709 4,9,1,7,4,8,8,7,2,1,6,8,1,5,3,3,5,0,9,9,3,7,8,7,7,2,3,7,3,4,8,7,1,8,
%T A295709 7,0,9,0,1,3,8,0,3,7,8,8,4,3,3,0,5,5,3,0,9,4,6,1,0,2,8,1,5,4,5,1,5,1,
%U A295709 2,9,3,0,1,3,3,4,9,2,1,0,8,6,7,7,9,3,5
%N A295709 Decimal expansion of the arc length of the loop of the Folium of Descartes, a curve given by x^3 + y^3 = 3axy, with a = 1.
%C A295709 The arc length for general value of "a" is 4.917...*a.
%H A295709 G. C. Greubel, <a href="/A295709/b295709.txt">Table of n, a(n) for n = 1..10000</a>
%H A295709 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FoliumofDescartes.html">Folium of Descartes</a>.
%H A295709 Wikipedia, <a href="https://en.wikipedia.org/wiki/Folium_of_Descartes">Folium of Descartes</a>.
%e A295709 4.91748872168153350993...
%t A295709 RealDigits[3*N[Integrate[Sqrt[1+x^2(4-4x-4x^3+4x^4+x^6)]/(1+x^3)^2, {x,0,Infinity}], 100], 10][[1]]
%Y A295709 Cf. A096877, A118289, A138500, A143150, A143180.
%K A295709 nonn,cons
%O A295709 1,1
%A A295709 _Amiram Eldar_, Nov 26 2017