A395394 - OEIS

%I #9 Jun 28 2026 15:50:57

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

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

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

%N Decimal expansion of the volume of the solid of revolution formed by rotating a unit half-width lemniscate of Bernoulli about the vertical axis.

%C The lemniscate of Bernoulli can be described by (x^2 + y^2)^2 = a^2*(x^2 - y^2) in Cartesian coordinates, or r^2 = a^2*cos(2*phi) in polar coordinates, where a is the half-width. Here we take a = 1.

%D Babu Ram, Engineering Mathematics, Pearson, 2009. See example 8.15.

%H Mandeep Beniwal, <a href="https://www.youtube.com/watch?v=MBXioI6FQhM">Volume of solid of revolution of lemniscate</a>, Smart study helper, YouTube video, 2021.

%H Amiram Eldar, <a href="/A395394/a395394.png">Illustration of the solid of revolution</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Lemniscate.html">Lemniscate</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SolidofRevolution.html">Solid of Revolution</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lemniscate_of_Bernoulli">Lemniscate of Bernoulli</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Solid_of_revolution">Solid of revolution</a>.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F Equals Pi^2/(4*sqrt(2)).

%F Equals 2 * A328895.

%F Equals Pi * A193887.

%e 1.7447160499097198835393902340423513224799665677370105...

%t RealDigits[Pi^2/(4*Sqrt[2]), 10, 120][[1]]

%o (PARI) Pi^2/(4*sqrt(2))

%Y Cf. A091476, A193887, A328895, A343392, A395392, A395393, A395395.

%K nonn,cons

%O 1,2

%A _Amiram Eldar_, Apr 21 2026