A395794 - OEIS

%I #12 May 07 2026 00:51:10

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

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

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

%N Decimal expansion of the moment of inertia of an oloid with unit mass density, formed by two unit circles, about an axis through the center of mass perpendicular to the line connecting the centers of the circles.

%C By choosing axes such that the origin is the midpoint of the line segment connecting the centers of the two circles and the x-axis passes through these centers, the moment of inertia tensor is diagonal. In this coordinate system, I_{xx} = A395793, and I_{yy} = I_{zz} both equal to this constant.

%H Robert Ferréol, <a href="https://www.mathcurve.com/surfaces.gb/orthobicycle/orthobicycle.shtml">Oloid</a>, MathCurve.

%H Sander G. Huisman, <a href="https://arxiv.org/abs/2603.15145">The moment of inertia tensor of an oloid</a>, arXiv:2603.15145 [math.MG], 2026.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteEllipticIntegraloftheFirstKind.html">Complete Elliptic Integral of the First Kind</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteEllipticIntegraloftheSecondKind.html">Complete Elliptic Integral of the Second Kind</a>.

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Moment_of_inertia">Moment of inertia</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Oloid">Oloid</a>.

%H <a href="/index/Mo#moment_of_inertia">Index entries for sequences related to moment of inertia</a>.

%F Equals (71/45)*E(sqrt(3)/2) - (19/90)*K(sqrt(3)/2), where K(x) and E(x) are the complete elliptic integral of the first and second kind, respectively.

%e 1.455512873469200344986345630652765039041821749434705...

%t RealDigits[(71/45) * EllipticE[3/4] - (19/90)*EllipticK[3/4], 10, 120][[1]]

%o (PARI) (71/45) * ellE(sqrt(3)/2) - (19/90)*ellK(sqrt(3)/2)

%Y Cf. A215447 (volume), A395734 (mean width), A395793, A138500, A249283.

%K nonn,cons

%O 1,2

%A _Amiram Eldar_, May 06 2026