A395794 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.

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, 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, 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

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..105.

Robert Ferréol, Oloid, MathCurve.

Sander G. Huisman, The moment of inertia tensor of an oloid, arXiv:2603.15145 [math.MG], 2026.

Eric Weisstein's World of Mathematics, Complete Elliptic Integral of the First Kind.

Eric Weisstein's World of Mathematics, Complete Elliptic Integral of the Second Kind.

Eric Weisstein's World of Mathematics, Oloid.

Wikipedia, Moment of inertia.

Wikipedia, Oloid.

Index entries for sequences related to moment of inertia.

Formula

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.

Example

1.455512873469200344986345630652765039041821749434705...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A222587 A222378 A360853 * A094848 A308740 A349990

Adjacent sequences: A395791 A395792 A395793 * A395795 A395796 A395797

Keyword

nonn,cons

Author

Amiram Eldar, May 06 2026

Status

approved