A395793 Decimal expansion of the principal moment of inertia of an oloid with unit mass density, formed by two unit circles, about the axis passing through the centers of the circles.

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

Offset

0,1

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} is equal to this constant, and I_{yy} = I_{zz} = A395794.

Links

Table of n, a(n) for n=0..104.

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 (32/45)*E(sqrt(3)/2) - (2/45)*K(sqrt(3)/2), where K(x) and E(x) are the complete elliptic integral of the first and second kind, respectively.

Example

0.765350257493142629396370284177037190890832292412461...

Mathematica

RealDigits[(32/45) * EllipticE[3/4] - (2/45)*EllipticK[3/4], 10, 120][[1]]

Prog

(PARI) (32/45) * ellE(sqrt(3)/2) - (2/45)*ellK(sqrt(3)/2)

Crossrefs

Cf. A215447 (volume), A395734 (mean width), A395794, A138500, A249283.

Sequence in context: A244921 A372951 A334380 * A101464 A072558 A022963

Adjacent sequences: A395790 A395791 A395792 * A395794 A395795 A395796

Keyword

nonn,cons

Author

Amiram Eldar, May 06 2026

Status

approved