A395168 Decimal expansion of the height of a uniform 9-gonal antiprism with unit edges.

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

Offset

0,1

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Polytope Wiki, Enneagonal antiprism.

Eric Weisstein's World of Mathematics, Antiprism.

Wikipedia, Antiprism.

Index entries for algebraic numbers, degree 6.

Formula

Equals sqrt(1 - (sec(Pi/18)^2)/4).

Equals sqrt((1 + 2*cos(Pi/9))/(2 + 2*cos(Pi/9))) = sqrt((1 + A332437)/(2 + A332437)).

Equals the largest real root of 3*x^6 - 3*x^2 + 1.

Example

0.861526087224617450394219811772086466962778416440...

Mathematica

First[RealDigits[Sqrt[1 - (Sec[Pi/18]^2)/4], 10, 100]]

Crossrefs

Cf. A395164 (volume), A395165 (surface area), A395166 (midradius), A395167 (circumradius).

Cf. A395169, A395170 (dihedral angles).

Cf. A332437.

Sequence in context: A153101 A281822 A130787 * A273774 A153493 A113212

Adjacent sequences: A395165 A395166 A395167 * A395169 A395170 A395171

Keyword

nonn,cons,easy

Author

Paolo Xausa, Apr 24 2026

Status

approved