A395946 Decimal expansion of the height of a uniform 10-gonal antiprism with unit edges.

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

Offset

0,1

Links

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

Polytope Wiki, Decagonal antiprism.

Eric Weisstein's World of Mathematics, Antiprism.

Wikipedia, Antiprism.

Index entries for algebraic numbers, degree 8.

Formula

Equals sqrt(1 - (sec(Pi/20)^2)/4).

Equals sqrt((1 + 2*cos(Pi/10))/(2 + 2*cos(Pi/10))) = sqrt((1 + A188593)/(2 + A188593)).

Equals the largest real root of x^8 + 8*x^6 - 11*x^4 + 2*x^2 + 1.

Example

0.8623970038594584834470526849078637981964587831234...

Mathematica

First[RealDigits[Sqrt[1 - (Sec[Pi/20]^2)/4], 10, 100]]

Crossrefs

Cf. A395804 (volume), A395805 (surface area), A395806 (midradius), A395807 (circumradius).

Cf. A387607, A387610 (dihedral angles).

Cf. A188593.

Sequence in context: A033952 A365254 A021847 * A029684 A200626 A388646

Adjacent sequences: A395943 A395944 A395945 * A395947 A395948 A395950

Keyword

nonn,cons,easy

Author

Paolo Xausa, May 21 2026

Status

approved