A394538 - OEIS

%I #13 May 22 2026 08:00:29

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

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

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

%N Decimal expansion of the height of a uniform octagonal antiprism with unit edges.

%H Paolo Xausa, <a href="/A394538/b394538.txt">Table of n, a(n) for n = 0..10000</a>

%H David I. McCooey, <a href="https://dmccooey.com/polyhedra/OctagonalAntiprism.html">Octagonal Antiprism</a>.

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Octagonal_antiprism">Octagonal antiprism</a>.

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

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

%F Equals sqrt(1 - (sec(Pi/16)^2)/4) = sqrt((3 - A393638)/4).

%F Equals sqrt((1 + 2*cos(Pi/8))/(2 + 2*cos(Pi/8))) = sqrt((1 + A179260)/(2 + A179260)).

%F Equals the largest real root of 2*x^8 + 8*x^6 - 16*x^4 + 8*x^2 - 1.

%e 0.8602955698629715664423007760041056923313852176566964...

%t First[RealDigits[Sqrt[1 - (Sec[Pi/16]^2)/4], 10, 100]]

%o (PARI) polrootsreal(2*x^8 + 8*x^6 - 16*x^4 + 8*x^2 - 1)[6] \\ _Charles R Greathouse IV_, May 13 2026

%Y Cf. A394534 (volume), A394535 (surface area), A394536 (midradius), A394537 (circumradius).

%Y Cf. A387320, A387323 (dihedral angles).

%Y Cf. A179260, A393638.

%K nonn,cons,easy

%O 0,1

%A _Paolo Xausa_, Apr 08 2026