A395807 - OEIS

%I #11 May 22 2026 08:08:37

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

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

%U 2,2,6,7,2,6,7,6,1,9,0,0,1,8,8,3,9,9,1,8,6,2

%N Decimal expansion of the circumradius of a uniform 10-gonal antiprism with unit edges.

%H Paolo Xausa, <a href="/A395807/b395807.txt">Table of n, a(n) for n = 1..10000</a>

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Decagonal_antiprism">Decagonal 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>.

%H <a href="/index/Al#algebraic_08">Index entries for algebraic numbers, degree 8</a>.

%F Equals sqrt(4 + csc(Pi/20)^2)/4.

%F Equals sqrt((3 - 2*cos(Pi/10))/(8 - 8*cos(Pi/10))) = sqrt((3 - A188593)/(8 - 8*A019881)).

%F Equals sqrt(1 + (2*sqrt(5) + sqrt(50 + 22*sqrt(5)))/8) = sqrt(1 + (A010476 + sqrt(50 + 22*A002163))/8).

%F Equals the largest root of 256*x^8 - 1024*x^6 + 976*x^4 - 344*x^2 + 41.

%e 1.6745047437425603067556345281467845735161384284804...

%t First[RealDigits[Sqrt[4 + Csc[Pi/20]^2]/4, 10, 100]]

%t (* Alternative: *)

%t First[RealDigits[PolyhedronData["DecagonalAntiprism", "Circumradius"], 10, 100]]

%Y Cf. A395804 (volume), A395805 (surface area), A395806 (midradius), A395946 (height).

%Y Cf. A387607, A387610 (dihedral angles).

%Y Cf. A002163, A010476, A019881, A188593.

%K nonn,cons,easy

%O 1,2

%A _Paolo Xausa_, May 21 2026