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%I #14 Nov 20 2024 23:44:24
%S 2,2,9,2,7,5,9,8,8,3,4,9,8,8,2,2,2,6,7,5,9,3,2,5,7,0,4,6,0,3,7,8,1,8,
%T 6,1,0,1,8,4,1,9,5,2,6,8,0,2,4,0,1,3,1,7,8,3,0,3,2,7,5,5,1,0,3,7,2,5,
%U 8,8,9,1,0,1,6,9,5,4,3,4,9,2,9,2,9,7,3,9,8,4
%N Decimal expansion of 24*arctan(sqrt(2)).
%C Dehn invariant of a regular octahedron and (small) rhombicuboctahedron with unit edge and (negated) of a cuboctahedron and truncated cube with unit edge.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DehnInvariant.html">Dehn Invariant</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Cuboctahedron.html">Cuboctahedron</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RegularOctahedron.html">Regular Octahedron</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmallRhombicuboctahedron.html">Small Rhombicuboctahedron</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TruncatedCube.html">Truncated Cube</a>.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals 24*A195696 = 2*A377277.
%e 22.9275988349882226759325704603781861018419526802...
%t First[RealDigits[24*ArcTan[Sqrt[2]], 10, 100]] (* or *)
%t First[RealDigits[PolyhedronData["Octahedron", "DehnInvariant"], 10, 100]]
%o (PARI) 24*atan(sqrt(2)) \\ _Charles R Greathouse IV_, Nov 20 2024
%Y Cf. A195696, A377277.
%K nonn,cons,easy
%O 2,1
%A _Paolo Xausa_, Oct 24 2024