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A375193 Decimal expansion of the apothem (inradius) of a regular 12-gon with unit side length.

%I A375193 #20 Feb 05 2025 10:00:53
%S A375193 1,8,6,6,0,2,5,4,0,3,7,8,4,4,3,8,6,4,6,7,6,3,7,2,3,1,7,0,7,5,2,9,3,6,
%T A375193 1,8,3,4,7,1,4,0,2,6,2,6,9,0,5,1,9,0,3,1,4,0,2,7,9,0,3,4,8,9,7,2,5,9,
%U A375193 6,6,5,0,8,4,5,4,4,0,0,0,1,8,5,4,0,5,7,3,0,9
%N A375193 Decimal expansion of the apothem (inradius) of a regular 12-gon with unit side length.
%C A375193 Apart from the first digit the same as A010527.
%H A375193 Paolo Xausa, <a href="/A375193/b375193.txt">Table of n, a(n) for n = 1..10000</a>
%H A375193 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RegularPolygon.html">Regular Polygon</a>.
%H A375193 Wikipedia, <a href="https://en.wikipedia.org/wiki/Apothem">Apothem</a>.
%H A375193 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.
%F A375193 Equals cot(Pi/12)/2 = (2 + sqrt(3))/2 = A019973/2.
%F A375193 Equals 1/(2*tan(Pi/12)) = 1/(2*A019913).
%F A375193 Equals A188887*cos(Pi/12) = A188887*A019884.
%F A375193 Equals A188887 - A375194.
%F A375193 Equals A332133^2 = 2 - A375069. - _Hugo Pfoertner_, Aug 04 2024
%e A375193 1.8660254037844386467637231707529361834714026269...
%t A375193 First[RealDigits[Cot[Pi/12]/2, 10, 100]]
%o A375193 (PARI) sqrt(3)/2 + 1 \\ _Charles R Greathouse IV_, Feb 05 2025
%Y A375193 Cf. A188887 (circumradius), A375194 (sagitta), A178809 (area).
%Y A375193 Cf. apothem of other polygons with unit side length: A020769 (triangle), A020761 (square), A375067 (pentagon), A010527 (hexagon), A374971 (heptagon), A174968 (octagon), A375152 (9-gon), A179452 (10-gon), A375191 (11-gon).
%Y A375193 Cf. A019884, A019913, A019973, A332133, A375069.
%K A375193 nonn,cons,easy
%O A375193 1,2
%A A375193 _Paolo Xausa_, Aug 04 2024