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A375152 Decimal expansion of the apothem (inradius) of a regular 9-gon with unit side length.

%I A375152 #20 Aug 29 2025 13:52:36
%S A375152 1,3,7,3,7,3,8,7,0,9,7,2,7,3,1,1,1,3,9,3,8,0,8,3,2,0,1,3,2,4,8,8,3,6,
%T A375152 3,5,8,8,7,5,9,3,6,2,9,9,5,8,5,4,1,2,9,1,0,7,5,2,6,3,6,5,0,1,2,5,9,9,
%U A375152 4,9,1,2,6,9,4,0,7,9,6,5,9,2,1,7,0,3,0,2,1,2
%N A375152 Decimal expansion of the apothem (inradius) of a regular 9-gon with unit side length.
%H A375152 Paolo Xausa, <a href="/A375152/b375152.txt">Table of n, a(n) for n = 1..10000</a>
%H A375152 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RegularPolygon.html">Regular Polygon</a>.
%H A375152 Wikipedia, <a href="https://en.wikipedia.org/wiki/Apothem">Apothem</a>.
%H A375152 <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>.
%F A375152 Equals cot(Pi/9)/2 = A019968/2.
%F A375152 Equals 1/(2*tan(Pi/9)) = 1/(2*A019918).
%F A375152 Equals A375151*cos(Pi/9) = A375151*A019879.
%F A375152 Equals A375151 - A375153.
%F A375152 Largest of the 6 real-valued roots of 192*x^6 -432*x^4 +132*x^2 -1=0. - _R. J. Mathar_, Aug 29 2025
%e A375152 1.3737387097273111393808320132488363588759362995854...
%t A375152 First[RealDigits[Cot[Pi/9]/2, 10, 100]]
%o A375152 (PARI) .5/tan(Pi/9) \\ _Charles R Greathouse IV_, Feb 05 2025
%Y A375152 Cf. A375151 (circumradius), A375153 (sagitta), A256853 (area).
%Y A375152 Cf. apothem of other polygons with unit side length: A020769 (triangle), A020761 (square), A375067 (pentagon), A010527 (hexagon), A374971 (heptagon), A174968 (octagon), A179452 (10-gon), A375191 (11-gon), A375193 (12-gon).
%Y A375152 Cf. A019879, A019918, A019968.
%K A375152 nonn,cons,easy,changed
%O A375152 1,2
%A A375152 _Paolo Xausa_, Aug 01 2024