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A374971 Decimal expansion of the apothem (inradius) of a regular heptagon with unit side length.

%I A374971 #20 Aug 29 2025 13:51:23
%S A374971 1,0,3,8,2,6,0,6,9,8,2,8,6,1,6,8,2,8,3,5,8,1,7,6,9,4,3,0,7,4,2,9,2,0,
%T A374971 1,6,5,3,5,2,8,6,0,1,0,3,3,1,2,9,8,4,2,6,2,0,4,1,7,0,8,6,8,8,4,3,1,5,
%U A374971 1,4,2,4,3,5,3,2,2,9,8,8,5,8,7,3,2,2,0,8,7,7
%N A374971 Decimal expansion of the apothem (inradius) of a regular heptagon with unit side length.
%H A374971 Paolo Xausa, <a href="/A374971/b374971.txt">Table of n, a(n) for n = 1..10000</a>
%H A374971 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RegularPolygon.html">Regular Polygon</a>.
%H A374971 Wikipedia, <a href="https://en.wikipedia.org/wiki/Apothem">Apothem</a>.
%H A374971 <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>.
%F A374971 Equals cot(Pi/7)/2 = A178818/2.
%F A374971 Equals 1/(2*tan(Pi/7)) = 1/(2*A343058).
%F A374971 Equals A374957*cos(Pi/7) = A374957*A073052.
%F A374971 Equals A374957 - A374972.
%F A374971 Largest of the 6 real-valued roots of 448*x^6 -560*x^4 +84*x^2 -1 =0. - _R. J. Mathar_, Aug 29 2025
%e A374971 1.0382606982861682835817694307429201653528601033...
%t A374971 First[RealDigits[Cot[Pi/7]/2, 10, 100]]
%o A374971 (PARI) .5/(Pi/7) \\ _Charles R Greathouse IV_, Feb 05 2025
%Y A374971 Cf. A374957 (circumradius), A374972 (sagitta), A178817 (area).
%Y A374971 Cf. apothem of other polygons with unit side length: A020769 (triangle), A020761 (square), A375067 (pentagon), A010527 (hexagon), A174968 (octagon), A375152 (9-gon), A179452 (10-gon), A375191 (11-gon), A375193 (12-gon).
%Y A374971 Cf. A178818, A073052, A343058.
%K A374971 nonn,cons,easy,changed
%O A374971 1,3
%A A374971 _Paolo Xausa_, Jul 26 2024