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A375067 Decimal expansion of the apothem (inradius) of a regular pentagon with unit side length.

%I A375067 #18 Feb 05 2025 10:07:07
%S A375067 6,8,8,1,9,0,9,6,0,2,3,5,5,8,6,7,6,9,1,0,3,6,0,4,7,9,0,9,5,5,4,4,3,8,
%T A375067 3,9,7,6,2,9,4,9,6,6,8,0,0,4,0,7,9,3,3,1,6,8,2,8,3,7,8,8,2,8,0,9,5,4,
%U A375067 7,5,9,6,8,8,3,5,8,6,4,9,2,5,3,2,9,7,6,4,9,6
%N A375067 Decimal expansion of the apothem (inradius) of a regular pentagon with unit side length.
%H A375067 Paolo Xausa, <a href="/A375067/b375067.txt">Table of n, a(n) for n = 0..10000</a>
%H A375067 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RegularPolygon.html">Regular Polygon</a>.
%H A375067 Wikipedia, <a href="https://en.wikipedia.org/wiki/Apothem">Apothem</a>.
%H A375067 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%F A375067 Equals cot(Pi/5)/2 = A019952/2.
%F A375067 Equals 1/(2*tan(Pi/5)) = 1/(2*A019934).
%F A375067 Equals sqrt(1/4 + 1/(2*sqrt(5))).
%F A375067 Equals (1/2)*csc(Pi/5)*cos(Pi/5) = A300074*A019863.
%F A375067 Equals A300074 - A375068.
%F A375067 Equals A131595/30. - _Hugo Pfoertner_, Jul 30 2024
%e A375067 0.688190960235586769103604790955443839762949668...
%t A375067 First[RealDigits[Cot[Pi/5]/2, 10, 100]]
%o A375067 (PARI) .5/tan(Pi/5) \\ _Charles R Greathouse IV_, Feb 05 2025
%Y A375067 Cf. A300074 (circumradius), A375068 (sagitta), A102771 (area).
%Y A375067 Cf. apothem of other polygons with unit side length: A020769 (triangle), A020761 (square), A010527 (hexagon), A374971 (heptagon), A174968 (octagon), A375152 (9-gon), A179452 (10-gon), A375191 (11-gon), A375193 (12-gon).
%Y A375067 Cf. A019934, A019952, A019863, A131595.
%K A375067 nonn,cons,easy
%O A375067 0,1
%A A375067 _Paolo Xausa_, Jul 29 2024