A375067 - OEIS

%I #16 Aug 07 2024 06:13:52

%S 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 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 7,5,9,6,8,8,3,5,8,6,4,9,2,5,3,2,9,7,6,4,9,6

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

%H Paolo Xausa, <a href="/A375067/b375067.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RegularPolygon.html">Regular Polygon</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Apothem">Apothem</a>.

%F Equals cot(Pi/5)/2 = A019952/2.

%F Equals 1/(2*tan(Pi/5)) = 1/(2*A019934).

%F Equals sqrt(1/4 + 1/(2*sqrt(5))).

%F Equals (1/2)*csc(Pi/5)*cos(Pi/5) = A300074*A019863.

%F Equals A300074 - A375068.

%F Equals A131595/30. - _Hugo Pfoertner_, Jul 30 2024

%e 0.688190960235586769103604790955443839762949668...

%t First[RealDigits[Cot[Pi/5]/2, 10, 100]]

%Y Cf. A300074 (circumradius), A375068 (sagitta), A102771 (area).

%Y 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 Cf. A019934, A019952, A019863, A131595.

%K nonn,cons,easy

%O 0,1

%A _Paolo Xausa_, Jul 29 2024