A375191 - OEIS

%I #15 Feb 05 2025 10:07:50

%S 1,7,0,2,8,4,3,6,1,9,4,4,4,6,2,5,0,0,4,5,2,4,0,6,5,1,7,3,3,2,4,4,2,4,

%T 4,1,5,9,7,8,6,4,9,9,9,3,0,6,0,9,1,4,0,7,0,4,8,8,9,6,7,0,3,0,5,3,5,9,

%U 7,6,5,3,4,5,1,3,2,9,1,0,4,8,1,1,1,4,5,7,0,2

%N Decimal expansion of the apothem (inradius) of a regular 11-gon with unit side length.

%H Paolo Xausa, <a href="/A375191/b375191.txt">Table of n, a(n) for n = 1..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>.

%H <a href="/index/Al#algebraic_10">Index entries for algebraic numbers, degree 10</a>.

%F Equals cot(Pi/11)/2.

%F Equals 1/(2*tan(Pi/11)).

%F Equals A375190*cos(Pi/11).

%F Equals A375190 - A375192.

%e 1.702843619444625004524065173324424415978649993...

%t First[RealDigits[Cot[Pi/11]/2, 10, 100]]

%o (PARI) .5/tan(Pi/11) \\ _Charles R Greathouse IV_, Feb 05 2025

%Y Cf. A375190 (circumradius), A375192 (sagitta), A256854 (area).

%Y 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), A375193 (12-gon).

%K nonn,cons,easy

%O 1,2

%A _Paolo Xausa_, Aug 04 2024