%I #20 Feb 04 2025 15:22:58

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

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

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

%N Decimal expansion of the sagitta of a regular hexagon with unit side length.

%H Paolo Xausa, <a href="/A375069/b375069.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 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Sagitta.html">Sagitta</a>

%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.

%F Equals tan(Pi/12)/2 = A019913/2.

%F Equals 1 - sqrt(3)/2 = 1 - A010527.

%F Equals A152422^2 = (1 - A332133)^2. - _Hugo Pfoertner_, Jul 30 2024

%F Equals A334843-1/2. - _R. J. Mathar_, Aug 02 2024

%e 0.133974596215561353236276829247063816528597373...

%t First[RealDigits[Tan[Pi/12]/2, 10, 100]]

%o (PARI) tan(Pi/12)/2 \\ _Charles R Greathouse IV_, Feb 04 2025

%o (PARI) polrootsreal(4*x^2-8*x+1)[1] \\ _Charles R Greathouse IV_, Feb 04 2025

%Y Essentially the same as A334843.

%Y Cf. A010527 (apothem), A104956 (area).

%Y Cf. sagitta of other polygons with unit side length: A020769 (triangle), A174968 (square), A375068 (pentagon), A374972 (heptagon), A375070 (octagon), A375153 (9-gon), A375189 (10-gon), A375192 (11-gon), A375194 (12-gon).

%Y Cf. A010527, A019913, A152422, A332133.

%K nonn,cons,easy

%O 0,2

%A _Paolo Xausa_, Jul 30 2024