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Decimal expansion of the angle (in degrees) between an edge and (the normal of) a face of the regular tetrahedron.
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%I #25 Sep 12 2022 03:59:40

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

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

%U 8,7,3,2,1,9,0

%N Decimal expansion of the angle (in degrees) between an edge and (the normal of) a face of the regular tetrahedron.

%C Also known as "magic angle", the angle t such that 3*(cos t)^2 - 1 = 0.

%C See more comments in A195696. - _Stanislav Sykora_, Nov 14 2013

%H C. O. Horgan and J. G. Murphy, <a href="https://www.ams.org/journals/notices/202201/rnoti-p22.pdf">On an angle with magical properties</a>, Notices Amer. Math. Soc., 69:1 (2022), 22-25.

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

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Magic_angle">Magic angle</a>

%F A195696 times 180 divided by Pi, see A072097.

%e 54.7356103172453... degrees.

%t RealDigits[t/.FindRoot[3Cos[t Degree]^2-1==0,{t,54},WorkingPrecision-> 120]][[1]] (* _Harvey P. Dale_, May 02 2014 *)

%o (PARI) acos(sqrt(1/3))*180/Pi \\ _Charles R Greathouse IV_, Nov 05 2017

%Y Cf. A195696 (in radians).

%K nonn,cons

%O 2,1

%A _Omar E. Pol_, Jul 17 2012