A210974 Decimal expansion of the angle (in degrees) between an edge and (the normal of) a face of the regular tetrahedron.

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

Offset: 2

Author

Omar E. Pol, Jul 17 2012

Keywords

• nonn
• cons

Comments

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

See more comments in A195696. - Stanislav Sykora, Nov 14 2013

Examples

			54.7356103172453... degrees.
		

Links

• C. O. Horgan and J. G. Murphy, On an angle with magical properties, Notices Amer. Math. Soc., 69:1 (2022), 22-25.
• Wikipedia, Tetrahedron
• Wikipedia, Magic angle

Crossrefs

Cf. A195696 (in radians).

Programs

Mathematica

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

PARI

acos(sqrt(1/3))*180/Pi \\ Charles R Greathouse IV, Nov 05 2017

Formula

A195696 times 180 divided by Pi, see A072097.