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

2,1

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

Links

Table of n, a(n) for n=2..76.

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

Formula

A195696 times 180 divided by Pi, see A072097.

Example

54.7356103172453... degrees.

Mathematica

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

Prog

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

Crossrefs

Cf. A195696 (in radians).

Sequence in context: A293380 A358663 A021870 * A177161 A154776 A188932

Adjacent sequences: A210971 A210972 A210973 * A210975 A210976 A210977

Keyword

nonn,cons

Author

Omar E. Pol, Jul 17 2012

Status

approved