[math-fun] Is 17 trying to tell us something?

2 Dec 2020

      {Cos[π/17]==1/16 (1-√17+√(34-2 √17)+2 √(17+3 √17+√(170+38 √17))),

 Sin[π/34]==1/16 (-1+√17+√(34-2 √17)-2 √(17+3 √17-√(170+38 √17)))}

or even

2 √(17 + 3 √17 - √(170 + 38 √17)) == √( 2 (3 + √17) (2 √17 - √(2 (17 -
√17))))

et al.  https://mathworld.wolfram.com/TrigonometryAnglesPi17.html includes
a messier version of Cos[π/17].

(People keep forgetting that Sin[π/5] is messier than Sin[π/10].)  —rwg

[math-fun] Is 17 trying to tell us something?

Bill Gosper