16 Aug
2011
16 Aug
'11
1:22 p.m.
On Mon, Aug 15, 2011 at 10:04 PM, Bill Gosper <billgosper@gmail.com> wrote:
[...] Simplify[Developer`TrigToRadicals[Sin[\[Pi]/25]]] (after the death threat) produces this marvelously simple quintic surd
-((I (-(-1 - Sqrt[5] - I Sqrt[10 - 2 Sqrt[5]])^( 6/5) + (-1 - Sqrt[5] + I Sqrt[10 - 2 Sqrt[5]])^(6/5)))/ (8 2^(2/5)))
And ToRadicals doesn't.-( --rwg _______________________________________________
I guess this must be related to x=4*(sin(Pi/25))^2 being a root of the marvelously simple quintic x^5 - 10*x^4 + 35*x^3 - 50*x^2 + 25*x - 3 + t where t is the golden ratio.