[math-fun] The breadth and depth of radical-denesting ignorance

https://en.wikipedia.org/wiki/Tetracontagon <https://en.wikipedia.org/wiki/Tetracontagon#:~:text=In%20geometry%2C%20a%20tetracontagon%20or,interior%20angles%20is%206840%20degrees.> expresses cot(π/40) in radicals. Hilariously. They reexpress the triply nested radical Sqrt[1 + (1 + √5 + Sqrt[5 + 2 √5])^2] four different ways, all longer(!), and all triply nested. In fact, it denests to √√5 √(1 + √5) + (3 + √5)/√2. —rwg https://community.wolfram.com/groups/-/m/t/980264