Okay, last one for tonight… since I upset √2 with the previous formula, I thought I’d have a go using square roots, but didn’t find anything yet. Maybe another day.
But… I did find something using cube roots… in fact, the cube roots of 2, 3, 5, and something derived from 7 …. and the accuracy is the best yet, even if the formula is horribly complex. Beauty and the beast, I suppose.
I suppose we could write 10 as cube root of 1000 as well.
The comparison table now looks as follows:
|Method||Value||Difference from π/6||Abs difference|
|π – φ²||0.52355866483991||-0.00004011075839||0.00004011075839|