Pi in base 12 problem

[kevolegend]

There is a hunch in the loony bin of the internet that mathematical constant Pi in base 12 makes for a rational answer. Converting decimal Pi to base 12 yields nothing rational. I suspect the problem might be it needs to be calculated in base 12 in the first place.

equation for Pi

4/sqrt((sqrt(5)+1)/2)



I need an Ad-Hoc calculator similar to the equation solver in Microsoft mathematics but that calculates in base 12.

If unsuccessful Base 9 would be my second guess.