Some formulas... Formula 1 %pi=2^(n)*sqrt(15-sqrt(15)*sqrt(28*2^(-10)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))))^5-13))/sqrt(70); Approx : n=9 2^(9)*sqrt(15-sqrt(15)*sqrt(28*2^(-10)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2))))))))^5-13))/sqrt(70); Formula 2 %pi=2^(n)*sqrt(6-sqrt(6)*sqrt(11*2^(-8)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))))^4-5))/sqrt(22); Approx : n=9 2^(9)*sqrt(6-sqrt(6)*sqrt(11*2^(-8)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2))))))))^4-5))/sqrt(22); Formula 3 %pi=2^(n)*sqrt(3-sqrt(16*2^(-6)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))))^3-7))/2^(3/2); Approx : n=9 2^(9)*sqrt(3-sqrt(16*2^(-6)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2))))))))^3-7))/2^(3/2); Formula 4 %pi=2^(n)*sqrt(3-sqrt(3)*sqrt(5*2^(-4)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))))^2-2))/sqrt(5); Approx : n=9 2^(9)*sqrt(3-sqrt(3)*sqrt(5*2^(-4)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2))))))))^2-2))/sqrt(5); Formula 5 %pi=2^(n)*sqrt(30-sqrt(30)*sqrt(59*2^(-40)*((2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2)))))))))))^20-29))/sqrt(590); Approx : n=11 2^(11)*sqrt(30-sqrt(30)*sqrt(59*2^(-40)*((2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2)))))))))))^20-29))/sqrt(590); Formula 6 %pi=2^(n)*sqrt(15-sqrt(3)*sqrt(149*2^(-100)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))))^50-74))/sqrt(745); Approx : n=11 2^11*sqrt(15-sqrt(3)*sqrt(149*2^(-100)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2))))))))))^50-74))/sqrt(745); Formula 7 %pi=2^(n)*sqrt(150-sqrt(30)*sqrt(1499*2^(-1000)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))))^500-749))/(5*sqrt(2998)); Approx : n=11 2^(11)*sqrt(150-sqrt(30)*sqrt(1499*2^(-1000)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2))))))))))^500-749))/(5*sqrt(2998)); Formula 8 2^(n)*sqrt(sqrt(15)*sqrt(121-61*2^(-80)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))^40)-30*2^(-40)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))^20)/(11*sqrt(10)*2^(-20)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))^10); Approx : n=9 2^9*sqrt(sqrt(15)*sqrt(121-61*2^(-80)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2))))))))^40)-30*2^(-40)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2))))))))^20)/(11*sqrt(10)*2^(-20)*(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2))))))))^10); Formula 9 %pi=2^(n)*(4*sqrt(10)*sqrt(sqrt(3)*sqrt(317-314*2^(-1/80)*sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))))^(1/80))-3))/sqrt(157); Formula 10 %pi=2^(n)*(4*sqrt(10)*sqrt(sqrt(3)*sqrt(326*2^(-1/80)*sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))))^(1/80)-323*2^(-1/40)*sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))))^(1/40))-3*2^(-1/80)*sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))))^(1/80)))/(sqrt(163)*2^(-1/160)*sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))))^(1/160)); Formula 11 %pi=2^(n)*(2*sqrt(5)*sqrt(sqrt(42*2^(-1/30)*sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))))^(1/30)-41*2^(-1/15)*sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))))^(1/15))-2^(-1/30)*sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))))^(1/30)))/(sqrt(7)*2^(-1/60)*sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt(2+cdots+sqrt(2+sqrt(2))))))))))^(1/60));