Bonjour à tous : Two small formulas for the day. formula 7 Golden ratio in an infinite nested root (Phi)^(-1)=(exp(-Pi)*sqrt(5*exp(2*Pi)-4)-1)/2+exp(-Pi)/sqrt(1+sqrt((5*exp(2*Pi)-4)+(5*exp(2*Pi)-4)*sqrt((5*exp(2*Pi)-4)+(5*exp(2*Pi)-4)*sqrt((5*exp(2*Pi)-4)+(5*exp(2*Pi)-4)*sqrt((5*exp(2*Pi)-4)+(5*exp(2*Pi)-4)*sqrt((5*exp(2*Pi)-4)+(5*exp(2*Pi)-4)*sqrt((5*exp(2*Pi)-4)+...))))))); formula 8 a small algorithm for Pi ^ 4 u_(0)=-1; u_(n+1)=(1/2)*sqrt(2+2*u_(n)); a_(n)=2^(4*n+5)*(3-2*sqrt(2+2*u_(n))+u_(n)); n → infinity ; a_(n) → Pi^4;