Buffon needle · Basel problem π²/6 · random coprime pairs · Gaussian integral √π · periodicity is everywhere · runs locally
π appears whenever periodicity, rotation, or the circle lurk · Basel: 1+1/4+1/9+…=π²/6 · Buffon: 2L/(D×P)=π · coprime: 6/π² · Gaussian: integral = √π · π is the constant of rotation