My favorite isn't an approximation, it's Euler's formula for calculating pi: pi/4 = arctan(1/2) + arctan(1/3). Use the Taylor series expansion for arctan(x): su

My favorite isn't an approximation, it's Euler's formula for calculating pi: pi/4 = arctan(1/2) + arctan(1/3). Use the Taylor series expansion for arctan(x): sum for n=0 to infinity of ((-1)^n)(x^(2n+1))/(2n+1). ie x^1/1 + x^3/3 - x^5/5 + x^7/7 - ... Not hard to memorize either part. Slow to calculate, but the accuracy is only limited by how far you expand the Taylor series.