MRAD is based upon 1000th of a radian. There are 6283.185 milradians in a circle. MOA is based upon Pi; literally. That is why 1 MOA = 1.047 and not 1 inch.
I think you meant to say that MIL was based on Pi. MOA is based on a simple Trigonometry calculation using angles and triangle geometry. With a known adjacent side distance (distance to target) and a known angle (measured in 1/60th degree), you can calculate the length of the side opposite the angle using a trig Tangent function. Tangent being the relationship between the opposite side of the right triangle over the adjacent side. if my old Math serves me right the 100 yard effect of a 1 MOA shift would be (100)XTan (1/16)=target impact change (in yards). which yields .0290yds or .0872 ft or 1.04719 in. That is why one MOA is 1.04" at 100 yards. Its all triangles these days!! For most of us we just round this off to 1" at 100 yards.