There was recently a post in the main PC-DMIS forum that discussed position formulae, namely 2D Cartesian and polar position. The post can be found at
https://www.pcdmisforum.com/forum/pc-dmis-enterprise-metrology-software/pc-dmis-for-cmms/489117-true-position-formulas
KIRBSTER269 proposed an interesting approximation of the actual value - You consider the two deviations from nominal, double the largest and add half the smallest. This works as an approximation to the actual value obtained using squares and square roots and it works pretty well until the deviations start to approach the same value. In the event that they are the same, the error in the approximation is about 33% of the largest deviation.
I was interested in the approximation scheme so I dug a little deeper and I found a "better" approximation. It is better in the sense that the largest error is only about 9% of the largest deviation. It is worse in the sense that it is not quite as simple, but it at least follows the same format. In my approximation, you multiply the largest deviation by 1.910 and add 0.828 times the smallest (instead of 2 and 0.5).
I wrote a short paper that goes through some of the mathematics if anybody is interested.
Position Approximations.pdf
