Polsby–Popper test
The Polsby–Popper test is a mathematical compactness measure of a shape developed to quantify the degree of gerrymandering of political districts. The method was developed by lawyers Daniel D. Polsby and Robert Popper, though it had earlier been introduced in the field of paleontology by E.P. Cox. The formula for calculating a district's Polsby–Popper score is formula_1, where formula_2 is the district, formula_3 is the perimeter of the district, and formula_4 is the area of the district. A district's Polsby–Popper score will always fall within the interval of formula_5, with a score  of formula_6 indicating complete lack of compactness and a score of formula_7 indicating maximal compactness. Compared to other measures that use dispersion to measure gerrymandering, the Polsby–Popper test is very sensitive to both physical geography (for instance, convoluted coastal borders) and map resolution. The method was chosen by Arizona's redistricting commission in 2000.