 From vector calculus in polar coordinates one gets the formula

Hence the slope of the spiral formula_19 is

In case of an "Archimedian spiral" (formula_21) the polar slope is formula_22

The "logarithmic spiral" is a special case, because of formula_23 "constant" !The curvature formula_24 of a curve with polar equation formula_13 is

For a spiral with formula_27 one gets

In case of formula_21 "(Archimedian spiral)"
formula_30.Only for formula_31 the spiral has an "inflection point".