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plane polar coordinates

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1: 1.5 Calculus of Two or More Variables
Polar Coordinates
2: 36.7 Zeros
There are also three sets of zero lines in the plane z = 0 related by 2 π / 3 rotation; these are zeros of (36.2.20), whose asymptotic form in polar coordinates ( x = r cos θ , y = r sin θ ) is given by …
3: 22.18 Mathematical Applications
§22.18(i) Lengths and Parametrization of Plane Curves
In polar coordinates, x = r cos ϕ , y = r sin ϕ , the lemniscate is given by r 2 = cos ( 2 ϕ ) , 0 ϕ 2 π . … With k [ 0 , 1 ] the mapping z w = sn ( z , k ) gives a conformal map of the closed rectangle [ - K , K ] × [ 0 , K ] onto the half-plane w 0 , with 0 , ± K , ± K + i K , i K mapping to 0 , ± 1 , ± k - 2 , respectively. …