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limaçons
inner loop
a/b<1

limaçons
cardioid
a/b=1

limaçons
dimpled
1<a/b<2

limaçons
not dimpled
a/b≥2
limaçons graphs
r = a±bcosθ
r = a±bsinθ
a>0, b>0

rose curves
r = acos3θ

rose curves
r = asin5θ

rose curves
r = asin2θ

rose curves
r = acos4θ
rose curves equation
r = acosnθ
r = asinnθ
a>0
rose curves petals
odd n → n petals
even n → 2n petals

circle
r = acosθ

circle
r = asinθ

circle
r² = a²sin2θ

circle
r² = a²cos2θ

spiral
r=aθ
θ≥0

spiral
r=akθ
0≤0
0<a<1
k>0
circles and lemniscates
a>0
spirals
a>0