Polar Rose Curves
r = cos(k·θ) — Rhodonea curves by Luigi Guido Grandi (1723)
r = cos(3θ)
Numerator k₁
3
Denominator k₂
1
Number of petals
3
Animation speed
1.0
Stroke width
2
Color theme
Rose gradient
Rainbow
Gold
Ocean
Animate Drawing
Toggle Fill
Rhodonea
r = cos(k·θ):
• k odd: k petals
• k even: 2k petals
• k = p/q (fraction): gcd-derived petal count
Period = π if k odd, 2π if k even.
Area
of one petal = π/4 (for integer k).
Total area: kπ/4 (k odd), kπ/2 (k even).
Discovered by Luigi Guido Grandi who called them
rhodonea
(rose-shaped).