Polar Roses

Petals from cosines

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Roses r = cos kθ: k petals for odd k, 2k petals for even k.
• Negative r plots on the opposite side; odd roses retrace themselves.
• Petal counts of 2, 6, 10, … are impossible with whole k.

Steps

1. Petals
2. Eight petals
3. Sine roses
4. Between the petals
5. Tracing twice
6. An impossible rose