I was curious if I could form a hexagon like the one on Saturn using polar coordinates. Here’s a picture of Saturn’s hexagon from Wikipedia^{[1]}:

My red blob logo^{[2]} uses polar coordinates to form a nice shape. I used the equation `r = 5 + cos(5 * angle)`

. I’m going to use the same pattern here, `r = base + cos(6 * angle)`

. When `base`

is small, it forms a star shape; when it’s large, it forms a circle. In the middle, it forms a **rounded hexagon**! I’ve highlighted `r = 30 + cos(6 * angle)`

:

**A sine wave in polar coordinates can form this shape**. There are sine-like waves in Earth’s atmosphere around the poles; they’re called Rossby waves^{[3]}.