## The Envelope of Chords

Assuming there are `N`

dots evenly distributed on a circle, named as `a_1`

, `a_2`

, `a_3`

, `\cdots`

, `a_{N}`

. We can draw chords between `a_{n}`

and `a_{kn}`

with `n\in [1,N]`

, `k=1,\ 2, \ 3, \cdots`

.

### Cardioid (k=2)

With `N=2M`

, `M`

is natural number, and `k=2`

, the envelope of these chords is a cardioid. Check this link for proof.

### Nephroid (k=3)

With `N=3M`

and `k=3`

, the envelope of these chords is a nephroid. Check this link for proof.

## 0 Comments