Back

@gsrdzl - I should indeed have said the perimeter of the *unit* circle is 2π. I'll fix that. Thanks. The rest, I think, is clear:

"Here's a formula for the lemniscate in polar coordinates:

r² = cos2θ

Just as the perimeter of [the unit] circle is 2π, the perimeter of this curve is 2ϖ where

ϖ ≈ 2.62205755..."

So, "this curve" is the curve I wrote down above.

Here's another way to put it: the perimeter of the curve

𝑥²+𝑦²=1

is 2π, and the perimeter of the following version of Bernoulli's lemniscate is 2ϖ:

(𝑥²+𝑦²)² = 𝑥²−𝑦²

This is the same as I wrote down in polar coordinates above.