TobyBartels on Nostr: : The circle is \( r = \cos \theta \), not \( r^2 = \cos \theta \). This suggests ...

: The circle is \( r = \cos \theta \), not \( r^2 = \cos \theta \). This suggests that the generalization is \( r^n = \cos(n\theta) \), but I haven't checked if this is the same as Leo's generalization. (Which for those who haven't clicked through is based on \( \arcsin x = \int_0 (1 - x^2)^{-1/2} \) and \( \operatorname{arcsl} x = \int_0 (1 - x^4)^{-1/2} \), so \( \int_0 (1-x^{2n})^{-1/2} \) in general.)