There are two curves known as the butterfly curve. The first is the sextic plane curve given by the implicit equation y^6=x^2-x^6 (1) (Cundy and Rollett 1989, p. 72; left figure). The total area of both wings is then given by A = 4int_0^1(x^2-x^6)^(1/6)dx (2) = (Gamma(1/6)Gamma(1/3))/(3sqrt(p…