#Limniscate

[mathart]

Equation of Time Cam turned 4 today!

[corpusmathematica]

Compare this with Bernoulli's Limniscate [in Mathematica], which Bernard Morin theorized should approximate the same curve:

(x^2 + y^2)^2 - a^2|x^2-y^2| == 0

r^2 == a^2 Cos[2 \[Theta]]

(From: "CRC Handbook of Mathematical Curves and Surfaces", David H. von Seggern, Boca Raton: 1990, CRC Press, Inc., ISBN 0-8493-0155-6)

r := Sqrt[ a^2 Cos[2 \[Theta]]] /. a -> 1

ParametricPlot[{Re[Z], Im[Z]} /. Z -> r Exp[I \[Theta]], {\[Theta], 0, 2 Pi}] Note that this, simpler representation, captures the abstract essence of the form, while discarding the eccentricities, in which the character of the figure may be encoded.