MacTutor logo MacTutor

Curves

Figure Eight Curve

Main
Cartesian equation:
x4=a2(x2−y2)x^{4} = a^{2}(x^{2}-y^{2})
Polar equation:
r2=a2cos⁡(2θ)sec⁡4(θ)r^{2} = a^{2}\cos(2 \theta )\sec^{4}( \theta )

View the interactive version of this curve.

Description


Curve studied by Grégoire de Saint-Vincent in 1647 and Cramer in 1750.
In 1895 it was named by Aubry after the French mathematician Camille-Christophe Gerono (1799 - 1891) and so is also known as the Lemniscate of Gerono.

Other Web site:

Xah Lee
MathCurve

Associated Curves

Definitions of the Associated curves

  • Evolute
  • Involute 1
  • Involute 2
  • Inverse curve wrt origin
  • Inverse wrt another circle
  • Pedal curve wrt origin
  • Pedal wrt another point
  • Negative pedal curve wrt origin
  • Negative pedal wrt another point
  • Caustic wrt horizontal rays
  • Caustic curve wrt another point