hippopede
Sign in to save500px|right|thumb|Hippopede (red) given as the pedal curve of an [[ellipse (black). The equation of this hippopede is: 4x^2 + y^2 = (x^2 + y^2)^2]]
~2 min read
Article
5 sectionsContents
- Special cases
- Definition as spiric sections
- See also
- References
- External links
500px|right|thumb|Hippopede (red) given as the pedal curve of an [[ellipse (black). The equation of this hippopede is: 4x^2 + y^2 = (x^2 + y^2)^2]]
In geometry, a hippopede () is a plane curve determined by an equation of the form (x^2+y^2)^2=cx^2+dy^2, where it is assumed that and since the remaining cases either reduce to a single point or can be put into the given form with a rotation. Hippopedes are bicircular, rational, algebraic curves of degree 4 and symmetric with respect to both the and axes.
Gallery (3)
Connections
geometry
Entity
Ancient Greek
Entity
rational number
Entity
ellipse
Entity
Cartesian coordinate system
Entity
torus
Entity
polar coordinate system
Entity
Eudoxus of Cnidus
Entity
Proclus
Entity
MathWorld
Entity
lemniscate of Bernoulli
Entity
degree of a polynomial
Entity
lemniscate
Entity
Eric W. Weisstein
Entity
algebraic curve
Entity
plane curve
Entity
fetters
Entity
pedal curve
Entity
list of curves
Entity
spiric section
Entity