Quartic Plane Curve - Examples

Examples

Bean curve Bicuspid curve Bow curve Cruciform curve with parameters (b,a) being (1,1) in red; (2,2) in green; (3,3) in blue. Cruciform curve with parameters (b,a) being (1,1) in red; (2,1) in green; (3,1) in blue. Spiric section Three-leaved clover in cartesian coordinates Three-leaved clover in polar coordinates

Various combinations of coefficients in the above equation give rise to various important families of curves as listed below.

Bicorn curve Klein quartic
Bullet-nose curve Lemniscate of Bernoulli
Cartesian oval Lemniscate of Gerono
Cassini oval Lüroth quartic
Deltoid curve Spiric section
Hippopede Toric section
Kampyle of Eudoxus Trott curve

Read more about this topic:  Quartic Plane Curve

Famous quotes containing the word examples:

    “It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
    —G.C. (Georg Christoph)

    “No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
    —André Breton (1896–1966)

    “Histories are more full of examples of the fidelity of dogs than of friends.”
    —Alexander Pope (1688–1744)