Trifolium curve

The trifolium curve (also three-leafed clover curve, 3-petaled rose curve, and paquerette de mélibée) is a type of quartic plane curve.

The name comes from the Latin terms for 3-leaved, defining itself as a folium shape with 3 equally sized leaves.

It is described as By solving for y, the curve can be described by the following function: Due to the separate ± symbols, it is possible to solve for 4 different answers at a given point.

It has a polar equation of

r = − a cos ⁡ 3 θ

and a Cartesian equation of

The area of the trifolium shape is defined by the following equation:

[2] The trifolium was described by J. Lawrence as a form of Kepler's folium when

[3] A more present definition is when

The trifolium was described by Dana-Picard as

He defines the trifolium as having three leaves and having a triple point at the origin made up of 4 arcs.

The trifolium is a sextic curve meaning that any line through the origin will have it pass through the curve again and through its complex conjugate twice.

[4] The trifolium is a type of rose curve when

[5] Gaston Albert Gohierre de Longchamps was the first to study the trifolium, and it was given the name Torpille because of its resemblance to fish.

[6] The trifolium was later studied and given its name by Henry Cundy and Arthur Rollett.