## foliumA folium is a curve, first described by Johannes Kepler in 1609, that corresponds to the general equation (The Latin folium means "leap-shaped." Three types, known as the
simple folium, the bifolium (or double
folium), and the trifolium, correspond to the
cases when b = 4a, b = 0, and b = a,
respectively. The folium of Descartes is given by the Cartesian equation
x^{3} + y^{3} = 3axy and was
first discussed by René Descartes in 1638.
Although he found the correct shape of the curve in the positive quadrant,
he wrongly thought that this leaf shape was repeated in each quadrant like
the four petals of a flower. The problem to determine the tangent
to the curve was proposed to Gilles de Roberval who, having made the same
incorrect assumption, called the curve fleur de jasmin
after the four-petal jasmine bloom – a name that was later dropped.
The folium of Descartes has an asymptote x + y + a
= 0. ## Related category• PLANE CURVES | |||||

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