Cartesian equation: x
+y = 3axy or x = 3at/(1+t), y = 3at
/(1+t)
Click below to see one of the 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
The problem to determine the tangent to the curve was proposed to Roberval who also wrongly believed the curve had the form of a jasmine flower. His name of fleur de jasmin was later changed.
The curve is sometimes known as the noeud de ruban.
The folium has an asymptote x+y+a = 0.
The equation of the tangent at the point with t = p is
p(p - 2)x + (1 - 2p)y + 3ap = 0.
The curve passes through the origin at t = 0 and approaches the origin a second time as t goes to infinity.
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