# Folium

**FOLIUM**, in mathematics, a curve invented and discussed by René Descartes. Its cartesian equation is x + y = 3axy. The curve is
symmetrical about the line x = y, and consists of two infinite branches asymptotic to the line x + y + a = o and a loop in the first quadrant. It may be traced
by giving m various values in the equations x = 3am / (1 + m), y = 3am (1 + m), since by eliminating m between these relations the equation to the curve is
obtained. Hence it is *unicursal* (see Curve). The area of the loop, which equals the area between the curve and its asymptote, is 3a/2.

*Note - this article incorporates content from Encyclopaedia Britannica, Eleventh Edition, (1910-1911)*