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FOLIUM

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Originally appearing in Volume V10, Page 600 of the 1911 Encyclopedia Britannica.
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FOLIUM , in See also:

mathematics, a See also:curve invented and discussed by Rene See also:Descartes. Its cartesian See also:equation is x3+y3=3axy. The curve is symmetrical about the See also:line x= y, and consists of two See also:infinite branches asymptotic to the line x+y+a=o and a See also:loop in the first quadrant. It may be . traced by giving m various values in the equations x=3am/ (t+m3), y=3am2 (1+m3), since by eliminating m between these relations the equation to the curve is obtained. Hence it is unicursal (see CURVE). The See also:area of the loop, which equals the area between the curve and its asymptote, is 3a/2.

End of Article: FOLIUM

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