FOLIUM  , in See also:

• MATHEMATICS (Gr. /saBnµar1Kil, Sc. vOcvn or E7rlQTt'µn; from p iN.La, "learning" or "science ")

mathematics, a See also:

• CURVE (Lat. curvus, bent)

curve invented and discussed by Rene See also:

• DESCARTES, RENE (1596-1650)

Descartes . Its cartesian See also:

• EQUATION (from Lat. aequatio, aequare, to equalize)

equation is x3+y3=3axy . The curve is symmetrical about the See also:

• LINE

line x= y, and consists of two See also:

• INFINITE (from Lat. in, not, finis, end or limit; cf. findere, to deave)

infinite branches asymptotic to the line x+y+a=o and a See also:

• LOOP

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

area of the loop, which equals the area between the curve and its asymptote, is 3a/2 .