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FOLIUM

Online Encyclopedia
Originally appearing in Volume V10, Page 600 of the 1911 Encyclopedia Britannica.
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FOLIUM  , in

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mathematics, a
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curve invented and discussed by Rene
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Descartes . Its cartesian
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equation is x3+y3=3axy . The curve is symmetrical about the
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line x= y, and consists of two
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infinite branches asymptotic to the line x+y+a=o and a
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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
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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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