Online Encyclopedia

STROPHOID L0G0CYCLIC CURVE

Online Encyclopedia
Originally appearing in Volume V16, Page 919 of the 1911 Encyclopedia Britannica.
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STROPHOID L0G0CYCLIC CURVE or FOLIATE, a cubic curve generated by increasing or diminishing the radius vector of a variable point Q on a straight line AB by the distance QC of the point from the foot of the perpendicular drawn from the origin to the fixed line. The polar equation is rcosO =a(r t sing), the upper sign referring to the case when the vector is increased, the lower when it is diminished. Both branches are included in the Cartesian equation (x2+y2) (2a—x) =a2x, where a is the distance of the line from the origin. If we take for axes the fixed line and the perpendicular through the initial point, the equation takes the form y sl (a—x) =x Al (a+x). The curve resembles the folium of Descartes, and has a node between x = o, x = a, and two branches asymptotic to the line x=-- 2a.
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