Logocyclic Curve, Strophoid
LOGOCYCLIC CURVE, STROPHOID 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 rcosfl = 0(1 sin0), 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 (x*+y>) (20. x) = a?x, 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 ^(ax) = x V(a+*)- The curve resembles the folium of Descartes, and has a node between x = o, x = a, and two branches asymptotic to the line* =2<i.
Note - this article incorporates content from Encyclopaedia Britannica, Eleventh Edition, (1910-1911)