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Strophoid Logocyclic Curve

1911 Encyclopedia Britannica

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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 rcose =a(1 sine), 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 2 +y 2) ( 2a - x) = a 2 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 -1 (a - x) = 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=