# 1911 Encyclopædia Britannica/Logocyclic Curve

**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 r cos θ
= *a*(1 ± sinθ), 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})(2*a*−*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* √(*a* − *x*) = *x* √(*a* + *x*). The curve resembles the
folium of Descartes, and has a node between
*x* = 0, *x* = *a*, and two branches asymptotic to the
line *x* = 2*a*.