For a plane curve (x(t),y(t)) its curvature
is given by
is called the radius of curvature. The point (xc,yc)
with coordinates given by
xc = x-
yc = y+
is called the center of curvature. The circle with center (xc,yc)
radius r is called the osculating circle or the circle
of curvature. The center of curvature (xc,yc)
lies on the normal of the curve at the point (x,y): the line
segment joining (x,y) with (xc,yc)
is perpendicular to the tangent at (x,y).
Construct the line segments joining points of the curve with the corresponding
center of curvature for each of the following: the nephroid, the astroid,
the deltoid and the cardioid.