Science Fair Project Encyclopedia Curvature is the amount by
which a geometric object deviates from being flat. The word flat
might have very different meanings depending on the objects
considered (for curves it is a straight line and for surfaces it
is a Euclidean plane). In this article we consider the most
basic examples: the curvature of a plane curve and the curvature
of a surface in Euclidean space. See the links below for further
reading. Curvature of plane curves For a plane curve C, the
curvature at a given point P has a magnitude equal to the
reciprocal of the radius of an osculating circle (a circle that
"kisses" or closely touches the curve at the given point), and
is a vector pointing in the direction of that circle's center.
The magnitude of curvature at points on physical curves can be
measured in diopters (also spelled dioptre); a diopter has the
dimension one per meter. The smaller the radius r of the
osculating circle, the larger the magnitude of the curvature
(1/r) will be; so that where a