Suppose the region is convex with a piecewise smooth boundary parameterized by
with a counter clockwise orientation. If the centroid is given by
then the curve created by the motion of the centroid is given by
where
and
Can you prove the following result?
Suppose the region is convex with a piecewise smooth boundary parameterized by
with a counter clockwise orientation. If the centroid is given by
then the curve created by the motion of the centroid is given by
where
and