While reading a book by David Wells on curious and interesting geometry, I came across the following remarkable theorem named after Holditch.
In Figure 1 the point R divides a straight stick ST into lengths p and q, where p, q
0. We restrict the end points of the stick, S and T, to lie on a plane, simple, closed, convex contour, C
1, and ST slides around C1
. Assuming C
1 is such that ST can pass around C
1 once, the locus of R is another plane closed contour, C, inside C