Two curves (boundaries of $2$-dimensional disks) of constant width in the plane, whose interiors intersect, must meet in an even or infinite number of omponents. Some new constant width curves are constructed. C0rollariesand partial converses suggest severalopen questions.
"Intersection properties of curves of constant width." Illinois J. Math. 17 (3) 411 - 420, September 1973. https://doi.org/10.1215/ijm/1256051608