No answer? I really don't know how to go about proving if this is true, (or finding a counter-example.) My experience in college has mainly been with algebra. Is there as way to abstract this problem to one in algebra? I've done some very basic work in algebraic geometry, but I wouldn't know how to express the equiangular shapes as subsets of . I don't think they can be expressed as algebraic sets (like the ellipses can be)...? (And how would I even know if my two algebraic sets represent two similar ellipses?)