On isoptic families of curves

Abstract

1. Imagine that a number of straight lines, coplanar and concurrent, are united so as to form as it were a rigid frame. Imagine that thiB frame is moved (continuously) in the plane in such a way that two selected lines always touch two cycloids traced in the plane. Then it will be found that Every line of the frame will move so as to envelope a cycloid. Isoptic (and orthoptic) are names used by Charles Taylor for loci on which two tangents of curves intersect at a constant angle. The cycloids form a family of curves in which each two members have the same isoptic locus; they may therefore be described as forming an isoptic family. Isoptic loci are of no great importance or interest. Our aim here is to investigate this and other instances in which curves of a uniform type are enveloped by the various lines of a rigid frame.