EJMT Abstract

We know that circular shapes we encounter in daily life may appear to be elliptical from some viewing points. It is reasonable to expect that an ellipse may appear to be circular from certain viewpoints. In this paper, we investigate the locus of viewpoints from which an ellipse appears circular. It will be shown that the locus of viewpoints is a hyperbola passing through the two foci of the ellipse. Conversely, the locus of viewpoints from which a hyperbola looks circular is an ellipse passing through the two foci of the hyperbola. Further, the locus of viewpoints from which a parabola looks circular is itself a parabola, passing through the focus of the original parabola. There is a simple duality between the object to be observed and the observer.