Notes on approximate golden spirals with whirling squares

Abstract

We have extended some known results of the approximate golden spirals to generalized m-spirals built with whirling squares for any $m$ ratio ($m>1$). In particular, we have proved that circumscribed circles around squares intercept the pole. This implies that poles of any m-spirals lie on a circumscribed circle about the first square. We show here that these and other fascinating properties are not exclusive of golden rectangles. The classical golden constructors may not be alone.