The Theodorus Variation

Abstract

The Spiral of Theodorus, also known as the "root snail" from its connection with square roots, can be constructed by hand from triangles made with from paper with scissors, ruler, and protractor.  See the Video Abstract.  Once the triangles are made, two different but similar spirals can be made.  This paper proves some things about the second spiral; in particular that the open curve generated by the inner vertices monotonically approaches a circle, and that the vertices are ultimately equidistributed around that inner circle.