Turtlegons: generating simple polygons for sequences of angles

In this paper we present an algorithm to create simple polygons with a particular sequence of exterior angles, given only the sequence of angles. The algorithm has worst case time complexity <italic>&Ogr;</italic>(<italic>Dn</italic>), where <italic>n</italic> is the number of angles and <italic>D</italic> is dependent on the angles. As a bonus, the algorithm proves an interesting converse of the ancient theorem that the sum of the exterior angles of a simple polygon is 2π radians.