Constructing Poncelet Polygons

Source abstract

Abstract We study the geometric structure of Poncelet n -gons from a projective point of view. In particular we present explicit constructions of Poncelet n -gons for $$n = 7,8$$ n = 7 , 8 and derive corresponding algebraic characterisations in terms of bracket polynomials, as well as describing a construction to produce a Poncelet 2 n -gon from a starting Poncelet n -gon.