A Family of Constructions of Approximate Ellipses

Ellipses have long played a part in architecture. For instance, more than 4000 years ago in the Middle Minoan period a large oval house was built in Crete [1], while up to the present day in many parts of Africa, India, and Europe oval huts and houses were commonplace [2]. The Romans embraced the ellipse, and employed it on a vast scale in their ampitheatres [3]. In the Baroque period of the Renaissance the ellipse was once again applied, mostly in the design of churches [4]. An elliptical theme recurs in Georgian architecture [5], appearing at all scales from decorative ceiling plaster details, to the plan for drawing rooms, to entire terraces of houses. Right through to modern times the ellipse has remained a popular form in architecture, and some more recent examples from the last five years are the Church of San Giovanni Battista, by Mario Botta [6], the Ruskin Library by Richard MacCormac [7], and Walsall bus station by Allford, Hall, Monaghan, and Morris [8]. Thus the ellipse remains one of the standard shape primitives (along with the circle, square, triangle, etc.) that figure prominently in ancient and modern design (architectural, engineering, graphical, etc.), and is therefore worthy of particular attention. Although the ellipse provides more dynamic possibilities than the relatively static forms of straight lines and circles it also introduces complications. In particular, it is more difficult to lay out, and its continuously varying curvature means that for precise building construction a large range of brick shapes should be used [9]. Another consideration is that its perimeter is difficult to calculate; this is important not only for the estimation of