Determination of the parameters of the Guildhall amphitheatre ellipse in London

The paper presents an algorithm for computing the parameters of an ellipse that fits, in a least-squares sense, the surveyed remains of Roman amphitheatre arena walls. The algorithm is validated using ideal data and the near complete remains of the amphitheatre at Sarmizegetusa in Romania. The technique is then applied to the partial remains of the amphitheatre at the Guildhall in the City of London, in the UK, which cover only the Eastern end of the monument. The underlying mathematical model and method of solution is presented. The method was developed with a view to determining firstly whether or not an ellipse is a feasible model for the actual constructed curve geometry, and secondly, where the Western end of the Guildhall amphitheatre might be located. One single ellipse was found to fit the Guildhall remains, with measurement residuals at the level of 30 mm in the eastings and 26 mm in the northings. The ellipse had a semi-major axis of 28.345 m and a semi-minor axis of 22.775 m. The issues of alternative geometries and the practicalities of their use in construction are considered.