The plan of London’s Roman amphitheatre has been reconstructed using the remains of the eastern end, found 20 years ago, and part of the north side detected in 1951. The design seems to have been a geometrical ellipse, which could have been laid out with the aid of only three wooden pegs and a loop of rope.

The discovery of the amphitheatre, partly below Guildhall Yard in the heart of the City, was one of the most exciting Roman finds to date. The curved walls at the eastern narrow end, together with an entrance passage, were uncovered. While it was clear that the structure was roughly oval, like other examples, the precise geometry employed was less apparent.

“How were the arena walls set out on the ground by the Roman engineers?”, Marek Ziebart of University College London and his colleagues ask in the Journal of Archaeological Science. “Did the geometrical pattern of these walls conform to an elliptical shape, to a set of interlocking ellipses, or to some other pattern?” Jean-Claude Golvin, a French scholar, suggested that, in general, arenas were oval, made up of multiple intersecting arcs, rather than pure ellipses, but the small difference between the results of the two methods has “made it difficult to be conclusive in this debate”, the authors say.

Dr Ziebart’s team tested the proposition that an ellipse was employed in the case of the London arena by applying a set of complex mathematical algorithms to create a theoretical model of an ideal ellipse that could be tested against on-the-ground data. Two clues were at their disposal: one came from part of a wall, now identified as the north wall of the arena, found by Ivor Nol Hume in 1951, which extended the potential plan beyond the recently excavated eastern end.

The other was the exposed amphitheatre at Sarmizegetusa in Romania, the new capital of the province of Dacia, conquered by the Emperor Trajan. The plan of this was used to test the model, and then the fragmentary plan of the London arena.

One surprising conclusion was that around the entry there was an “embrasure” where the arena walls were pulled back slightly, departing from a pure ellipse by a short distance; another was that “the fit of the single elliptical curve to the data outperforms the fit at Sarmizegetusa, a strong indication that the ellipse models successfully the original geometric form of the curve”, although not conclusive proof, since an eight-arc oval could also be fitted to the data.

There “is no overwhelming case to support one approach as the basis for all amphitheatre design, and each site should be considered on an individual basis”, they conclude. The western end of the London arena can, however, be predicted as lying directly under the west wing of the Guildhall complex, but unfortunately this modern building has deep basements, and “there is no chance that any of the amphitheatre survives beneath it”, according to Nick Bateman of the Museum of London Archaeology Service.

Plotting the depths of basements in buildings rebuilt after the Blitz will also allow the likely survival of the rest of the amphitheatre to be estimated, and appropriate measures taken if further development is planned. “Bits of the south side, including another entrance, appear to survive beneath the approach into Guildhall Yard from King Street and could well survive beneath the footings of St Lawrence Jewry,” said Mr Bateman.

Journal of Archaeological Science 34: 1505-14.