Nexus Network Journal: Architecture and Mathematics Online

Coming from a rather different angle I too wondered why amphitheatres were elliptical or oval? Earlier respondents have given good practical explanations of 'how' in terms of geometry and why- lack of awkward corners, the opportunity for linear progression. I also thought that the emperor, seated in the middle of one of the long sides would also get an optimum view in and oval- everything visible, nothing too far away. But a circle or a rectangle with hemicyclical ends could have achieved the same result and would have been easier to lay out, to cut stone for and to build. I wonder if the ellipse or oval form had any antecedents in the world of sacred architecture, thinking of the shows in the amphitheatre as originally funeral games? The design of the amphitheatre could have had a cosmological inspiration, the building representing a massive convocation of the community, seated internally in reverse of the normal spatial order of their ranks and assembled for a purpose which may originally have been (quasi) religious.

In the normal sense society would have been imagined with the emperor, magistrates and vestals at the top, then the 'knights' and then the mass of the free populace at the bottom of the (tripartite) social pyramid (with slaves below that again). To pursue this reverse analogy, it might have been imagined that the contests and shows were taking place in another region either above in the 'sky' or below in an infernal region. The idea that the amphitheatre, or rather its arena, was a portal to the infernal regions is reflected in the dress of the slaves who removed the bodies of fallen gladiators and the name of the gate from which they were removed.

Back to the initial question again, but slightly re-stated, is it possible that defining the arena in an oval or ellipse also symbolised its 'otherness' as well has having practical advantages for the organisation of the dreadful spectacles?

There have been quite a few responses already, so there is not call for much more comment. However, as the inquirer notes, not many of the responses address the problem of why amphitheatres should be the sahape they are (whether elliptical or oval). Golvin's work (cited in one reply) is the most extensive to tackle this theme, and I have also written on the subject in an article: "Designing amphitheatres," Romische Mitteilungen 100, 1993, 391-441.

The following is lifted (more or less) from pp. 391-2:

"The origin of the architectural form of the amphitheatre is somewhat obscure. ... No doubt it actually evolved by a process of adapting rectangular spaces, often in the context of civic fora, the setting for early gladiatorial combats. In a rectangular arena the action could get "trapped", as it were, in a corner; and every corner is a relatively long way from spectators at the opposing one. Cutting off or rounding off corners naturally leads towards the smoother shape of the ellipse/oval, which may be likened to a stretched circle, or a circle with a tendency towards linearity. This form has further advantages as a compromise between those suited both to spectacles (centric) and processions (linear).

It is generally assumed that this evolution took place in Campania ... However, influential prototypes may (also) have been the wooden structures erected for occasional gladiatorial shows in the Forum Romanum. ... At some stage the elliptical/oval arena layout took hold, a novelty which, quite apart from the functional justification mentioned above, may have been suggested by the splayed or oblique shape of the Forum. ... (a parallel sided arena would have implied uncomfortable tapering spaces on the outside.) Did someone reason as did Michealangelo, who in the 16th century chose an elliptical pavement for the similarly shaped Campidoglio piazza, precisely so as to avoid this sort of formal conflict? Otherwise the ellipse may have recommended itself for the simple reason that it represented a departure from established building types such as the theatre and stadium, besides making a decisive break with forms which ultimately descended from Greek usage.

In contrast to relatively static rectilinear or centralised groundplans, the formal qualities of the ellipse are quite literally dynamic. Successive rings change in their proportions,the perimeter being much rounder than the arena [Plates iii and iv]. The varying curvature and the lack of a single focus naturally generate a sense of movement, and, without a good view of a large portion of the structure,it can be quite difficult to percieve exactly where one stands in relation to the whole. All this was quite revolutionary for its time..."

In the book Earth from Above by Arthus Bertrand www.amazon.com/exec/obidos/ASIN/0810934957/thenexusnetworkj/ there is an aerial view of a horse like figure in Oxfordshire. If you compare the form of it to the African Animal trap relic also in the same book you can see the movement through space as in hunting or horse riding as a giver of forms. If you look at Sterlin's book of Architecture you can see Precidents as Tarxien Temple in Malta etc. Then if you look at the main purpose of the Collosium as Chariot Racing, the purpose of enlonging one axis becomes so clear. Besides the Centriato( if I spell it correctly) the unit that Romans used to calculate farm land is very linear. Which makes the most minimum turns for the cattle driven plow to turn more efficient. Even in 18th-19th century Edo (Tokyo) which had a million population, you can see a similar form for horse training(with bow & arrow shooting range perpendicular to it).

seems to me quite simple... at least for the oval... it is a true test of charioteers to drive straight for awile... and then have to make a half circle... and then keep doing it!!!

Regarding the setting out of amphitheaters, I'd say they are generally made of circular arcs to simplify the builder's work. While there are means of drawing ellipses on a drawing board or even on a builder's lofting floor, these techniques are difficult to transfer to a large scale building project. This is especially true in the case of an amphitheater, because as the "ellipse" expands with each additional row of seats its aspect ratio (or angle of projection) changes, and it become gradually more circular. Determining the foci, etc., of each row would become quite a chore. On the other hand, four circular arcs can be combined into quite a presentable pseudoellipse. (They seem to look best when they are tangent to a circumscribed rhombus, touching at at the center of each side) The task of creating equally spaced "ellipses" on this type of plan is reduced to increasing the radii of the component cirular arcs by equal increments.

Regarding the shape of the arena floor, it would appear that the ellipse has several descendants, including the circus ring, the square "ring" of boxing and wrestling, and the rectangular court. Perhaps one should say that the ellipse achieves a balance of the central and bilateral geometries. The former seems to be suited for staging direct combat between men and/or beasts, whereas the latter lends itself to territorial contests*. I think the Roman amphitheater was used for both forms of competition. Additionally, an elongated plan establishes seating closer to and farther from the center of action, suitable for accommodating a socially stratified audience.

*Of modern playing areas, one might wonder if the more rounded ones (ellipses in the case of Australian Rules Football, and radiused rectangles in the case of ice hockey) don't promote a higher proportion of physical combat relative to territorial objectives. And perhaps tennis, played in virtually square arenas, should be seen as an indirect form of combat rather than an intimate game of territory.