ORIGINAL QUERY:
Date: Tuesday 20 May 2003
From:
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Norwegian University of Technology and Science (NTNU)
In taking over some lectures for our retired professor, I had to illuminate our first year students on the, to them, strange subject of of classical antiquity. The notion of architectural history is still so foreign to them that they don't know what to ask about. Or, maybe I overload them with information and slides - it's not that easy to squeeze it all into just three lectures.
Standing there, speaking about Roman theatres and amphi-theatres, I started wondering. I am embarrassed to admit that it was the first time it struck me that there must be a reason why the Colosseum and other amphitheatres are elliptical in plan, while their derivations -- the Iberian bull-fighting arenas, and the modern circus -- are circular, and the Roman theatres are semi-circular. I can't remember having seen any explanation in the literature. And -- are they true ellipses, or made up from circle arcs of different radii?
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Comments
(I don't know if this is the exact response, but I have always thought that the elliptical shape was due to the property of the ellipse that the sum of the distances from two privileged loci (the focuses) is constant.)
As for their overall shape, he says that a square or rectangular ampitheatre would result in combatants getting stuck in the corners. Circles/ovals make better use of the space. And finally, ovals/ellipses are better than circular ampitheatres since they have a dominant direction, giving a structure to the fight, whereas a circle would lead to an impression of confusion.
(You can find the answers to your questions in the periodical Disegnare, idee, immagini, no. 18-19, Editore Gangemi, Roma. In any case, Roman amphitheatres are all ovals with four or more centers.)
Have a look at the following web sites (some in German) :
lilt.ilstu.edu/drjclassics/lectures/theater/ancient_greek_theater.shtm
www.gottwein.de/Hell2000/theat02.php
www.oeaw.ac.at/kal/rezensionen/antra04.html
www.open.ac.uk/Arts/CC99/green.html#[3]
About the reason for elliptical, one should also question the probable need for a rectangularlike stage instaed of a circular one...
(Editor's note: Sylvie Duvernoy addressed the ellipse-oval issues in her Nexus 2002 presentation, "Architecture and Mathematics in Roman Amphitheaters" www.nexusjournal.com/.../, published in Nexus IV: Architecture and Mathematics.)
The references that I give are:
The important thing to remember is that conic sections in Roman times were all defined as cuts of cones; equation forms did not exist! So laying out an elliptical field is something that may not have even entered someone's mind.
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A property of truly elliptical amphitheaters is that sound emitted from one of its foci is concentrated onto the other focus. That is, although sound may travel in all directions from one of the foci, each "sound wave" is reflected off the wall at just the correct angle so as to arrive at the second focus.
APPLICATION:
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This means that a person can whisper while standing at one focus, and be heard clearly by someone else, standing at the second focus. (This feature is shown to visitors in several government buildings and museums.) People not located at either focus can not hear the whispers.
A LINK?
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Whether the Romans used this "secret channel" to communicate, I do not know. Could be.
ATTACHMENT:
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The (original) graphic,"Elliptical Arena," will illustrate more exactly, the ideas presented in my verbal response to why amphitheaters may be elliptical.
(|x|/a)^p + (|y|/b)^p = 1
with p a real number, typically between 2 and 3, but it might be larger. If p equals 2, we get an ellips, and if p tends to infinity, we get a rectangle. Superellipses (or Lamé ovals) are a "compromise" between ellipses and rectangles.
These super shapes often appear in nature since they perform better than circles (ellipses) and squares (rectangles) in matters like optimal fluid transport (e.g., a plane section of a bamboo stem). I 've been told that Piet Hein (mathematician? town architect?) designed a traffic square in Stockholm using a super-ellipse as model (I should look up again about the exponent p here), optimizing the traffic around the square.
I don't think that the ancient designers of the Colosseum were aware of the existence of super-ellipses, but maybe they had the right intuition?