I am hoping that you can suggest references on history, locations, and methods of layout of landscaped large ellipses? From Clark Kimberling, Professor of Mathematics, University of Evansville

I am hoping that you can suggest references on history, locations, and methods of layout of landscaped large ellipses. The main example seems to be the Ellipse in President’s Park, near the White House? So far, I’ve been unable to find any description of a method for laying out an ellipse (at least 100,000 sq ft).
The Ellipse in President’s Park was first laid out soon after 1851, and it was almost certainly redone in the 1880’s. Can you suggest where a description of method of layout for this particular ellipse can be found? (The National Park Service 2001 book, “The White House and President’s Park mentions the Ellipse on several pages but does not tell the method of layout.)
By “ellipse�, I mean an ellipse in the mathematical sense: the locus of a point P such that the sum of distances from P to two fixed points stays constant. (There are some landscaped “ovals� that are called “ellipses� but are not really elliptical.)
Thanks. Clark.
Forum (Diana Harris, Assistant Professor of Landscape Architecture and Architecture, University of Illinois):Dear Hugh, This is a bit out of my range, so I don’t know of any manuals or guides to this problem’s solution. But it was a compelling problem for architects during the 17th century in Italy. Gianlorenzo Bernini adored the elipse as a form. His piazza in front of St. Peter’s Cathedral is one of the most famous elliptical outdoor spaces in the world. There is a book about its design and the use of the elipse by Timothy Katao (I think that’s his name) which was published in the 1980s I believe—the title is something like _The Circle and the Square in the Oval at St. Peter’s_. Good luck, Dianne Harris
Forum (Bruce Rawles, Elysian Publishing): Hi Hugh & Clark: If my memory is correct, the simplest method is to make a loop of twine one of whose triangular sides is the (fixed) major axis, the other two dynamically changing to reach all the various points tracing the surface of the ellipse. Maybe there is invisible twine between the planets and the sun and the invisible other focus of each elliptical orbit. I think there should be lots of web sites with a graphic of this, if a search on google was done. This method would work well with two tall poles at the focii, and not much existing other landscaping! If twine (or a suitable substitute) is chosen with minimal elasticity, it should still work for large areas as you suggest. I hope this is helpful! 🙂 Cheers! Bruce
Clark Kimberling: Dear Hugh and Bruce, Thanks. Since writing to Hugh with the Ellipse (Washington DC) in mind, someone has mentioned that Bernini’s “ellipse” in St. Peter’s Square at the Vatican is another possibly-accurate ellipse for which I’d like to find a record of the method of layout. Bruce, it would be interesting to know if the method you described was what was used on the Washington Ellipse. The major axis, according to the National Park Service, measures 1057 feet, and the minor axis, 880 feet. These measurements yield a distance of 567 feet between the foci. So, the length of twine required would be 567 + 1057, or 1624 feet. If that’s the method that was actually used (in both Washington and Rome?), I hope that a record can be found confirming this. That seems like a remarkable way to lay out such large ellipses! The NPS also gives the area of the Ellipse as 696,960 sq ft. However, when area is computed from NPS’s measurements of axes (Area = pi times “a/2” times “b/2”), the result is 6% larger than 696,960. I’ve written to NPS about this and am awaiting an answer. (Perhaps the Ellipse isn’t one – but at this point I suspect it is, and that possibly the axes were measured with the walkway included, whereas the area may have been measured without including the walkway.) Conclusion — if the Washington and Rome ellipses were laid out by the twine method, that is interesting enough to warrant a search for historical confirmation. If either ellipse was laid out some other way, that’s also interesting, both historically, and I hope, “landscapingly”. Best regards, Clark
Richard Sneesby, University of Gloucester: Interesting. Any ideas about setting out spirals?
Forum (Hugh O’Connell):There are two good illustrations of setting out spirals – one can be found in “The Gentleman & Cabinet Makers Director” by Thomas Chippendale, the other illustrating the use of the logarithmic spiral is in “Landscape Design with Plants” Edited by Brian Clouston. Best Hugh
Forum (Hugh O’Connell):Dear Clark, This link http://www.xahlee.org/SpecialPlaneCurves_dir/Ellipse_dir/ellipse.htmlalso shows some ellipse layout methods. When it is drawn out on plan to scale, it should be possible to set out on the ground by using a theodolite. Best Hugh
Clark Kimberling: Dear Hugh and fellow correspondents, Thanks, Hugh, for assembling the messages into a thread. I’ve got some deeper-than-email inquiries out regarding the manner in which the Ellipse (President’s Square South, Washington, DC) was laid out. Eventually, I may write an article for The Mathematics Teacher (journal of the National Council of Teachers of Mathematics). Meanwhile, an interesting interlibrary loan book has arrived: Timothy K. Kitao, Circle and Oval in the Square of Saint Peter’s: Bernini’s Art of Planning., New York University Press, 1974. The author notes that the “Ellipseâ€? in St. Peter’s Square is composed of circular arcs and is not an ellipse. From page 34: “The ovato tondo was, in short, the standard oval in architectural practice—at least in Bernini’s Italy. The true ellipse was not unknown…but awkward to plot…â€? From page 71: “The ellipse is a conic section; the oval, composed of circular segments, is an approximation. (The terms ellipse and oval are interchangeable in common usage, but…) The true ellipse is awkward to plot and build. The oval suffices in architectural design unless a property peculiar to the ellipse is specifically sought. Kitao does not specifically name any post-Bernini true large landscaped or other architectural ellipses. His reference to awkwardness of plotting and building lends more interest, I think, to the possibility that the Ellipse in Washington is a “true ellipseâ€? and that the laying out or plotting must have been quite a feat. Within mathematics (as contrasted to art, gardening, landscape, and architecture), the properties and methods of generation, as nicely summarized on Xah Lee’s highly respected and often cited website – well – all geometry teachers know what a “true ellipseâ€? is. Best regards, Clark