Yesterday, I had said:
The construction is very simple, requiring only arcs of circles of three different radii. Surely someone can find it...
Hmm. Maybe not. :-( Anyway, the figure at <http://img255.imageshack.us/img255/498/eggconstructzn0.gif> should make the construction abundantly clear. I suspect that that beautiful egg shape was used a good bit during the Middle Ages (perhaps in architecture?) but have no supporting evidence. Having been a maker of historical instruments, I analyzed the outlines of many lutes (and some other instruments) from the Renaissance. The outlines were always done, it seemed, by ruler-and-compass constructions. But the outlines of lutes in the later Renaissance involved somewhat more complicated constructions than did Arnault's lute. David
----- Original Message ----- From: "Fred lunnon" <fred.lunnon@gmail.com> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Thursday, February 15, 2007 18:39 Subject: Re: [math-fun] Re: sections of quadratic surfaces
On 2/15/07, David W. Cantrell <DWCantrell@sigmaxi.net> wrote:
Here's the simplest egg-shape known to me: http://img179.imageshack.us/img179/7915/eggxw7.gif.
IIRC, it is the shape used by Arnault of Zwolle (ca. 1450) in describing his lute. Its construction is so simple that I think, before giving it, I should ask if others can figure it out first.
David
Huh --- I fiddled (or maybe luted) around here trying to join a circular arc to a parabolic arc, matching both tangent and curvature --- eventually realising to my disgust that it cannot be done! WFL
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