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-- Lune and lens: correct definitions?
Posted:
Jan 20, 2008 10:25 AM
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The notion of a crescent or lune was discussed recently in
alt.math.recreational. Interested readers might look at my second posting
(Nov. 12) in the thread "crescent shapes"
<http://groups.google.com/group/alt.math.recreational/msg/377799ffe126a44c>
In particular, I expressed doubt about the definitions of lune and
lens given at MathWorld: <http://mathworld.wolfram.com/Lune.html> and
<http://mathworld.wolfram.com/Lens.html>. My guess is that the distinction
based on whether the radii are equal or not is solely due to Eric
Weisstein. OTOH, I am also slightly uneasy with my suggestion there that
the distinction between lune and lens should be one of convexity. After
all, an optical lens need not be convex in section and, when the Moon is
gibbous, the lighted part that we see from Earth is convex. Partially due
to my uncertainty, I have not yet written to Eric to try to get his entries
for lune and lens corrected. If anyone can shed light on what is "correct",
historically or otherwise, I would appreciate it!
My idea:
Given two circular disks, A and B, having a nonempty intersection and such
that neither is entirely contained in the other, three regions are formed.
(Think of a Venn diagram.) One of the regions, A /\ B, is convex; I suggest
that "lens" be used to name that kind of shape. Neither of the other two
regions, A-B and B-A, is convex; I suggest that "lune" be used to name that
kind of shape.
I also suggest that a circular disk itself should be considered a
degenerate case of both the lune and the lens.
Comments please!
David W. Cantrell
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