Reuleaux polygon
Mark A. Mandel
mamandel at UNAGI.CIS.UPENN.EDU
Wed Apr 30 17:59:37 UTC 2003
On a University of Pennsylvania local newsgroup I mentioned the
"Rouleaux triangle". That elicited the following response (prefixed with
':'), and my appended followup:
>>>
: Yes! Though I believed it's spelled Reuleaux. There is a nice page about
: them here,
: http://mathworld.wolfram.com/ReuleauxTriangle.html . I should mention that
: any Reuleaux Polygon http://mathworld.wolfram.com/ReuleauxPolygon.html
: will work too.
Fascinating!
I first recall hearing of these in a story by Poul Anderson, who I think
used the "ou" spelling. I always thought it was "Rouleaux", and I ran 4
Google searches to start checking (after failing to find either spelling
in OED Online):
triangle polygon
Reuleaux 606 214
Rouleaux 1330 30
I found the opposite skews for the two nouns interesting. And some of
the hits led to the evident origin of the term. As Amazon.com presents
it:
Kinematics of Machinery: Outlines of a Theory of Machines
by Franz Reuleaux
He lived 1829-1905, according to
http://www.seiflow.co.uk/Franz%20Reuleaux.htm, and was quite an expert
on kinematics and small machines (also
http://www.mae.cornell.edu/Reuleauxcoll/Sp.feat5.html).
I gather that he developed the theory of the polygons that are known by
his name. Each edge is an arc of a circle, and as the polygon rolls
along a flat surface, its upper limb maintains a constant distance from
the surface, just as with a circle, so that a Reuleaux-polygonal
cylinder can be used as a roller. And, I would guess, the spelling
"Rouleaux" arose from association with the verb "roll" ("rouler" in
French).
<<<
-- Mark A. Mandel
Linguistic Data Consortium, University of Pennsylvania
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