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,
: . I should mention that
: any Reuleaux Polygon
: will work too.


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 presents

        Kinematics of Machinery: Outlines of a Theory of Machines
        by Franz Reuleaux

He lived 1829-1905, according to, and was quite an expert
on kinematics and small machines (also

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


-- Mark A. Mandel
   Linguistic Data Consortium, University of Pennsylvania

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