Re: Mathematical name of curved triangle

[Bernard Cleyet <anngeorg@PACBELL.NET>]

This thread reminds me of the wheels on a dolly used to carry loads up (and down)
stairs. I took a photo' of one in use  in the Kremlin when the statues of Marx
and Lenin were still in the park overlooking the Moscow river ('90).  I haven't
seen one since.  The wheel is three wheels mounted on a fourth larger wheel that
is on the axle of the dolly.

bc



Larry Cartwright wrote:

> That's called the Reuleaux triangle, named after 19th century engineer
> Franz Reuleaux.  Applied physics connection:  It is the shape of the
> rotor in the famous Wankel engine, which I believe Honda is still
> tweaking in hopes of someday conquering the gremlins.
>
> BTW, mathguy Paul Kunkel has a couple of Reuleaux java applets at
> <http://www.nas.com/~kunkel/reuleaux/reuleaux.htm>.
>
> Best wishes,
>
> Larry
>
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Larry Cartwright   <exit60@cablespeed.com>
> Retired (June 2001) Physics Teacher
> Charlotte MI 48813 USA
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
> "Paul O. Johnson" wrote:
> > We are making a tabletop exhibit at The Science Place that I remember seeing
> > in the Exploratorium Snackbook. It consists of an axle and two wheels that
> > can be made to roll across the table. The explorer makes the wheels roll by
> > pushing either a long narrow board over the axle or a long wider board over
> > the two wheels.
> >
> > If we used normal circular wheels, either board would have a smooth ride
> > (not rise and fall) as the wheels roll. But the wheels are not circular;
> > they are curved equilateral triangles--each side is defined by scribing an
> > arc from the opposite vertex. The radius of these wheels thus varies with
> > rotation angle but the diameter remains constant. Therefore, the narrow
> > board riding the axle has a bumpy ride while the wide board riding the
> > wheels has a smooth ride.
> >
> > In writing the sign for this exhibit, I found that I do not know the
> > mathematical name for this curved triangle. I feel there must be such a
> > name, mathematicians name every conceivable geometric figure. Can anyone
> > help me with this?