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?
Dr. Paul O. Johnson
Exhibit Developer
The Science Place
Dallas, Texas
pjohnson@scienceplace.org