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The Garden of Archimedes
A Museum for Mathematics |
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Figures with constant thickness
One might think that circles are the only figures with this
property, that is the only curves with a constant thickness.
In fact, this is not the case: we can construct many other figures
that always touch two parallel curves. The simplest is a sort of
triangle with the sides formed by circular arches. sliding inside
a guide with parallel sides. From this, cutting near the angles
to make them sharp, we obtain the point of an (eccentric) drill
to make square holes. One can find drills to make
hexagonal holes on sale.
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