| This kind of thing is quite common. The coin has a constant width. It
doesn't really have a constant radius, as it doesn't have a centre. You
couldn't make a wheel or tyre with this shape (as there is no 'centre'
to it, and it rotates about various points), but you could make a
roller with this cross section, and the roller would support something
at constant height above the ground. Of course the C of G of the roller
would go up and down as it rotates, so you wouldn't get a truly smooth
ride out of it.
Non-circular coins are usually made in this way, as they can be handled
by slot machines much more easily than it they did not have a constant
width.
The sides of the 50p piece are not arbitrary arcs - the centre of the
circle from which the arc is formed is at the opposite corner on the
coin. The 'diameter' of the coin is the radius of the arc.
If you have the coin resting on one edge and rotate it slightly the
opposite corner will remain at the same height above the surface. As
you continue to rotate the coin it will come to a point where it rests
on a corner. As it rotates further the highest point on the side
opposite this corner will always be the same height above ground.
This is one of the simplest forms of shapes with constant width. You
can make more complicated ones which have arcs of different radius and
are based on irregular polygons.
Andrew
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| The 20p coin is a similar, but slightly more interesting shape.
It also has 7 sides, but the sides dont meet at a point. Each 'point'
is somewhat more rounded. The coin is really much more like a 14 sided
figure, with each side being an arc. There are 2 radiuses of these
arcs, used alternately. A small one of about 4 mm, and a larger one of
about 17mm. The result is much rounder than the 50p piece.
The actual curve may be more complicated still, involving a
continuously variable 'radius' to the arc - its not easy to tell from
the sample in my pocket.
Actually the 50p might also be such a shape, with radii of about 0.5mm
and 30mm. This would remove the 'sharpness' of a corner, which would be
subject to rapid wear resulting in a variation of diameter which might
be difficult for slot machines to deal with.
Andrew
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