In the diagram the point P' can move to different places along the
dotted line. Each position P' takes will fix a corresponding
position for P. If P' moves along a straight line what does P do ?
In the diagram the point P can move to different places around the
dotted circle. Each position P takes will fix a corresponding
position for P'. As P moves around on that circle what will P' do?
A cheap and simple toy with lots of mathematics. Can you interpret
the images that are produced? Can you predict the pattern that will
be produced using different wheels?
A pattern continues forever in both directions.
Imagine it's on a roll of paper and two strips are torn off, one
of which is turned upside-down and placed underneath the other.
It is not possible to shift the lower strip horizontally so that
it lines up and matches the upper strip.
This problem is about that kind of symmetry.
The pattern is a trace from a point on a rolling wheel.
Before starting, you may find it useful to explore How far does it move? .
Point 1 is on the circumference of the wheel and its trace looks
Forget the wheel for a moment and just concentrate on the trace
If this trace was turned upside-down you would certainly not be
able to line it up with itself.
Would "Trace Two" line up with itself upside-down?
Justify your answer, if you can.
The third trace is made where a horizontal line from Point 1
intersects with a vertical line through the centre of the wheel. It
looks like this :
Can "Trace Three" line up with itself upside-down?