Points off a rolling wheel make traces. What makes those traces
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 ?
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?
Two points, one inside a circle and the other outside, are
related in the following way :
A line starting at the centre of the circle and passing through
the first point ( P ) goes on to pass through the second point ( P'
For example if OP happened to be 2/3 of the radius then OP'
would be 3/2 of the radius.
In the diagram above, 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 that circle what will P' do ?
You might find the interactivity below helpful.
Holding down the mouse button leaves a trace of the points.