### Roaming Rhombus

We have four rods of equal lengths hinged at their endpoints to form a rhombus ABCD. Keeping AB fixed we allow CD to take all possible positions in the plane. What is the locus (or path) of the point D?

### Rolling Coins

A blue coin rolls round two yellow coins which touch. The coins are the same size. How many revolutions does the blue coin make when it rolls all the way round the yellow coins? Investigate for a line of 'n' coins

### Triangles and Petals

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

# Just Rolling Round

##### Age 14 to 16 Challenge Level:

 Created with GeoGebra The smaller circle, radius $r$, rolls around without slipping inside the circumference of the larger circle, radius $2r$. $P$ is a point on the circumference of the smaller circle . What is the locus of $P$?

NOTES AND BACKGROUND

This dynamic image is drawn using Geogebra, free software and very easy to use. You can download your own copy of Geogebra from http://www.geogebra.org.