This resource contains a range of problems and interactivies
on the theme of loci. Some of the resources, such as Roundabout and
Rollin' Rollin' Rollin', enable you to change the settings and
therefore open up lots of opportunity for further investigations
and extensions to the problem posed in the text.

### Turning triangles

In

this problem you are asked to think about a triangle rolling
along a horizontal line. Describe the paths of each of the vertices
and the relationships between them and the original triangle.

### Roundabout

Start by considering the locus of hte centre of a circle as it
rolls around a square. What happens when the circle rolls around
different polygons? How about different polygons of different
sizes?

This interactivity offers the flexibility to change the number
os sides of he poygon and the sizes of the polygon and rolling
circle.

### Is there a theorem?

One square slides around another of the same size maintaining
contact and keeping the same orientation. How far does a dot on the
sliding square travel? Investigate

this problem with different sized squares and then consider
different polygons.

### Rollin' rollin' rollin'

In

this problem - two circles of equal radius kiss at P. One
circle is fixed whilst the other moves, rolling without slipping,
all the way round. How many times does the moving coin revolve
before returning to P? The interactivity also offers opportunity to
extend the investigation to other polygons.

The next
two problems are more challenging and will extend your
understanding of loci .

### The Line and Its Strange Pair

In

this problem the points P and P' are connected by the following
rule:

P' can move to different places along a dotted line. Each
position P' takes will fix a corresponding position for P. If P'
moves along the straight line what does P do and can you explain
what the rule that connects them is?

### Mapping the Wandering Circle

In

this problem 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
and can you explain what the rule that connects them is?