Toppling Loci
Topple a square along a line. Draw the locus of one corner of the square. How many topples does it
take to get the square back to its starting orientation? What is the length of the locus? Now use a
triangle instead of a square. Or a rectangle. Or another shape. Or find the locus of the centre of the
square.
More Toppling Loci
Topple a square round another square. Draw the locus of one corner of the
square. How long is the locus? What about a triangle round a triangle?
A square round a hexagon?
Polygons along a line
Topple a regular polygon along a line. Choose the size of the polygon so
that the radius of the circumcircle is 1 unit. What is the length of the locus of a corner for one
rotation of the polygon? What is the area enclosed
between the locus and the line? What about an Nsided polygon? What happens when N tends to
infinity?
Polygons around polygons
Now topple a regular polygon round an identical regular polygon.
What is the length of the locus of a corner? What is the area
enclosed by the polygon? What about an N-sided polygon?’ What
happens when N tends to infinity?
Inside and outside
Topple a unit square round a 2-by-2 square. What is the length of the locus of one corner? Is there
more than one answer? What about a 3-by-3 square? Other squares?
Now topple a unit square inside a 2-by-2 square. A 3-by-3 square. Other squares. Are any of your
inside locus lengths the same as your outside locus lengths? Can you explain? Now try toppling a
square round or inside a rectangle.