Locus/loci

problem
Favourite

Is There a Theorem?

Age

11 to 14

Challenge level

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
problem
Favourite

How Far Does It Move?

Age

11 to 14

Challenge level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.
problem
Favourite

Rolling Around

Age

11 to 14

Challenge level

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
problem
Favourite

An Unusual Shape

Age

11 to 14

Challenge level

Can you maximise the area available to a grazing goat?
problem
Favourite

Speeding Up, Slowing Down

Age

11 to 14

Challenge level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.
problem
Favourite

Rollin' Rollin' Rollin'

Age

11 to 14

Challenge level

Two circles of equal radius touch 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?
problem
Favourite

Up and Across

Age

11 to 14

Challenge level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.
problem
Favourite

Triangles and Petals

Age

14 to 16

Challenge level

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

Roaming Rhombus

Age

14 to 16

Challenge level

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?
problem

Like a Circle in a Spiral

Age

7 to 16

Challenge level

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?