Locus/loci

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?
problem

Mach Attack

Age

16 to 18

Challenge level

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.
problem

Construct the Solar System

Age

14 to 18

Challenge level

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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

Rolling Triangle

Age

11 to 14

Challenge level

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.
problem

Symmetric Trace

Age

14 to 16

Challenge level

Points off a rolling wheel make traces. What makes those traces have symmetry?
problem

Making Spirals

Age

7 to 11

Challenge level

Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.
problem

The Old Goats

Age

11 to 14

Challenge level

A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't fight each other but can reach every corner of the field?
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.