Visualising and representing

problem

Five Circuits, Seven Spins

Age

16 to 18

Challenge level

A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.
problem

Maths Shop Window

Age

16 to 18

Challenge level

Make a functional window display which will both satisfy the manager and make sense to the shoppers
problem

Hyperbolic Thinking

Age

16 to 18

Challenge level

Explore the properties of these two fascinating functions using trigonometry as a guide.
problem

Gosh Cosh

Age

16 to 18

Challenge level

Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.
problem

Curvy Equation

Age

16 to 18

Challenge level

This problem asks you to use your curve sketching knowledge to find all the solutions to an equation.
problem

Euler Meets Schlegel

Age

16 to 18

Challenge level

Discover how networks can be used to prove Euler's Polyhedron formula.
problem

To Swim or to Run?

Age

16 to 18

Challenge level

The famous film star Birkhoff Maclane wants to reach her refreshing drink. Should she run around the pool or swim across?
problem

Ford Circles

Age

16 to 18

Challenge level

Can you find the link between these beautiful circle patterns and Farey Sequences?
problem

Rational Request

Age

16 to 18

Challenge level

Can you make a curve to match my friend's requirements?
problem

Sheep in Wolf's Clothing

Age

16 to 18

Challenge level

Can you work out what simple structures have been dressed up in these advanced mathematical representations?