### Spirostars

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

### Which Twin Is Older?

A simplified account of special relativity and the twins paradox.

### Snookered

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

# A Different Differential Equation

##### Age 16 to 18 Challenge Level:

This is an investigation concerning differential equations -- it is both difficult and open-ended. You might wish to discuss the problem in groups and make good use of computers or other tools to get started before closing the problem down to explore a particular route.

Can you find any solutions to a differential equation of the form

$$f'(x)= cf(x^2)\quad\mbox{ or } \quad f'(x^2)=cf(x)\,,$$
where $c$ is a constant?