Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Angle Trisection

## You may also like

### Doodles

### Russian Cubes

### Polycircles

Or search by topic

Age 14 to 16

Challenge Level

*Angle Trisection printable sheet*

A classical Greek problem was to find a way to trisect an angle using just a ruler and a pair of compasses. However, this is impossible.

It is possible though, to trisect an angle using a carpenter's square, as demonstrated in the video below.

Can you explain why this works?

Can you extend the idea to trisect an obtuse angle?

Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?

I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?