Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Platonic Planet

## You may also like

### Just Rolling Round

### Coke Machine

### Just Opposite

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

Age 14 to 16

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

How much of the planet's surface can the alien see if she is in the
middle of one of the faces?

What about on one of the edges?

Or at a vertex?

Try to picture a route around the planet either in three dimensions or on a net. Can you be sure every point on the surface is visible from your route? Can you make a more efficient route? Some diagrams might help!

What about on one of the edges?

Or at a vertex?

Try to picture a route around the planet either in three dimensions or on a net. Can you be sure every point on the surface is visible from your route? Can you make a more efficient route? Some diagrams might help!

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?