# Dotty Grids

Take a dotty grid. Draw a few lines. What can you draw? What can you discover? The more you explore, the deeper you are drawn in...

We have suggested some starting points to stimulate your curiosity. We hope you will be playful, pose some questions of your own, and make some unexpected discoveries.

### Are We Nearly There?

Try to visualise the route taken by the arrows in our animation. What patterns do you notice?

### Squares from Diagonals

If you were given a diagonal of a square, do you think you could figure out where all four corners go?

### Drawing Polygons

I wonder what polygons can be drawn on dotty paper... Take a look at our images, draw some of your own, and see what you can discover...

### Exploring Area

Drawing shapes on squared paper is a great way to work out their area. There are some well-known theorems to discover too...

### Exploring Coordinates and Vectors

Coordinates and vectors are very useful tools for working out properties of lines and shapes drawn on a dotty grid. Have a look at the problems and see how you can use these tools to understand what's going on.

### Exploring Distance

We usually measure distance as the crow flies. These problems explore the mathematics that emerges when we express distance in different ways, using ideas from taxi-cab geometry.