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Four vehicles travelled on a road. What can you deduce from the times that they met?

### Enclosing Squares

Can you find sets of sloping lines that enclose a square?

### Intersections

Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?

# Painting Between the Lines

##### Age 11 to 16Challenge Level

In abstract or computer generated art, a real object is often represented by a simplified set of shapes, lines or curves.

Take a look at the picture below:

The picture could be represented in an abstract way using straight lines:

If you wanted to describe mathematically the line segments used to draw this picture, all you would need to do is decide where to put the axes and then work out the equations of all the straight lines.

Here is a set of instructions to create an abstract representation of another well known landmark (download as a Word or PDF file).

Now try this for yourself - choose an image, perhaps a photograph of a famous location, or a famous painting.
Think how it might be broken down into shapes or segments of lines.
Can you create a set of instructions for your picture?
Once you have created your instructions, give them to a friend to follow.

Can you devise a way to describe mathematically each region so that you can give instructions for colouring your image?

You may wish to use curves as well as straight lines. To explore abstract art using more complicated mathematical functions, take a look at Painting by Functions.

Have a go at creating your image using a graphing software package such as Geogebra.