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Enclosing Squares

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

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Parallel Lines

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

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Perpendicular Lines

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

Painting Between the Lines

Stage: 3 and 4 Challenge Level: Challenge Level:1

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:
Photo of pyramids
(Photo: Przemyslaw "Blueshade" Idzkiewicz)

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

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.
Please send us any of your creations (together with your instructions).