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'Moving Squares' printed from http://nrich.maths.org/

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This problem is inspired by a picture created by the artist Bridget Riley entitled "Movement in Squares" (1961)

Take two pieces of squared paper and colour alternate squares, giving a checkerboard pattern.

checkerboard pattern
Now, curve your pieces round to create two cylinders, and stand them up together.
cylinders

When you look straight at the two cylinders, the squares appear as rectangles getting narrower and narrower as the page curves away from you:
closeup of cylinders

How could you represent this effect on a flat piece of paper?


The diagram below shows what you might see if you looked at the cylinder from above. The construction lines may help you to work out how to recreate the image of the cylinders in two dimensions.

bird's eye view
You could vary the effect of your final image by altering the size of the black and white squares.

We look forward to seeing your calculations and finished products!