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Moving Squares

Age 14 to 16
Challenge Level

Why do this problem?

This problem gives a rather unusual take on two-dimensional representations of three-dimensional shapes. It is based on the artwork of Bridget Riley, so could provide an excellent opportunity for forging cross-curricular links with Art and Design departments.

Recreating the three-dimensional object as a two-dimensional image provides a totally non-routine application of trigonometrical calculations in a very creative context.

Possible approach

If images of Bridget Riley's work can be found, a nice starting point would be to share these with the class, particularly "Movement in Squares" (1961) which provided the inspiration for this task.

Explain that the task is to create in two dimensions an image that appears to show two cylinders, like the photo in the problem. Give learners time to discuss in pairs or small groups ways that they could do this, and then share these as a class. The image at the bottom of the problem could be used to prompt a trigonometrical or scale drawing approach.

Once learners have devised a way to work out the measurements needed to create the image, allow plenty of time to actually make the images - an excellent opportunity for a classroom display!

Key questions

How do the squares appear to change as the paper curves away?
How can we calculate the changing widths of the squares?

Possible extension

Investigate creating images based on other curves, such as a sphere, or a parabola.
Do you think Bridget Riley's "Movement in Squares" is based on cylinders? Make sure you can support your answer mathematically!

Possible support

Offer learners the image showing the view from above the cylinder at an early stage.