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
Recreating the three-dimensional object as a two-dimensional
image provides a totally non-routine application of trigonometrical
calculations in a very creative context.
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
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
How do the squares appear to change as the paper curves
How can we calculate the changing widths of the squares?
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!
Offer learners the image showing the view from above the cylinder
at an early stage.