Can you find all of the angles in this drawing? How could you label each of the angles?

How do the circle theorems confirm what you find?


Investigating Tilings

Draw a point on a sheet of paper. Arrange regular polygon plastic blocks around this point so that they all meet at the vertex with no gaps. Record your findings using a diagram - why do some combinations of polygons fit together perfectly while others don't? Work out all the angles in your pattern and mark them on your diagram.

How many different combinations are there? What if you didn't have to just use the regular polygon blocks you have at school - would any other regular polygons fit into the spaces? If so which ones?

Try to find all the different combinations of arrangements of shapes at a point.

Which of the combinations that you have found will enable you to create a tiling that will cover a large sheet of paper with no gaps? Try to draw this tiling accurately, or photograph your arrangement of plastic blocks. I would love to receive photos of your polygon tilings!

Find out more about tilings, including the work of Roger Penrose - try to create some of your own!


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