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A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

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Pie Cuts

Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).

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Getting an Angle

How can you make an angle of 60 degrees by folding a sheet of paper twice?

Angle A

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Nichola Coreltt and Sarah Platten (Willaston School,Douglas,Isle Of Man) and experimented with the diagram and made the following comments. (The last sentence is particularly interesting!)

"The smallest angle a can be is 0.049 degrees
The largest angle a can be is 179.508 degrees
We found that the largest angle is in the smallest triangle."