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'Making Sixty' printed from http://nrich.maths.org/
Take a piece of paper.
Fold it along the long axis and then open it up.
Now fold one corner over and onto the centre crease so that the
fold line passes through the corner next to it (on the short side
of the paper).
You have created some angles. There are angles of $60^o$ and of
$30^o$. Can you prove this?
Does the paper have to be A4?
You are now able to fold the paper to
make an equilateral triangle which can be used in lots of different
ways. For example, see
Equilateral Triangle Folding .