With a single cut ...
Presented by Dr Misha Feigin
In this Masterclass we will explore some geometric shapes and how they can be cut from a piece of paper. The paper should be properly folded and flat and only one straight cut is allowed.
Start by trying to fold a sheet of paper so that when you cut it you get a square. Note that your paper can have irregular edges. So you might first sketch a square in the middle of your paper and then try to get it by a single cut.
Now sketch a triangle and try to obtain it by a single cut after you fold the paper appropriately. Notice that it is easier to do when your triangle is symmetric. However this is always possible due to the remarkable property that the three bisectors of the angles in a triangle pass through a single point.
Japanese mathematicians were interested in obtaining different shapes by such a fold and cut process in 18th century as this was related to origami, the Japanese word for the art of folding paper. It was only some 15 years ago that mathematicians realised that any collection of polygons can be cut in this way.
Don't forget to bring your scissors and ruler!
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