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Hyperbolic paper craft

By David Shaw, 21 April 2015

Make your own piece of non-Euclidean geometry with this hyperbolic paper craft.

You will need

You will need these items.

• Scissors
• Sticky tape
• Lots of heptagons – download a sheet of heptagons in PDF

What to do

1. Cut out the heptagons. You need eight heptagons to make the first basic shape that you can tape more heptagons onto.
   

   Start sticking heptagons to each side of the centre heptagon.

2. Choose one heptagon to be the centre. Tape a heptagon to every side of this central heptagon so you make a flower shape. Each heptagon will overlap each other a bit.
3. Bending the paper slightly, match the edges of each pair of adjacent heptagons and tape them together. Your paper construction will no longer sit flat.
   

   Match edges of adjacent heptagons and tape them together.

4. You can keep adding more heptagons to this shape. Just remember that three heptagons will meet at every intersection!

What’s happening?

From windows to whiteboards, smartphones to paper, we use flat surfaces every day. Mathematicians use them too – Euclidian geometry is the study of flat shapes, such as those drawn on a piece of paper.

A hyperbolic sheet of paper.

Not all surfaces are flat, however. The surface of a ball is round, and the surface of a foam is wonderfully twisted. Each of these surfaces is curved, and curved surfaces allow for very different shapes. Maths conducted on curved surfaces is known as non-Euclidian geometry.

The surface created in this activity is called hyperbolic. It is a bit like the opposite of a sphere. A sphere is contained – it wraps around on itself. A hyperbolic surface goes on forever, and it gets bigger and more wrinkled the further out you go!

More information

Try another hyperbolic craft activity

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