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Hyperbolic paper craft

By David, 21 April 2015 Activity

You will need

scissors, sticky tape, hepatgons.

You will need these items.

  • Scissors
  • Sticky tape
  • Lots of heptagons – you can download a sheet to print out in pdf or Word document.

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.
    Someone has sticky-taped heptagons to two sides of another heptagon.

    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.

    a flower shape of heptagons. someone is taping two ajacent heptagons together.

    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 wierd curvy 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
More about non-Euclidean geometry

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