Art and Design

Arithmetic spirals

Spirals on ancient tombs go back 5,000 years. Barclodiad y Gawres in Anglesey is an ancient tomb that dates from the Neolithic era. There are spirals on the stones inside the tomb’s passage and chambers. They were very carefully carved, especially when you think that the people who made them had no iron tools. No one today knows what the spirals meant to people thousands of years ago. Perhaps they were just decorations, or perhaps they stood for life or eternity.

Spirals on stones, Barclodiad y Gawres, Anglesey

Tim Pugh works in the natural environment with stones, leaves, twigs and other things he finds. In this piece he arranged fallen leaves in autumn at the base of a tree. The spiral is circular and grows the same amount on each rotation, so it is an arithmetic spiral. Can you count how may turns he made? How did he change the design when it met the trunk of the tree?

Tim Pugh's work


In the classroom, you will need paper, adhesive putty such as Blu Tack, some string and two pencils. If you can use a beach or sandpit you could do the exercise with two sticks and some string.

  • You are going to use a pencil as a column to wind string around.
  • Tack your sheet of paper to a table or board.
  • Tie a piece of string to the blunt end of the first pencil with some tack to stop it slipping.
  • Stand this pencil in the middle of your paper as a column, point upwards. Tack it in place at the bottom and ask someone to hold the point and keep it vertical.
  • Tie the other end of the string to the point of the second pencil near the edge of your paper.
  • Keeping the string taut, move the pencil around the column so that it begins to draw the spiral.
  • Every time the string winds around the column your line will get closer to the centre. When you get to the middle you will have a complete spiral.
  • You could try again with a thicker column (for example a marker pen or a piece of dowel) to see how the spiral changes.

Sbiral / Spiral