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Mazes are very ancient and appear throughout history. According to ancient legend, Daedalus constructed the 'Cretan Labyrinth' in Knossos, to house the legendary Minotaur. Half man and half bull, the fearsome Minotaur was killed by Theseus who escaped the labyrinth with the aid of a ball of string provided by his lover Ariadne.

Although we don't have direct evidence for the shape of the Cretan Labyrinth in the form of buried walls, there is a traditional idea about its shape, and a very nice geometrical construction for drawing one. The labyrinth can be drawn on paper. It also looks very good on a beach drawn in the sand with a stick. To draw a traditional Cretan Labyrinth, start with the cross and dots on the right.

The picture to the right shows how to complete the Cretan Labyrinth. Notice that the lines are connected alternately left and right around the square. Try following the route from the entrance to the centre. This path is surprisingly long and in a full size labyrinth it would have taken some time to get to the centre. However, there is a further surprise in store. Although the path to the centre is very long there is only one way in and one way out! Theseus had to make no difficult decisions at all on his way to kill the Minotaur. Indeed, it was easy with this design to get to the centre and just as easy to get out again. In short there was no need for threads, Ariadne, broken hearts, suicide or any of the other features of the story.

Above: Medieval Labyrinth in Chartres Cathedral
Left: Portrait of a Gentleman attributed to Bartolommeo Veneto, Fitzwilliam Museum, Cambridge.

The geometric pattern of the Cretan Labyrinth is quite a common artistic image appearing in many different cultures. It is found scratched into caves in Cornwall, on Roman coins and in pictures drawn by native American Indians, as well as in the examples shown here. The pattern is of interest to mathematicians because it packs a very long path into a small space. 

Text by Chris Budd and Chris Sangwin.