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Amusements in Mathematics

Mazes And How To Thread Them
"In wandering mazes lost."
Paradise Lost.
The Old English word "maze," signifying a labyrinth, probably comes from the
Scandinavian, but its origin is somewhat uncertain. The late Professor Skeat thought that
the substantive was derived from the verb, and as in old times to be mazed or amazed was
to be "lost in thought," the transition to a maze in whose tortuous windings we are lost is
natural and easy.
The word "labyrinth" is derived from a Greek word signifying the passages of a mine.
The ancient mines of Greece and elsewhere inspired fear and awe on account of their
darkness and the danger of getting lost in their intricate passages. Legend was afterwards
built round these mazes. The most familiar instance is the labyrinth made by Dædalus in
Crete for King Minos. In the centre was placed the Minotaur, and no one who entered
could find his way out again, but became the prey of the monster. Seven youths and
seven maidens were sent regularly by the Athenians, and were duly devoured, until
Theseus slew the monster and escaped from the maze by aid of the clue of thread
provided by Ariadne; which accounts for our using to-day the expression "threading a
The various forms of construction of mazes include complicated ranges of caverns,
architectural labyrinths, or sepulchral buildings, tortuous devices indicated by coloured
marbles and tiled pavements, winding paths cut in the turf, and topiary mazes formed by
clipped hedges. As a matter of fact, they may be said to have descended to us in precisely
this order of variety.
Mazes were used as ornaments on the state robes of Christian emperors before the ninth
century, and were soon adopted in the decoration of cathedrals and other churches. The
original idea was doubtless to employ them as symbols of the complicated folds of sin by
which man is surrounded. They began to abound in the early part of the twelfth century,
and I give an illustration of one of this period in the parish church at St. Quentin (Fig. 1).
It formed a pavement of the nave, and its diameter is 34½ feet. The path here is the line
itself. If you place your pencil at the point A and ignore the enclosing line, the line leads
you to the centre by a long route over the entire area; but you never have any option as to
direction during your course. As we shall find in similar cases, these early ecclesiastical
mazes were generally not of a puzzle nature, but simply long, winding paths that took
you over practically all the ground enclosed.
In the abbey church of St. Berlin, at St. Omer, is another of these curious floors,
representing the Temple of Jerusalem, with stations for pilgrims. These mazes were
actually visited and traversed by them as a compromise for not going to the Holy Land in
fulfilment of a vow. They were also used as a means of penance, the penitent frequently
being directed to go the whole course of the maze on hands and knees.