


Art and Geometry  H.M.S. Coxeter
"I'm engrossed again in the study of an illustration
which I came across in a publication of the Canadian professor H.S.M. Coxeter,
of Ottawa (whom I met in Amsterdam some time ago), A Symposium on Symmetry.
I am trying to glean from it a method for reducing a planefilling motif which
goes from the centre of a circle out to the edge, where the motifs will be
infinitely close together. His hocuspocus text is no use to me at all, but
the picture can probably help me to produce a division of the plane which
promises to become an entirely new variation of my series of divisions of
the plane."
(Escher in Locher, 1992, p. 91)
H.S.M. COXETER'S SYSTEM
In 1957, the Canadian mathematician H.S.M.
Coxeter sent Escher one of his articles on hyperbolic geometry. Escher was
most inspired by one of the illustrations. He had always been frustrated by
the boundary imposed by the edge of the paper, wich limited the tiling and
cut off the recognizable forms. Coxeter's geometric representation offered
a solution. In addition, this model enabled Escher to suggest the infinitely
small in his work.
Applying geometric principles to his representation of infinity, Escher proceeded
by similarity, which may be simply defined as a transformation changing the
size but not the shape of the figure. The figures remain identical, but their
size can be reduced. Escher made a number of prints based on this principle.