mysterious, "magical"; each separate number is as a spider at the
center of an amazing mathematical web. That is to say, every number
is discovered to be half of the sum of the pairs of numbers which
surround it, vertically, horizontally, and diagonally: all of the
pairs add to the same sum, and the central number divides this sum by
two. A graphic indication of this fact on the calendar face by means
of a system of intersecting lines yields that form of classic grille
dear to the heart of every tyro draughtsman. [Figure 2.] Here is
an evident relation between mathematical fact and ornamental mode,
whether the result of accident, or by reason of some subconscious
connection between the creative and the reasoning part of the mind.

To show, by means of an example other than this acrostic of the days,
how the pattern-making instinct follows unconsciously in the groove
traced out for it by mathematics, the attention of the reader is
directed to the design of the old Colonial bed-spread shown in Figure
3. Adjacent to this, in the upper right hand corner, is a magic
square of four. That is, all of the columns of figures of which it is
composed: vertical, horizontal and diagonal add to the same sum: 34.
An analysis of this square reveals the fact that it is made up of
the figures of two different orders of counting: the ordinary order,
beginning at the left hand upper corner and reading across and down in
the usual way, and the reverse-ordinary, beginning at the lower right
hand corner and reading across and up. The figures in the four central
cells and in the four outside corner cells are discovered to belong
in the first category, and the remaining figures in the second. Now
if the ordinary order cells be represented by white, and the reverse
ordinary by black, just such a pattern has been created as forms the
decorative motif of the quilt.

It may be claimed that these two examples of a relation between
ornament and mathematics are accidental and therefore prove nothing,
but they at least furnish a clue which the artist would be foolish not
to follow up. Let him attack his problem this time directly, and
see if number may not be made to yield the thing he seeks: namely,
space-rhythms which are beautiful and new.

We know that there is a beauty inherent in _order_, that necessity of
one sort or another is the parent of beauty. Beauty in architecture
is largely the result of structural necessity; beauty in ornament
may s