The 16 vertexes of the hypercube in the program are numbered from 0 to 15
according to a simple scheme. If each number is rewritten in binary form
and converted into an array of four bits, a miniature coordinate system
emerges. The binary digits of 13, for example, are 1 (that is, one 8), 1
(one 4), 0 (zero 2's) and 1 (one 1). The binary number can then be written
as the array
Dimensions seem to creep in everywhere as HYPERCUBE
is
written. A two-dimensional matrix, or array, called vert
preserves the vertexes as they are initially defined. Since there are 16
vertexes with four coordinates each, vert is a 16-by-4 matrix of 64
numbers; vert(i,j)
is the jth coordinate of the
ith vertex. The program HYPERCUBE
holds the matrix
vert
inviolate; vert
is defined at the beginning
of the program and its contents are then transferred to a second 16-by-4
matrix called cube
. The matrix cube
can be
thought of as a working matrix; its contents are continually altered by the
rotations carried out in the program.
Mathematics Awareness Month is sponsored each year by the Joint Policy Board for Mathematics to recognize the importance of mathematics through written materials and an accompanying poster that highlight mathematical developments and applications in a particular area. |