Hinton - The Fourth Dimension.pdf

126
THE FOURTH DIMENSION
could be taken out of the cube and placed on a plane.
k
It is a figure which will fill a
plane by equal repetitions of itself.
102 012 The plane being representing this
construction in his plane would
201
021
take three squares to represent the
cube. Let us suppose that he
takes the ij axes in his space and
i 210 120
Fig. 67.
j
k represents the axis running out
of his space, fig. 68. In each of
the three squares shown here as drawn separately he
could select the points given by the rule, and he would
A D 1 D
210
F
then have to try to discover the figure determined by
the three lines drawn. The line from 210 to 210 is
given in the figure, but the line from 210 to 201 or FG
is not given. He can determine FG by making another set
of drawings and discovering in them what the relation
between these two extremities is.
102
201 A
G
B
120
K
D
201
G
Fig. 68.
210
012
Fig. 69.
Let him draw the i and k axes in his plane, fig. 69.
The j axis then runs out and he has the accompanying
figure. In the first of these three squares, fig. 69, he can
C 1
021
102
120
K
021
C
120