Hinton - The Fourth Dimension.pdf

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THE FOURTH DIMENSION
selin, selat, selel, salet, salat, salan, sil. The whole
interior is salat.
Shapes can be easily cut out of cardboard which, when
folded together, form not only the tetrahedron and the
octahedron, but also samples of all the sections of the
tesseract taken as it passes cornerwise through our space.
To name and visualise with appropriate colours a series of
these sections is an admirable exercise for obtaining
familiarity with the subject.
EXTENSION AND CONNECTION WITH NUMBERS
By extending the letter sequence it is of course possible
to name a larger field. By using the limit names the
corners of each square can be named.
Thus “en sen,” “an sen,” etc. will be the names of the
points nearest the origin in “en” and in “an.”
A field of points in which each one is indefinitely small
is given by the names written below.
ensen etsen elsen
ansen atsen alsen
insen itsen ilsen
The squares are shown in dotted lines, the names
denote the points. These points are not mathematical
points, but really minute areas.
Instead of starting with a set of squares and naming
them, we can start with a set of points.
By an easily remembered convention we can give
names so such a region of points.