Shapes can easily be 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 of which each one is indefinitely small is given by the names written below.
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 to such a region of points.
Let the space names with a final “e” added denote the mathematical points at the corner of each square nearest the origin. We have then