ABSTRACT

In the space of one dimension the number determines the point. Space of three or of less than three dimensions may be visualised in a geometrical representation, but this is not the case with spaces of more than three dimensions. It is common knowledge that the point is said to have no dimensions, that the line has one dimension, the surface two and the volume three. If therefore, a cube is represented in a surface, there will be lines which will be repeated twice, and points which will be repeated three times. It will then be seen that, just as the triangle has its vertices repeated and the cube its lines, so spaces of dimensions higher than three represented in terms of two or three dimensions will have volumes repeated. The line is one-dimensional space. The line has two vertices or end points. The triangle has three vertices and three sides.