Understanding the Fourth Dimension Through a New Mathematical Approach

Abstract

This paper establishes a new concept of dimensions in an effort to understand the fourth dimension. From school days, we are accustomed to a square as two dimensional primitive, a cube as three dimensional primitive. We will try to imagine the fourth dimension in the same lines and so it is difficult to imagine and visualize it. As we know, point is having zero dimensions and a line is having one dimension. After that, the two dimensional primitive is not a square but it is a triangle. Precisely, it is an equilateral triangle. So if we move in this direction, it will be easier for us to visualize and understand the 4\textsuperscript{th} dimension. After the equilateral triangle, we will think of the next solid which is a tetrahedron, in which all the sides are equal and there are four equilateral triangular faces. This is the solid primitive of three dimensions and not the cube. On these lines, if we move on to the next dimension, we can easily analyse that the fourth dimensional point will appear inside this tetrahedron having five volumes like tetrahedron, which will be discussed in detail in this paper. This paper logically arrives at equations for finding vertices, edges, surfaces, centre of masses and volumes of \lq n' dimensional object.