I am currently exploring if whether or not a fourth dimension exists or can be drawn. According to my professor, I have to use mathematical induction. I know that 2^n is the equation and "n" equals the dimension. Therefore 2^1 is 2. The first dimension is a line with 2 terminal points and 2^2 =4 because the second dimension is four terminal points. For mathematical induction, I guess I'm trying to prove that 2^n is true and 2^n+1. The only way I can prove this is by drawing it. I can draw that 2^4 = 16 terminal points and 2^n+1, I can show that you can end up with 4 terminal points, 16 terminal points...However, I don't know what type of equation to use.