Consider:
> 1D (line): 1 unit
> 2D (sqr): 1 square units
> 3D (cbe): 1 cubic units
> etc.
Notice that the units technically change with each dimension. It's why you had to say the is the same as the , they aren't really though but the numbers are.
It's like saying the length of a 1 unit long line is equal to the area of 1 unit by 1 unit square. The fallacy is in saying that length is the same as area.
Suppose I multiplied the length of a line one unit long by 3, what is the geometric analogy of that?
It's ambiguous if we ignore dimensions: either we are making the line thrice as long as before or we're extending it into the 2nd dimension by 3 units.
