So I'm sure everyone here knows of the basic spacial dimensions. 1D is a line, 2D a plane and 3D a cube. There is even a 4th dimension (theoretical), the tesseract. And an infinite number of dimensions beyond, represented by various hypercubes. Finding the space taken up by one of these objects (length, area, volume) is easy. The length of a line is x^1, the area of a plane is x^2, and the volume of a cube is x^3 continuing ad infinitum. But what about partial dimensions, do they exists (theoretically of course)? For example, a 2.5 dimension. It might make sense to think of dimensions as discrete, but then how would you account for the ability to find the space taken up by these objects (length, area, volume)? For example, you can find the "area/volume" of a 2.5 dimension "square/cube" by x^2.5. If the length of a side of this "square/cube" was 2 than 2^2.5 = 5.65685425 is the "area/volume" of this mythical partial dimensional object. If partial dimensions don't exists, what am I measuring? I have searched the internet far and wide and have found no mention of partial dimensions. Can someone please elaborate on them or if they are even possible? And if they are, could someone explain how I could go about drawing one?