Odd thought about PI

I was just looking at an article that suggests replacing PI with Tau which is not shocking in any way. The relationship to the circle is just a multiple of what we're used to. However, in thinking about this I thought that the reason PI and indeed Tau is such an odd number is because they are based on a single dimension rather than a geometric relation between two two-dimensional values. A radius is always the same radius whether it is thought of in two dimensions making a circle or three dimensions making a sphere. It occurs to me that the complex nature of PI is so because it has to do with the relationships of a particular value expressed in different dimensions.