> For Pi to have any meaning requires a universe with at least two dimensions There is no such requirement. Mathematical constructs have meaning even outside o

> For Pi to have any meaning requires a universe with at least two dimensions There is no such requirement. Mathematical constructs have meaning even outside of their most immediately obvious manifestation (such as the application of geometry to the understanding of physical space). Even a one-dimensional intelligent being, if such a thing is even possible, would eventually encounter pi, alongside the basics of euclidian geometry, as soon as they start doing math on datasets measuring more than one feature, as such datasets are embedded in n-dimensional spaces, where n is the number of independent features, even if physical space has less than n dimensions.