Remarks on d-Dimensional TSP Optimal Tour Length Behaviour

The well-known $O(n^{1-1\mathrm{/}d})$ behaviour of the optimal tour length for TSP in d-dimensional Cartesian space causes breaches of the triangle inequality. Other practical inadequacies of this model are discussed, including its use as basis for approximation of the TSP optimal tour length or bounds derivations, which I attempt to remedy.