Ah yes Hilary, Hamiltonian Quaternians! Also used in CAD programming. Back in the days when every byte was precious they saved a lot of file space. You'll still find them in MicroStation DGN files.

And Joe F, you're right of course, it's the weight of the road that makes suspension bridges parabolic enough to use quadratic equations to solve for the forces in the cables. A catenary would be much more awkward to solve.