This paper looks at some familiar results, concepts, and ideas in a different way, drawing out some common unifying threads. The topics addressed are one-, two-, and three-dimensions; axisymmetry and its breakdown; gaps and leakage paths; and computation fluid dynamics (CFD) and the limitation of perfection. Certain overlapping issues come up in each of the topic areas. [DOI: 10.1115/1.4001222]