I have what some might think is an unhealthy interest in sewers. It’s not really unhealthy, because, as I never tire of telling Mrs. R., I’m only interesting in theoretical sewerology, not the kind where I might actually visit a sewer (I tell her this whenever she wants me to do some plumbing repair in the house. I leave that to her. I prefer electricity. Truth to tell, I have actually taken a boat through the Paris sewers and visited a sewage treatment plant, but those were aberrations). I once edited a book that reprinted important papers and documents in 19th century sewer history. I ascribe my sewer fixation to their importance in the sanitary revolution of that century, which probably did more for public health than any medical advance.
Anyway. I’ve been thinking about manhole covers.
Originally sewers were visually inspected through small lamp-holes but these didn’t allow getting in to do maintenance. So the bigger man-holes were cut in the large sewer pipes. Pipes big enough for manholes usually carried storm drainage as well as “domestic drainage” needed to be sized to carry the much larger volumes produced by rain events. Many of these systems move the drainage by gravity (“downhill”). The manholes allowed for venting.
Where is all this leading, you may wonder (besides the sewer)? One feature of round manhole covers is that unlike oval or square ones they cannot fall into the hole. I began to wonder what other shapes have that property and an obvious one (although not very practical for man holes) is an equilateral triangle. That raises the question of what are the characteristics of a plane figure that can’t fall into a hole it just rests on. At first I thought that the circle might be the only convex such shape but then the triangle example occurred to me. Then I wondered about five pointed stars. Here the question is whether you could get them through the hole by tipping them a bit and levering them through that way. Then the two dimensional problem becomes three dimensional.
This is probably a well known problem that has been solved. Anyone know what the solution is?
This preoccupation is clearly the symptom of either someone with not enough work to do or too much work to do. I’ll let you guess which category I fall into.