Feynman and the Manhole covers...

A week before, i would not have imagined that soon, i might be blogging about something as trivial (or is it?) as the shape of the Manhole Covers!!

i was posed with this question by a friend this week, and my immediate answer was, "is it because its easier to dig circular holes ?" Supposedly, Microsoft and IBM (since the 60s ?!) have been asking this question in their interviews to test lateral thinking ability and the expected answer is that "manhole covers are round because round is the only shape that can never fall into the manhole..."

Though given the popularity of this question and this answer, if i were an interviewer, and if someone gives this politically correct answer, i might doubt that the person is not thinking laterally to explore other answers besides this cliched one ;-) And there are also other complex shapes fitting this requirement of having a constant diameter like the Reuleaux triangles and similar shapes drawn using any odd sized polygon...

Though the expected answer is a very creative one, here's a more realistic reason on how the circular shape has, indeed become the universal standard: "circle seems to be a default (and natural too ?) shape for underground drains and pipes, probably due to reasons like their ability to withstand pressure better, and it has been the case since the roman empire!! and hence the covers were made to fit the circular holes :-) also, i have not seen any evidence yet that, there were some other shapes in use, before the circular ones, and we then moved to circular covers due to their advantage..."

and here's some manhole trivia from the net...

* Nashua, a town in New Hampshire, US has triangular manhole covers, which is being phased out in favor of circular ones (not because triangular covers are falling inside the manholes)

* India is the world leader in manufacturing manhole covers

* China faces the problem of manhole cover thefts and its govt has taken steps to reduce manhole cover thefts in Beijing from 24,000 in 2004 to 4000 in 2005

and how would somebody as clever and mischievous as Richard Feynman answer this question ? below is the snippet of this entertaining imagination from this interestng site about Microsoft Interview experiences:

Interviewer: Now comes the part of the interview where we ask a question to test your creative thinking ability. Don't think too hard about it, just apply everyday common sense, and describe your reasoning process.

Here's the question: Why are manhole covers round?

Feynman: They're not. Some manhole covers are square. It's true that there are SOME round ones, but I've seen square ones, and rectangular ones.

Interviewer: But just considering the round ones, why are they round?

Feynman: If we are just considering the round ones, then they are round by definition. That statement is a tautology.

Interviewer: I mean, why are there round ones at all? Is there some particular value to having round ones?

Feynman: Yes. Round covers are used when the hole they are covering up is also round. It's simplest to cover a round hole with a round cover.

Interviewer: Can you think of a property of round covers that gives them an advantage over square ones?

Feynman: We have to look at what is under the cover to answer that question. The hole below the cover is round because a cylinder is the strongest shape against the compression of the earth around it. Also, the term "manhole" implies a passage big enough for a man, and a human being climbing down a ladder is roughly circular in cross-section. So a cylindrical pipe is the natural shape for manholes. The covers are simply the shape needed to cover up a cylinder.

Interviewer: Do you believe there is a safety issue? I mean, couldn't square covers fall into the hole and hurt someone?

Feynman: Not likely. Square covers are sometimes used on prefabricated vaults where the access passage is also square. The cover is larger than the passage, and sits on a ledge that supports it along the entire perimeter. The covers are usually made of solid metal and are very heavy. Let's assume a two-foot square opening and a ledge width of 1-1/2 inches. In order to get it to fall in, you would have to lift one side of the cover, then rotate it 30 degrees so that the cover would clear the ledge, and then tilt the cover up nearly 45 degrees from horizontal before the center of gravity would shift enough for it to fall in. Yes, it's possible, but very unlikely. The people authorized to open manhole covers could easily be trained to do it safely. Applying common engineering sense, the shape of a manhole cover is entirely determined by the shape of the opening it is intended to cover.

Interviewer (troubled): Excuse me a moment; I have to discuss something with my management team. (Leaves room.)

(Interviewer returns after 10 minutes)

Interviewer: We are going to recommend you for immediate hiring into the marketing department.