# Math Photo: Pothole Pentagon

I’ve read that there are over 500,000 manhole covers in New York City, but I’d never noticed these pentagonal bolts before.  A nice mathematical surprise among the grit and grime.

#### Jerome Dancis · September 7, 2014 at 10:44 am

And the reason manholes covers are circles not squares is?

A square manhole cover could be accidentally dropped down the manhole.

#### Chris Harrow · September 7, 2014 at 1:18 pm

Cool & unexpected. Started wondering WHY on the bolt shape as soon as I saw it.

My first guess is that a pentagon prevents all but a special wrench from being able to loosen/tighten the bolts (you don’t want *everyone* to be able to open the manholes) as the pentagon has no parallel sides standard wrenches would leverage. If so, perhaps equilateral triangle heads were also considered, but then rejected, because the corners of such would wear faster as a result of their narrower vertices.

It also might be to guarantee some businessman an exclusive contract with the city on the bolts AND the wrenches to open them. Perhaps I’m a little pollyanna-ish, but I actually hope it was for a constructive (and mathematical!) reason.

#### MrHonner · September 8, 2014 at 6:25 pm

I ran through much the same thought process. But I’m not sure they’re all pentagonal. I’ll certainly be paying closer attention now, though!

#### Chris Harrow · September 7, 2014 at 1:22 pm

@ Jerome & all teachers:

Encourage your students to see if any polygonal shape other than squares could work as a manhole cover. It should be relatively easy to discover why square manholes are a bad idea, but are circles the only reasonable shape that could be used?

#### Fung · October 4, 2014 at 11:23 pm

Well math and shapes are all around us, the problem is that people usually don’t paid much attention to them…

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