Simple Geometry

[RocketManJames]

I'm asking this, because for some reason I was recently convinced by someone of one thing, but I no longer believe it. I can no longer recall in detail how I was convinced.

So, let me just ask the question, and you all can tell me which is right.

You have a manhole and cover that is shaped as an equilateral triangle.

Is there any way to have the cover fall back into the manhole? An exact length will not be counted as being able to fall in.

For a square manhole, it is obvious that the cover could fall back in the hole, by simply letting the edge fall in along the diagonal.

What about for a equilateral triangular manhole and cover?

Thanks.

-RMJ

[dragon14]

A few links on this question

Triangle Manhole Covers in New Hampshire (http://www.drainspotting.com/mirror/nhtelegraph-2003-11-26/)

Discussion of issue with name of triangle that won't fall in manhole (http://www.straightdope.com/classics/a1_247a.html)

[Nottom]

With a triangular manhole cover you can kind of rotate the cover as you go through the hole to make it fit.

Think about walking a couch through a doorway that seems too small.

[RocketManJames]

Thank you... I suppose I had a total brain fart about this.

Yes, of course, you can make it fall in as described in the links provided. And, it doesn't require any special manuevering... if you orient the cover so that the altitude of triangle is at 0 degrees, it can then drop down along the edge of the triangular manhole.

Doh, I'm so dumb sometimes.

-RMJ

[dragon14]

No problem,

It was actually worth my while to look it up, those triangular manhole covers were cool.

[purnell]

Definitely worth the time it took to read the article- Thanks.