Originally Posted by Hank Fletcher

I thought so, too, at first. I think an equilateral triangle would also do the same trick, or maybe a hexagon. Given that, I think Ambient's answer that because it's easier to roll than pick up is a pretty good one. I put it to my girlfriend, she said that if the cover ever came loose, it would cause the least amount of damage to cars (i.e. no pointy bits). There seems to be a lot of good answers for "circle," it's the why that demonstrates imagination, I think.

Well, as Roff noted, if you are allowed free reign with the width of the lip that the cover sits on when in place, then you can do it with many shapes. If you want to maximise clearance through the hole and use the least material to make the cover, then I don't think any shape but a circle or a regular polygon which approximates a circle fairly closely can be guaranteed to never fall through its own hole.

This is my line of reasoning--and please shoot any stupid points down. I'm just thinking about this because it's fun (I'm a sad, sad man):

It seems to me that a circle is the only shape which has equal maximum and minimum lines of bisection. So for any non-circle, there is a way that you can rotate it so that the minimum width of the cover passes through the maximum width of the hole.

This is using ideal shapes of two-dimensional planes. The thickness of the cover and the width of the lip will both matter. If you are allowed to make the lip width greater than the difference between the shape's maximum and minimum widths, you can make other shapes work. But then you increase the amount of material you need and reduce the room for access through the hole.

You could also increase the thickness of the cover to a greater fraction of the shape's size, but then you're also wasting material.

I think that a circle also uses the least material overall (as Robert-Jan noted) and as a couple people have also said, the holes are round.

Please post a picture of what you mean.

I'd like to see that picture too.


Torben

Originally Posted by Roff

A triangle can fall through. A hexagon can fall through. Of course, you can make the hole substantially smaller than the lid, and you can keep either one of them from falling through, but with a circle, the hole only has to be infinitesimally smaller than the lid.

I suppose you're right! It kind of hurt my brain trying to think of a non-circular shape that wouldn't, then hurt it again sorting out why the non-circular would still fall through!

I better brush-up on my spatial reasoning skills. I'm hoping to join the army here soon, and part of the entry test is a portion I guess designed to gauge some aspect of recruits' aptitudes. It's multiple choice, but it involves looking at pictures of shapes and determining what goes where, e.g. choosing the right two dimensional fold-out that will fold up into a given three dimensional figure. Not the sort of thing you'd find on your average job application, I don't think!

Originally Posted by Hank Fletcher

Quixotron's advice is great for anyone who wants to work for a living, just bear in mind that it's an ethos that will never make you a millionaire. The subordinate will always be subjugated, they just go hand in hand.

Thats not necessarily true. One of my bosses enjoys a six figure salary, has about .5 million dollars in company stock at reduced price, travels to europe and japan at least a dozen times out of the year and has a nice pension/retirement bonus. He spends half the time in meetings, enjoys 5 weeks plus of paid vacation and enjoys calling the plays. yes, he's been there for 25 years or so at Lexmark, but he seems happy and content. I couldn't see what more a man could want.

slow and steady wins the race. cheney is a great example. the guy will retire filthy rich. he also has deep political connections within the GOP party, so he gets to make the big decisions and noone messes with him. same with mccain, he started off as a foot soldier for reangan look at him now, one step away from being president of the US. of course, these guys PUT IN THEIR TIME! we're talking a minimum of 20 years service.

Originally Posted by kchriste

Why doesn't it surprise me that you would admire Cheney?

Join the Navy. You'll live longer.

I was going to say the airforce. but i'd avoid serving altogether. i'd refer to design military hardware instead.

Originally Posted by kchriste

Join the Navy. You'll live longer.

That'd be my preference, and the Navy tends to have great bands, but the local Artillery needs a trombone player!