Let go of the lip issue. It is irrelevant. The relevant question is "Is an equilateral triangular shaped manhole cover immune from being dropped into its hole?"
The only things I said were obvious were that if there was no lip any shape would fall through , and that the lip can be made large enough that no lid can fall through. One reason manhole covers are round is that circles have the property that if there is any lip whatsoever, it cannot pass through it's hole.
NerveGas claimed that equilateral triangles also have this property, that if there is any lip whatsoever, it cannot pass through its hole. This is false. I explained how to do it.
"What is it you want, Mary? What do you want? You-you want the moon? Just say the word and I'll throw a lasso around it and pull it down. Hey, that's a pretty good idea. I'll give you the moon...Well, then you could swallow it. And it'll all dissolve, see. And the moon beams that shoot out of your fingers and your toes and the ends of your hair...Am I talking too much?"
- George Bailey (James Stewart), It's A Wonderful Life (1946)
Well, basically because triangles are the topic of conversation. Specifically, the point of the discussion is whether a manhole cover shaped like an equilateral triangle can pass through its own hole. Obviously, any shape will pass through it's own hole if there is no lip to the hole. Equally obviously, any shape can be blocked if you make the lip big enough. But what if there is a trivial lip, say one cm wide lip on a metre sized hole. A circular lid cannot fall into such a hole, but can an equilateral triangle shaped manhole cover fall into its hole in that case?
In the great^n-grandpappy post, NerveGas said that equilateral triangle manhole covers cannot fall through their own holes. I gave him a counterexample: If one of the edges of the lid is normal to the plane of the hole, and the lid is parallel to and just inside one of the edges of the hole, it can fall in.
Well *OBVIOUSLY* if you make the lip big enough, the lid will not go through. You could do that for a square cover as well. That's not the point.
The parent post of this thread put forth the notion that an equilateral triangle has the same "not-able-to-go-through-a-hole-of-the-same-size (with a trivial lip)" property that a circle does. It does not. I presented two ways of visualizing how to pass it through.
Now that I think of it, you are helping my case, because you are saying you need a non-trivial lip in order to prevent the lid from falling through.
As has been stated time and time again in this thread, equilateral triangle covers can be dropped through their holes. Here's how:
Lift the cover up by one of the corners, pivoting at the base until the cover is standing perpendicular to the hole, at the edge of the hole.
Now lift one of the remaining corners, pivoting the cover on the remaining corner, until the oposite edge is vertical.
Push the remaining corner off of the lip.
Lid falls in.
If you're having trouble imagining that one, try this:
Push one corner down, and lift one corner up, so that the lid pivots down it's center line, and is sitting vertically in the hole, supported by one corner, and the middle of the opposite side.
Rotate the lid horizontally around the remaining corner towards one of the adjacent sides. The lid will no longer reach to the opposite side, because the centerline of the lid
is shorter than the edge of the lid.
Nope, you are wrong. The distance from the corner of the triangle to the nearest point on the opposite side is (SQRT(3)/2)*BASE. If the cover had a 1m base, the altitude would be approx 0.866m. That would fit through a 1m wide hole with 13cm to spare.
Well, First you develop a highly contageous, but harmless virus that affects only pigs*. Next you develop a highly contageous, but relatively harmless virus that affects only humans. However, his second virus becomes extremely virulent in the presence of the first virus.
The result: All of us ham-eatin' heathens curl up and die, leaving only those who have "kept themselves pure" to rule the world.
*Feel free to substitute any religeously unclean food.
The flux capacitor allowed for Time Travel, not FTL travel. The DeLorean doesn't travel more than say... 88MPH. Mind you, you could set up your time travel so that your "arrival time" would be the same as a vehicle that travelled faster than light, but you wouldn't go faster than 88.
Let's say you want to travel 186000 miles in a FTL vehicle. At c that would take you one second. At 2c that would take you half a second. In the DeLorean, at 88MPH, it would take you roughly 88 days to travel the distance. Just before you arive, you set the clock back to your departure date/time - 1/2 second. Although you arrive at the same time as an FTL vehicle, your speed is always sublight.
Company develops and sells security system.
Campus buys it.
Student cracks it.
Student helpfully goes to Company to inform them of problem.
Company blows them off.
Student goes to Campus to inform them.
Campus blows them off as well.
Student prepares to tell other students.
Company brings the DCMA hammer down on Student.
???
Massive Slashdot squabble!
Well, I guess that might fall into the "When the cat's away, the mice will play" category... or rather it's opposite. Just like when you see a police officer who's pulled over a speeder. Most people slow down, but when they are out of range, they speed up, and may even drive faster to make up for "lost time".
Slashdot Mirror
Let go of the lip issue. It is irrelevant. The relevant question is "Is an equilateral triangular shaped manhole cover immune from being dropped into its hole?"
The only things I said were obvious were that if there was no lip any shape would fall through , and that the lip can be made large enough that no lid can fall through. One reason manhole covers are round is that circles have the property that if there is any lip whatsoever, it cannot pass through it's hole.
NerveGas claimed that equilateral triangles also have this property, that if there is any lip whatsoever, it cannot pass through its hole. This is false. I explained how to do it.
Wow! You had a lake?!
Why put the storage in the camera? Because WiFi is not available in Algonquin Park.
Exactly! The British managed to send it out of the solar system. Surely the Americans can coax it into a closer orbit.
Well, basically because triangles are the topic of conversation. Specifically, the point of the discussion is whether a manhole cover shaped like an equilateral triangle can pass through its own hole. Obviously, any shape will pass through it's own hole if there is no lip to the hole. Equally obviously, any shape can be blocked if you make the lip big enough. But what if there is a trivial lip, say one cm wide lip on a metre sized hole. A circular lid cannot fall into such a hole, but can an equilateral triangle shaped manhole cover fall into its hole in that case?
In the great^n-grandpappy post, NerveGas said that equilateral triangle manhole covers cannot fall through their own holes.
I gave him a counterexample: If one of the edges of the lid is normal to the plane of the hole, and the lid is parallel to and just inside one of the edges of the hole, it can fall in.
Well *OBVIOUSLY* if you make the lip big enough, the lid will not go through. You could do that for a square cover as well. That's not the point. The parent post of this thread put forth the notion that an equilateral triangle has the same "not-able-to-go-through-a-hole-of-the-same-size (with a trivial lip)" property that a circle does. It does not. I presented two ways of visualizing how to pass it through.
Now that I think of it, you are helping my case, because you are saying you need a non-trivial lip in order to prevent the lid from falling through.
- Lift the cover up by one of the corners, pivoting at the base until the cover is standing perpendicular to the hole, at the edge of the hole.
- Now lift one of the remaining corners, pivoting the cover on the remaining corner, until the oposite edge is vertical.
- Push the remaining corner off of the lip.
- Lid falls in.
If you're having trouble imagining that one, try this:The cover would have to be a third of it's side thick in order to not fall through. Do the math.
Nope, you are wrong. The distance from the corner of the triangle to the nearest point on the opposite side is (SQRT(3)/2)*BASE. If the cover had a 1m base, the altitude would be approx 0.866m. That would fit through a 1m wide hole with 13cm to spare.
How about:
t es
Slashdot's
Lazy
Admins
Seldom
Have
Duplica
Of
Topics
That gives it the self referential flavour found in most of our favorite acronyms.
I was wondering the same thing (except with Canadian football fields which are longer and wider (four downs to make ten yards? Sheesh!)).
Since all of these fields are based on imperial measurements, I say we ditch them all, and use volleyball courts, which are metric.
Most 486s don't have PCI slots.
If it was really that bad they'd replace their front page with a clear and concise instructions on how businesses can fix the problem.
Assuming Microsoft knows how to fix it.
Well, First you develop a highly contageous, but harmless virus that affects only pigs*. Next you develop a highly contageous, but relatively harmless virus that affects only humans. However, his second virus becomes extremely virulent in the presence of the first virus.
The result: All of us ham-eatin' heathens curl up and die, leaving only those who have "kept themselves pure" to rule the world.
*Feel free to substitute any religeously unclean food.
Simple: Nobody really cares about Municipal politics in Ontario.
The flux capacitor allowed for Time Travel, not FTL travel. The DeLorean doesn't travel more than say... 88MPH. Mind you, you could set up your time travel so that your "arrival time" would be the same as a vehicle that travelled faster than light, but you wouldn't go faster than 88.
Let's say you want to travel 186000 miles in a FTL vehicle. At c that would take you one second. At 2c that would take you half a second. In the DeLorean, at 88MPH, it would take you roughly 88 days to travel the distance. Just before you arive, you set the clock back to your departure date/time - 1/2 second. Although you arrive at the same time as an FTL vehicle, your speed is always sublight.
Well, Lunchtime's over... Back to reality.
It isn't Calculus. It's Topology.
There are programs that do that... along the lines of Jive.
Here's the breakdown as far as I've read.
Company develops and sells security system.
Campus buys it.
Student cracks it.
Student helpfully goes to Company to inform them of problem.
Company blows them off.
Student goes to Campus to inform them.
Campus blows them off as well.
Student prepares to tell other students.
Company brings the DCMA hammer down on Student.
???
Massive Slashdot squabble!
Well, if they can convince the ATMS on the campus network to dispense funds through the security hole, they can afford lawyers.
Nice try. Of all of the people ever born, half of them are still alive.
Well, I guess that might fall into the "When the cat's away, the mice will play" category... or rather it's opposite. Just like when you see a police officer who's pulled over a speeder. Most people slow down, but when they are out of range, they speed up, and may even drive faster to make up for "lost time".
Grandma would be a lot safer with a decent door and deadbolt than with a gun.