Calc Problem....? coffee spill, grid, and vertices

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Muteki

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I'm working on a problem for extra credit that my calc prof threw at us at the end of class today. It seems pretty simple, but I wanted to get some opinions regarding the question.

The situation is that you have an infinite plane going in every direction, and on this plane is a grid with squares that are 1 inch by 1 inch. You spill coffee on this plane, but the spilled coffee covers less than 1 in^2. Is it possible to move the grid so there will be no coffee on the vertices's? If so, why, if not, why not?
 
Is it possible to move something that is intangible and stretches without bound? Just what should you do if you wanted to "shift" something that recedes into the distance indefinitely? At what point in 3 dimensional space will the plane have moved to once you shift it? It doesn't really make much sense to me. Think of the distance west/north/east/south of the coffee spill as a limit tending to infinity, if that helps.
 
I am only in Algebra 2, but here is my thought:

No, you cannot move the spill off. You need to move the spill, but any way you move it is a definate, measurable amount, therefore it is limited and cannot be moved to infinity. Hope it makes sense but this is a guess.
 
I think he meant moving the grid independently of the coffee spill, but I am not sure. I honestly do not think he thought the problem out much when he offered it as extra credit.
 
I'd be interested to see what the more knowledgeable posters on this message board think about your teacher's problem.
 
Nature of the spill:

Does it all stick together, or is there spashing? A few drops landed over there somewhere...

If you build a trough, and spill in that, you can get a very long line that crosses no vertex of you lattice, but that may be more control that you would want.

Is the spill entirely random? If so, there is non-zero probability that you would be able to find a patern with no vertex interference.
 
The question is nonsense. It could mean anything.
Don't waste any time on it.
 
I kind of thought the same thing, pka. Why would a professor pose something wacky like that when there are an endless amount of other worthwhile problems that could be given?.
 
So here is the solution he gave us today....

If you take the grid on the plane and cut the plane using the grid and stack the squares on top of each other, there will be at least one point in each square where there would be no coffee since the area covered by coffee is less than 1 in^2. You mark this point and replace the squares to their original positions. Now take the grid and move the grid so the vertices's are on these points.
 
I must say, that is a rather frivolous problem. I wonder what pka has to say about that one. Your professor may just have a good sense of humor.
 
galactus said:
I must say, that is a rather frivolous problem. Your professor may just have a good sense of humor.
Click to expand...
I AGREE!
Only I would not dignify that instructor with the title ‘Professor’.
I standby my original statement: The problem is nonsense and the solution is total nonsense! Read tkhunny post. He is absolutely right. If we ignore the physical properties of a liquid, we can construct sets that make any solution impossible. Moreover, if the grid is “put back together” any ‘glide transformation’ of one vertex would change all other vertices.
 
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