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RWarehall: Ah shit, an edit over silliness...
I am outRAAAAAGED.

Deadline is now 6:40 am.
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cristigale: I often use this in class. After they figure out the 3 line solution, my next question is; How can you do it in one line?
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Krypsyn: Assuming the lines must be perfectly straight, and the points lay on a plane that is unbendable, it isn't possible.
Actually, it is, but you have to think outside the box.
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cristigale: Actually, it is, but you have to think outside the box.
Nope. Not given the requirements I gave:

1) Never picking up the pencil (or whatever), but draw straight lines (a change in straightness constitutes a new 'line')
2) the points are dimensionless, the lines are single dimension
3) the points are on a Euclidean plane that cannot be manipulated

Do tell, how that would be possible?
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cristigale: I often use this in class. After they figure out the 3 line solution, my next question is; How can you do it in one line?
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Krypsyn: Assuming the lines must be perfectly straight, and the points lay on a plane that is unbendable, it isn't possible.
9 dots on a square, 3 perfectly straight lines can cover all of them, even with the points being on a single unbendable euclidean plane. Why? Because you missed the "don't raise your writing utensil" part ;)
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cristigale: Actually, it is, but you have to think outside the box.
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Krypsyn: Nope. Not given the requirements I gave:

1) Never picking up the pencil (or whatever), but draw straight lines (a change in straightness constitutes a new 'line')
2) the points are dimensionless, the lines are single dimension
3) the points are on a Euclidean plane that cannot be manipulated

Do tell, how that would be possible?
I use a marker instead of pencil, you probably wouldn't think of pencil in this way. Does that help?
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cristigale: I can verify, RWarehall's posts merged. The original post was just the first line.
scumpatriots working together?!!!!!! *jokes*

dooodooodooooo
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JMich: ... you missed the "don't raise your writing utensil" part ;)
I did not.

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cristigale: I use a marker instead of pencil, you probably wouldn't think of pencil in this way. Does that help?
A single dimension marker wouldn't change the results at all.
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JMich: ... you missed the "don't raise your writing utensil" part ;)
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Krypsyn: I did not.
Read the post I quoted. Read the post you quoted in the post I quoted. No "no raising" :)
It would if it was a REALLY thick marker. :)
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JMich: No "no raising" :)
I said "never picking up". So, unless you wish to interpret it as did dreamler7 (still the best answer), it means the same thing.

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cristigale: It would if it was a REALLY thick marker. :)
Single dimensional items have thickness? :P
dootdoooo
Deadline is 6:35 am 19 hours from now.

I'll be out for 3-5 hours this afternoon, just fyi. Family easter gathering then driving back north.
doooooooooooo
Missed the single part. :-O

Yes, a single dimension utensil is impossible.
doooooodoooooo

zipzip!