A line with 3 corners...

Want to know your ideas/philosphy on this project… I have my ideas (posted below) on a line with 3 corners… seems impossible… but then again this is a creative/philosophical assignment.

The assignment states the following:
“Draw a line with three corners”

Black ink on 7 3/4" x 7 3/4" sheet of paper

No mounting, borders, frames, folding, or cutting into the paper.
No use of photos, drawings, images, or letters / type.

Only present one sheet.

My ideas:
If you have a square peice of paper. there are only a few ways I think it is possible to draw a line. If you consider a line a continual entity. If it breaks, bends or turns, it is the make up of multiple line segments.

Picture: notjustawall.com/Lineidea1.jpg

This has a few flaws. For one, the line itself doesn’t have 3 corners but it divides each space into having 3 corners. and in fact it actually divides the entire papyer into having 6…

Picture: notjustawall.com/Lineidea1.jpgLineidea…,

This one is actually of a line segment which is just looked at from one side. Allowing the remaining lines to be under the others, as in an arial view. When looked at sideways it shows a triangle that has 3 corners…

This has a few flaws, as stated above, it is a line segment. Secondly, it is actually a compilation of several line segments to make up a triangle. And thus bringing me to my last idea (lineidea1.jpg) that the line itself doesn’t actually have 3 corners but mearly only 2, the rest of the lines compose the other 2 corners…

Please feel free to attack this any way you see fit. and try to the best of your knowledge to explain your thoughts/ideas. Mine seemed to have too many flaws to be a good enough answer. So I’m looking around for other peoples ideas.


It rather depends on how you define “line”. If you mean straight line, then it is not possible to have any corners, by definition. If you do not mean straight line, then you simply draw a square without joining the final right angle.

Thanks, Obw. I thought it was just me.

Chad, I think this is obviously a creative assignment…so I’m going to be creative. I’d draw a line on the piece of paper, and call it done. Why? I’m glad you asked.

The piece of paper has three corners. True, it also has a fourth, but it doesn’t say anything about a fourth. In order to get to four, one necessarily has three corners. The line itself doesn’t have them, but I’m not sure it has to. A line with three corners could simply mean a line accompanied by three corners just as easily as it could mean a line that actually itself has three corners.

The fourth corner, if anything, simply proves there are three corners, and since it is not forbidden, you’ll have completed your assignment with relative ease.

well i actually have another idea, and those are great responses, thanks guys…

Well as stated above, a line, continuous, never ended… is near impossible…

near i say? yes…

well if you the paper, (the space) the line sstill continues in the same path as originally set. so you can easily form a triangle with the concept that the paper rotates at the corner each time you come to it making an infinite amount of overlaps, thus making one line with 3 corners!

If this was a Zen-do question, you’d all be getting your butts whipped! :smiley:

Well in class today I started looking around and came up with a correct answer to this problem.

I feel that this assignment has no REAL answer. All answers, if justified, can be correct. So, the real reason for this assignment is to simply get the class interacting with one another to discuss the “complexity” of this assignment. When in reality it is all based off of everyones own interpritations of a line, corner, space, etc…

SO that being said… I think i’m going to leave it at that, and hope for some more feed back on this response!

Talk to you guys later!

Did you pay money for this class?

heh! Well I just came up with a GREAT idea. What would you guys think of this? We think of a line as a straight object moving in a continuous motion, for instance, ----------------- is a line.

Well lets jump back and think of this a little differently. There are many other types of lines. We have a football line which have corners…

This brings me to a problem though, it says No use of pictographs, images, or letters. How can I do this without using a pictograph?

Well, I started thinking some more on this project since it has been bothering me a great deal. The assignment requirements state that there can be no use of pictographs. The definition of a pictograph is “A picture representing a word or idea; a hieroglyph” - Dictionary.com

That would mean that anything we put down on that paper would be against the rules of the assignment. Is this one big trick? ponders

As well, I figured out how to make 3 corners without any additional corners. Simply put an arrow ------> , 2 near the shaft of the arrow head, and one at the point of the arrow head. making 3 corners.

This assignment is 3 orders of magnitude too stupid.

Please eloborate.

chadz - we don’t think of a line as moving at all. They’re just fucking with your head.

well , if u think of a number line …

or a line at all… it has to go in a certain direction, not necessarily moving… but to draw a whole line, not a segment…

I still like my original solution.

Is it true that you’ve drawn a line with one corner? Yes.
Two? Yes.
Three? Yes.***
Four? Yes.

Done deal!

My opinion of what a line is defined in basic geometry. Basically, infinite until given a point which then makes the line a line segment.

Going by any rules posed in mathemetics and its many areas, a line can’t have a corner. The point of the corner is exactly that. A point. If you decide to add another line there then it’s the point in which the two lines meet thus creating an angle. All you would be accomplishing is creating three points at which three different lines meet making three angles.

As for creating a line with three arrows…that’s just adding three angles with six other lines onto a line already there.

It’s impossible for one line to have three corners…

“A line with three corners” is a very vague sentence. By itself it is not at all clear what it means. To me it seems the exercise would either illustrate the need for precise definitions and distinctions in philosophy, or it could be a free-association creative thinking kind of thing. In that case, I offer some ‘creative’ possibilities:

  1. A (USA) football line with three cornerbacks
  2. A straight line drawn on a paper with three folds in it, and looked at obliquely so the line projects onto our vision like this: //\
  3. A straight drawn line, adjacent to three L’s: “a line ‘with’ three corners”
    etc. etc… this sort of thing just keeps feeding itself. Maybe there is something interesting about perception or language to be learned here. But to my critical faculties the ambiguity is just annoying. Maybe that’s a problem with my brain…

Is there such a thing as a line or is it a human generalization?

This has a few problems.

For one, the requirements state:

which kills your football idea, it is a good one, and was already thought of by another friend of mine. The basis thats its wrong is for the fact that the only way I can demonstrate that is to draw small figures to represent a football player, (requirement: No pictorgraphs)

secondly, the folding of the paper is also against the requirements.

I re-read the requirements several times to come to the conclusion that we can’t draw anything on this peice of paper. It is to represent the ideas of our “line” with 3 corners… That isn’t possible because that would be a picture representing our idea or word, which is a pictograph!

Let me know what you guys think of this scenario

heh. I thought about this solution, actually. Here’s the problem with my original solution:

“No use of photos, drawings, images, or letters / type”

Here’s the problem with the command:

Draw a line with three corners.

If I can’t use drawings, I can’t draw a line. What you are told to do is then later prohibited. That means, to me, anything is fair game–even nothing.

To say, “I didn’t even think of this assignment and so therefore have nothing to turn in is fair game.” After all, with a contradiction in place, what is there to think about?