Timeline for Make exactly 101 squares using as few lines as possible
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| May 30 at 16:39 | comment | added | Daniel Wagner | @Deusovi Ahhhh, whoops! That looks hard to fix indeed. My mistake. | |
| May 30 at 8:55 | comment | added | apg | Its not difficult to get a vector space from any surface embeddable in $\mathbb{R}^3$, the conditions should just follow naturally, you don't need any metric or anything. | |
| May 30 at 0:28 | comment | added | Deusovi♦ | @DanielWagner Those operations aren't well-defined. The point (0.5,0) should be the same as (1.5,0), but what do you get when you scale them by 1/2 ? | |
| May 29 at 22:16 | comment | added | Daniel Wagner | @Deusovi Why can't a vector space over the reals wrap around? For my vector space I choose $(\mathbb R\hspace{3pt}/\sim)\times\mathbb R$, where $x\sim y$ iff $x-y\in\mathbb Z$; addition and scalar multiplication are the obvious pointwise ones. Looks like it satisfies all the vector space laws listed on Wikipedia to me. | |
| May 29 at 17:12 | comment | added | Deusovi♦ | @DanielWagner Sorry, but this isn't a vector space - a vector space over the reals can't wrap around. It is, at best, a manifold... but if you're fine with lines on any manifold, why not just cut 'wormholes' in the plane to make it one line? | |
| May 29 at 11:07 | history | edited | Daniël van den Berg | CC BY-SA 4.0 |
added 88 characters in body
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| May 29 at 5:18 | history | edited | Daniël van den Berg | CC BY-SA 4.0 |
added 141 characters in body
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| May 29 at 1:41 | comment | added | Hearth | I believe you'd also get some squares that wrap around the cylinder, if your circumference is an integer multiple of the square size. Make the circumference not an integer (or even irrational just to be safe) to avoid this. | |
| May 29 at 1:39 | comment | added | Hearth | This is 2-dimensional anyway--it's just that one of the dimensions loops. | |
| May 29 at 1:07 | comment | added | Will.Octagon.Gibson | @DanielWagner Thanks for posting your model. I now understand your design. | |
| May 28 at 21:16 | comment | added | Xander Henderson | I am too lazy to try to draw this up right now, but you can do it with just two lines on a torus using a similar kind of idea. | |
| May 28 at 19:35 | comment | added | Daniel Wagner | @WillOctagonGibson I can't draw, so I made a model out of string and scotch tape. Although these lines aren't straight in traditional Euclidean 3-space, there is a well-defined vector space where they are indeed exactly straight (and exactly orthogonal, unlike my quick+sloppy model)! I think there's one detail that needs attention and is glossed over in the answer, but it should be easily handled, namely, you have to be careful that you don't make large squares that wrap around the cylinder the "long" way! | |
| May 28 at 18:29 | comment | added | Will.Octagon.Gibson | Regardless of whether your solution is valid or not, it is interesting. I hope you or someone else posts an image of it. | |
| May 28 at 18:27 | comment | added | Will.Octagon.Gibson | In my puzzle, I did not say that the solution had to be 2-dimensional so I will allow a 3-dimensional solution. I can’t quite visualize your solution. Your first line that wraps around the cylinder might be a problem. I suspect that it is not a straight line in 3-dimensional space. I required lines to be straight. Also squares in 2-dimensional and 3-dimensional space consist of perfectly straight line segments. | |
| May 28 at 8:03 | history | answered | Daniël van den Berg | CC BY-SA 4.0 |
