If you can do this then you can also solve it in one stroke: just choose a pen stroke wider than the entire diagram.bobsbarricades wrote:To me this makes perfect sense - it's like zooming out and the only problem then becomes, "well how big is the dot and how wide is your pen stroke..."

## Search found 198 matches

- Mon Nov 10, 2008 4:48 pm UTC
- Forum: Logic Puzzles
- Topic: The 9-dot/point problem
- Replies:
**11** - Views:
**8369**

### Re: The 9-dot/point problem

- Mon Oct 27, 2008 9:17 pm UTC
- Forum: Logic Puzzles
- Topic: Portal Paradox
- Replies:
**137** - Views:
**33753**

### Re: Portal Paradox

I think a lot of this discussion comes down to what rules people are playing by, or rather, the discussion is over what rules we could be playing by. In the game of course, portals do not move continuously, which is one set of consistent rules. We seem to be arguing about or whether they can move or...

- Sun Oct 26, 2008 10:47 pm UTC
- Forum: Logic Puzzles
- Topic: Portal Paradox
- Replies:
**137** - Views:
**33753**

### Re: Portal Paradox

This is getting kindof close to Zeno's arrow paradox , although maybe we shouldn't go there yet. Let's go down another dimension for a different example. The world is a 1 dimensional line (-\infty,\infty) . Someone opens up a portal entrance and exit. Instead of disks in 2d they are now inte...

- Sun Oct 26, 2008 9:56 pm UTC
- Forum: Logic Puzzles
- Topic: Portal Paradox
- Replies:
**137** - Views:
**33753**

### Re: Portal Paradox

Ok, so put the hole back in, punch a new hole epsilon to the right, reconnect the tube... so what? Everything is continuous here, nothing "breaks" as far as I can see...

- Sun Oct 26, 2008 9:20 pm UTC
- Forum: Logic Puzzles
- Topic: Portal Paradox
- Replies:
**137** - Views:
**33753**

### Re: Portal Paradox

Lines are really geodesics in a space like this, which you can specify by saying that they start at some location with some initial direction, and extend in either direction. E.g. in the left hand diagram there is a vertical line that joins the two red arrows. The geodesic you get on that line just ...

- Sun Oct 26, 2008 6:27 pm UTC
- Forum: Logic Puzzles
- Topic: Portal Paradox
- Replies:
**137** - Views:
**33753**

### Re: Portal Paradox

Ok, so your question is how to move the tube without compressing/stretching space. The answer is that you cannot, the only meaningful sense of "moving the tube" that is intrinsic to the 2d space is "stretching", or changing the metric on the space. But so what? I think maybe the ...

- Sun Oct 26, 2008 6:27 am UTC
- Forum: Logic Puzzles
- Topic: Portal Paradox
- Replies:
**137** - Views:
**33753**

### Re: Portal Paradox

I don't see where you're getting your intuition on this from, either from the game or from something else. Hmm, as I was thinking about how to answer you I realised that there is something undefined so far about how portals work. Suppose we fire entry and exit portals at a wall as usual. Now go arou...

- Sat Oct 25, 2008 5:00 pm UTC
- Forum: Logic Puzzles
- Topic: Portal Paradox
- Replies:
**137** - Views:
**33753**

### Re: Portal Paradox

Now, in order for this portal to 'move through the world', one would have to move the slit. This is equivalent to trying to move a hole. You can't move a hole, you can only move the matter around the hole. Why? We can imagine continuously varying the geometry of the space so that the position of th...

- Thu Oct 23, 2008 3:18 am UTC
- Forum: Logic Puzzles
- Topic: Polynomial of two variables
- Replies:
**9** - Views:
**1946**

### Re: Polynomial of two variables

Didn't seem to take you long though!skeptical scientist wrote:This one was surprisingly tricky.

- Thu Oct 23, 2008 1:22 am UTC
- Forum: Logic Puzzles
- Topic: Polynomial of two variables
- Replies:
**9** - Views:
**1946**

### Polynomial of two variables

Find a polynomial of two variables [imath]p: \mathbb{R}^2 \rightarrow \mathbb{R}[/imath] such that the range of [imath]p[/imath] is [imath](0,\infty)[/imath].

- Sat Oct 18, 2008 5:55 pm UTC
- Forum: Logic Puzzles
- Topic: Portal Paradox
- Replies:
**137** - Views:
**33753**

### Re: Portal Paradox

Ah yes, I see my mistake. The 2nd largest horizontal slab should have the red portal on the lower side. The picture scales down and rotates 90 degrees at each step.

- Sat Oct 18, 2008 5:31 am UTC
- Forum: Logic Puzzles
- Topic: Portal Paradox
- Replies:
**137** - Views:
**33753**

### Re: Portal Paradox

nsmjohn: It isn't a singularity in the black holes and relativity sense. That requires curvature of space, and there isn't any curvature in Portal, it's all just Euclidean space with unusual connectivity (besides, if that were an event horizon, you wouldn't be able to see inside of it would you?). t...

- Sun Oct 12, 2008 4:50 am UTC
- Forum: Logic Puzzles
- Topic: Portal Paradox
- Replies:
**137** - Views:
**33753**

### Re: Portal Paradox

Not true. You can certainly have differently sized portals. Repeatedly passing an object through the two portals shrinks or grows the object. I think it might look something like this halfway through, but there's definitely some weird stuff going on here: http://www.segerman.org/random/portal.jpg

- Fri Oct 10, 2008 6:10 am UTC
- Forum: Logic Puzzles
- Topic: Portal Paradox
- Replies:
**137** - Views:
**33753**

### Re: Portal Paradox

See alt text of xkcd 199.

- Mon Oct 06, 2008 8:09 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0485: "Depth"
- Replies:
**145** - Views:
**32590**

### Re: "Depth" Discussion

Would have been nice to see Maxwell's Demon doing its thing somewhere down there.

- Sat Oct 04, 2008 10:33 pm UTC
- Forum: Mathematics
- Topic: Volume of a not-really hexahedron
- Replies:
**12** - Views:
**2347**

### Re: Volume of a not-really hexahedron

It sounds like you have something that you can cut up into a cuboid (the middle of the shape) with other bits on the top and bottom, which I think you can further cut up into right isoceles triangular prisms and tetrahedra with one trianglular face being another right isoceles triangle. All of these...

- Fri Oct 03, 2008 4:18 am UTC
- Forum: Logic Puzzles
- Topic: Draw a straight line
- Replies:
**63** - Views:
**7339**

### Re: Draw a straight line

It depends of course on how you interpret the question. It was intended, fwiw, as a mathematical question about constructing the line, although it can be stated in a colloquial way.

- Wed Oct 01, 2008 8:03 pm UTC
- Forum: Logic Puzzles
- Topic: Draw a straight line
- Replies:
**63** - Views:
**7339**

### Re: Draw a straight line

Well done all, in the end we get a solution better than the one I knew of. The version I knew before involved a construction using Pappus' theorem, which depending on how you draw it lets you connect two points that are Sqrt(2) - epsilon units apart, where 1 is the length of the straight edge. You t...

- Thu Sep 25, 2008 7:12 pm UTC
- Forum: Logic Puzzles
- Topic: Draw a straight line
- Replies:
**63** - Views:
**7339**

### Re: Draw a straight line

Ok, here's a (pretty strong) hint:

**Spoiler:**

- Thu Sep 25, 2008 4:36 pm UTC
- Forum: Logic Puzzles
- Topic: Draw a straight line
- Replies:
**63** - Views:
**7339**

### Re: Draw a straight line

Ok, that's fair, although the solution I know doesn't need that use of it. Perhaps it is an evil straight edge that continually alters its length within some small range of values around a foot

- Thu Sep 25, 2008 5:59 am UTC
- Forum: Logic Puzzles
- Topic: Draw a straight line
- Replies:
**63** - Views:
**7339**

### Re: Draw a straight line

The puzzle as originally intended does not allow you to use the straightedge as a compass. I think this will formalise what you're intended to be able to do: You can: ⋅ Draw a straight line segment between two points p and q you have previously marked (or p or q is one of A or B) that are ...

- Thu Sep 25, 2008 2:51 am UTC
- Forum: Logic Puzzles
- Topic: Draw a straight line
- Replies:
**63** - Views:
**7339**

### Re: Draw a straight line

Ok, I buy it, another neat solution! So we can do it with a zero thickness straight edge and a zero thickness set square in two different ways.

- Thu Sep 25, 2008 12:22 am UTC
- Forum: Logic Puzzles
- Topic: Draw a straight line
- Replies:
**63** - Views:
**7339**

### Re: Draw a straight line

How do you get the midpoint between a and the intersection of A and B?

I can see how you could use the length of the straightedge if the total length was an even multiple of the length of the straightedge, but it won't be in general.

I can see how you could use the length of the straightedge if the total length was an even multiple of the length of the straightedge, but it won't be in general.

- Wed Sep 24, 2008 4:59 pm UTC
- Forum: Logic Puzzles
- Topic: Draw a straight line
- Replies:
**63** - Views:
**7339**

### Re: Draw a straight line

The problem statement indicated you were standing on an infinite plane . Also, the instructions did not specify to draw a line from point A to B with the shortest distance. Ok, sure the statement of the problem wasn't set up to unnecessarily complicate things in order to nail it down to only the on...

- Wed Sep 24, 2008 4:35 am UTC
- Forum: Logic Puzzles
- Topic: Draw a straight line
- Replies:
**63** - Views:
**7339**

### Re: Draw a straight line

In what geometry is that path a geodesic deezie?

- Wed Sep 24, 2008 4:01 am UTC
- Forum: Logic Puzzles
- Topic: Draw a straight line
- Replies:
**63** - Views:
**7339**

### Re: Draw a straight line

Buttons: nice! I hadn't seen that solution before.

Now do it with a straight edge of 0 width.

Now do it with a straight edge of 0 width.

- Tue Sep 23, 2008 10:54 pm UTC
- Forum: Logic Puzzles
- Topic: Draw a straight line
- Replies:
**63** - Views:
**7339**

### Re: Draw a straight line

It's solvable without either of those two things, but by all means, assume them if you wish. You also don't need to use that the pencil is straight, or that it has a particular length. We are assuming that the straight edge is perfectly straight, and that we can draw lines perfectly against it, draw...

- Tue Sep 23, 2008 7:24 pm UTC
- Forum: Logic Puzzles
- Topic: Draw a straight line
- Replies:
**63** - Views:
**7339**

### Draw a straight line

You have a straight edge, approximately a foot long, with no markings of any sort on it. You are standing on an infinite plane of paper next to a point which is marked on the plane and labelled 'A'. Approximately a mile away there is another point, labelled 'B'. You have a pencil. Draw a straight li...

- Mon Sep 22, 2008 11:35 pm UTC
- Forum: Mathematics
- Topic: Question about Infinity
- Replies:
**72** - Views:
**5265**

### Re: Question about Infinity

Here is a very nearly right way to map the unit square (the set of (x,y) with 0 <= x,y <= 1) to the unit interval (the set of z with 0 <= z <= 1) in a one to one fashion: Suppose the decimal expansions of x and y are 0.x_1x_2x_3 \ldots and 0.y_1y_2y_3 \ldots . Choose as a corresponding point on the ...

- Mon Sep 22, 2008 9:38 pm UTC
- Forum: Mathematics
- Topic: Question about Infinity
- Replies:
**72** - Views:
**5265**

### Re: Question about Infinity

The "size" (the word is really "cardinality") of the natural (or whole) numbers is the same as for the integers. Ditto for the rational numbers (p/q where p and q are integers with q not equal to 0). The cardinality of the real numbers is larger than that of the natural numbers. ...

- Tue Sep 16, 2008 6:38 am UTC
- Forum: Mathematics
- Topic: Randomly Generated Images
- Replies:
**26** - Views:
**4384**

### Re: Randomly Generated Images

But there are many more images that are meaningful than will ever be produced by humanity. If we just look at the subset of images that look like a page from a book then we get any meaningful sequence of 500ish words, and there are far more of them that we will never write down than those that we wi...

- Mon Sep 15, 2008 5:33 pm UTC
- Forum: Mathematics
- Topic: Randomly Generated Images
- Replies:
**26** - Views:
**4384**

### Re: Randomly Generated Images

A couple of thoughts: What percentage of images get their data size reduced by (insert your favourite) lossless image compression algorithm? This isn't quite the same as "meaningful", but given that the compression algorithms are designed to hopefully reduce the data size of images that pe...

- Mon Sep 01, 2008 6:28 pm UTC
- Forum: Logic Puzzles
- Topic: Very, very, very, easy.
- Replies:
**57** - Views:
**15596**

### Re: Very, very, very, easy.

I can't take credit for those answers, I just asked a similar question and set up the website. I will however donate the gold stars to the appropriate people.

- Mon Sep 01, 2008 3:18 pm UTC
- Forum: Logic Puzzles
- Topic: Very, very, very, easy.
- Replies:
**57** - Views:
**15596**

### Re: Very, very, very, easy.

http://www.segerman.org/autological.html#autological_numbers

These aren't answering exactly the same question, but some of them do work, in particular "twocubed", "phi(7)" and "thenumberofmembersofthejedicounciltimesfivelessten".

These aren't answering exactly the same question, but some of them do work, in particular "twocubed", "phi(7)" and "thenumberofmembersofthejedicounciltimesfivelessten".

- Sun Aug 31, 2008 5:53 am UTC
- Forum: Mathematics
- Topic: Math for Particle Movement
- Replies:
**21** - Views:
**1621**

### Re: Math for Particle Movement

Trig functions are pretty slow in comparison to a lot of other stuff, and there's usually a way to avoid using them. Even better if you can avoid having to square root things, although I don't think you can manage that here. It doesn't look like you have a class set up for vectors, which would make ...

- Thu Jul 31, 2008 5:06 pm UTC
- Forum: Mathematics
- Topic: Math Websites
- Replies:
**125** - Views:
**179292**

### Re: Math Websites

Self links, but seem like the kinds of things people here might be interested in: http://www.segerman.org/printgallery/index.html - Escher's printgallery redone with photographs, based on a project by Hendrik Lenstra that worked out the mathematics behind Escher's image ( http://escherdroste.math.le...

- Thu Jul 31, 2008 2:49 pm UTC
- Forum: Mathematics
- Topic: Careers for Mathematicians EXCEPT Finance, Teaching or Stats
- Replies:
**15** - Views:
**2448**

### Re: Careers for Mathematicians EXCEPT Finance, Teaching or Stats

The UK equivalent of the NSA is called GCHQ.

- Fri May 30, 2008 10:06 pm UTC
- Forum: Mathematics
- Topic: Doing original work in mathematics
- Replies:
**8** - Views:
**2040**

### Re: Doing original work in mathematics

But the number of interesting facts worth proving and publishing doesn't necessarily increase with the number of facts proven. Areas of math can get "mined out" if all the interesting questions get settled, or nobody has any idea how to progress.

- Sat May 24, 2008 7:55 pm UTC
- Forum: Mathematics
- Topic: The golden ratio, spirals, in 3d
- Replies:
**3** - Views:
**1394**

### Re: The golden ratio, spirals, in 3d

A couple of thoughts: An algorithm rather than a formula might still be interesting. That is, we can just require the k^{th} node to go on the sphere of radius \sqrt[3]{k} and choose it so that it maximises the distance to any previously plotted node. I'd like to see what this looks like, I think it...

- Wed May 21, 2008 6:19 pm UTC
- Forum: Mathematics
- Topic: so maths is useful for what now?
- Replies:
**31** - Views:
**3582**

### Re: so maths is useful for what now?

mathematicians often blatantly disregard "proper" mathematics in favor of "this should work out, so I'm going to do it." It then takes other mathematicians a while to catch up to providing proper justification for why the mathematician can (or can't) do that. same happens in all...