## Search found 179 matches

Fri Jun 15, 2012 2:46 am UTC
Forum: Mathematics
Topic: Curvy Pareto Frontiers?
Replies: 3
Views: 1100

### Re: Curvy Pareto Frontiers?

It seems to me that in many cases, the things being traded off between are pretty linear (in, for example, the classic case of government spending on guns vs butter, one billion spent on guns is a billion that can't be spent on butter), so the front should be a line. I think when you normally look ...
Wed Mar 21, 2012 3:06 am UTC
Forum: Mathematics
Topic: Curve fitting
Replies: 25
Views: 6146

### Re: Curve fitting

This seems like a stupid question after that big discussion, but isn't the OP somewhat contradictory? When I see "complexity" related to algorithms, I think big O notation. I.e. mathematically analyzing the algorithm to determine worst case behavior. When I see "time" for an algo...
Wed Mar 21, 2012 2:59 am UTC
Forum: Mathematics
Topic: Is there a name for this?
Replies: 12
Views: 3285

### Re: Is there a name for this?

Therefore for any rational number, squaring it twice has a 10% chance of ending in 0; 10% ending in 5; 40% ending in 6; and 40% ending in 1. I'm surprised that no one has mentioned this part yet. This statement is meaningless without a probability distribution on the integers [I assume that's what ...
Wed Mar 21, 2012 2:55 am UTC
Forum: Mathematics
Replies: 54
Views: 9566

Rather than continuing to beat this dead horse, I would like to see arbiteroftruth come up with some basic axioms. Either they will be rife with contradictions, or the system will be basically useless, or he'll develop an entirely new, exciting branch of math. Regardless of the outcome, it will be a...
Sun Sep 25, 2011 9:32 pm UTC
Forum: Mathematics
Topic: Traversal across 3D object
Replies: 9
Views: 1353

### Re: Traversal across 3D object

What I'm trying to do is create a distributed-geometry application where, for instance, you could specify objects of grass, rocks, etc and it would distribute them over a surface. The double-interpolating method works decently well but it does tend to create quite a few clumps. The method you descr...
Thu Sep 01, 2011 1:50 am UTC
Forum: Mathematics
Replies: 187
Views: 277024

My paper was published in the Journal of Number Theory. Unfortunately there doesn't seem to be a free way to access it... all I have is the reference info.

J. Number Theory
131 (2011), 2442-2460.
Sun Aug 14, 2011 5:24 am UTC
Forum: Mathematics
Topic: Lawnmower Problem
Replies: 12
Views: 2531

### Re: Lawnmower Problem

I figured that much out. Actually getting the answer I'm less sure about.
Sun Aug 14, 2011 4:51 am UTC
Forum: Mathematics
Topic: Minecraft Shorelines are loops?
Replies: 18
Views: 3004

### Re: Minecraft Shorelines are loops?

>> you pick a shoreline near your spawn point and start following it, what is the probability that you will end up back where you started? It is 1. If you start at a finite lake or at a finite landmass, you will surround the lake/landmass and end up where you started. To walk for infinity time, bot...
Sat Aug 13, 2011 11:24 pm UTC
Forum: Mathematics
Topic: Lawnmower Problem
Replies: 12
Views: 2531

### Lawnmower Problem

Suppose you have a lawn of width W and of an arbitrary length (we'll come back to that later). Conveniently, your lawnmower has a blade of width W, which spins at rate of R radians/second. If you push your lawnmower straight across your lawn at a constant speed of S units/second, what percentage* of...
Sun Jul 24, 2011 1:49 am UTC
Forum: Mathematics
Topic: John and his internet history
Replies: 12
Views: 2360

### Re: John and his internet history

I approve of math forum people pointing out all the assumptions required that I didn't even realise I was making (and probably that the OP didn't realise needed to be made explicit). Pedantry is nice to a point, but eventually you're just being a jerk and trying to avoid the intended question. Anot...
Fri Jul 22, 2011 5:08 am UTC
Forum: Mathematics
Topic: Example of a non-surjective function
Replies: 7
Views: 8159

### Re: Example of a non-surjective function

"range" is somewhat ambiguous, unfortunately. The term "range" almost always means image, and using it that way should never cause confusion (while using it otherwise will often lead to confusion). The set that the function maps into is usually called the "codomain" or...
Fri Jul 22, 2011 4:31 am UTC
Forum: Mathematics
Topic: John and his internet history
Replies: 12
Views: 2360

### Re: John and his internet history

Are we assuming that all the commands clear the most recent existing history? I.e. Clearing the past hour twice in a row clears the past two hours? That makes the problem more interesting than undecim's trivial interpretation. It also matters whether we're considering order when we count the number ...
Fri Jul 22, 2011 4:08 am UTC
Forum: Mathematics
Topic: A criminal hides in a room with 99 innocent people...
Replies: 13
Views: 4477

### Re: A criminal hides in a room with 99 innocent people...

This is clearly a case of different interpretations resulting in different answers. I agree with skeptical scientist's answer, but apparently the question was removed from the OP and replaced with a different one?
Sat Jul 16, 2011 7:38 am UTC
Forum: Mathematics
Topic: Wrong on the Internet II: Norman J. Wildberger
Replies: 85
Views: 50329

### Re: Wrong on the Internet II: Norman J. Wildberger

I resent words being put in my mouth. I know what I meant, and I have edited the OP to make clear the distinction.
Fri Jul 15, 2011 5:07 am UTC
Forum: Mathematics
Topic: Wrong on the Internet II: Norman J. Wildberger
Replies: 85
Views: 50329

### Re: Wrong on the Internet II: Norman J. Wildberger

Well... anyway. I'm sorry that my rhetoric offended you, jesting. I said that Wildberger and Gabriel would be "best friends" because they both want to abolish irrational numbers. That's it. I have already pointed out that I am aware that their approaches are fundamentally different. You se...
Sat Jul 09, 2011 11:01 pm UTC
Forum: Mathematics
Topic: Wrong on the Internet II: Norman J. Wildberger
Replies: 85
Views: 50329

### Re: Wrong on the Internet II: Norman J. Wildberger

Well I'd like to clarify that I was not equating Wildberger and Gabriel. I am aware that Wildberger does get published in journals and that he appears to have a legitimate background in mathematics (unlike Gabriel). However I still maintain that Wildberger is fundamentally wrong regarding mathematic...
Sat Jul 09, 2011 6:44 am UTC
Forum: Mathematics
Topic: Wrong on the Internet II: Norman J. Wildberger
Replies: 85
Views: 50329

### Wrong on the Internet II: Norman J. Wildberger

So here's another mathematician I found on the internet with some pretty strong, interesting views. He has draws the same conclusions as the infamous John Gabriel , however his approach and argumentation is fundamentally different. Here he explains the basics of "Universal Hyperbolic Geometry&q...
Mon Jun 27, 2011 5:21 pm UTC
Forum: Mathematics
Topic: Scailing up a plush toy.
Replies: 9
Views: 1932

### Re: Scailing up a plush toy.

You probably don't want to scale all the distances by 5. As jaap pointed out, that will increase the volume by a staggering factor of 5 3 . You should think about in what sense you mean "bigger". If you mean "wider and taller" then scale by 5. If you mean "more surface area&...
Thu Jun 23, 2011 7:45 pm UTC
Forum: Mathematics
Topic: PhD in hand
Replies: 43
Views: 6248

### Re: PhD in hand

Congrats! Seriously though. I just got my Masters degree in math and that one year of grad school was enough to turn me off of going for a PhD. Maybe I'll think about it again in a few years, but five years of college was plenty for me.
Thu Jun 02, 2011 9:14 am UTC
Forum: Mathematics
Topic: Philosophy of mathematics reading suggestions
Replies: 2
Views: 1009

### Re: Philosophy of mathematics reading suggestions

"Is God a Mathematician?" is a pretty good read if you're just starting to delve into the philosophy of mathematics and don't have a strong math background. My only qualm with it is that it takes a historical approach and so spends 90% of the book discussing many outdated beliefs before it...
Thu Jun 02, 2011 9:01 am UTC
Forum: Mathematics
Topic: Proof that there are at least 5 regular polyhedra?
Replies: 11
Views: 3149

### Re: Proof that there are at least 5 regular polyhedra?

If such a general proof does exist, I doubt it would be particularly illuminating since we already know it only applies to five specific cases.
Tue May 31, 2011 9:51 pm UTC
Forum: Mathematics
Topic: An inspiring mathematician
Replies: 20
Views: 3951

### Re: An inspiring mathematician

If we're looking for relatively recent mathematicians with lots of popular appeal, I would go with Erdos and Conway. The former for his notoriety (though I imagine few people can name his contributions) and the latter for the simplicity and novelty of his ideas.
Tue May 31, 2011 9:13 pm UTC
Forum: Mathematics
Replies: 51
Views: 8251

Age 22
M.S. in mathematics (not applied, no specialization)
I'm a programmer, but I get to use math every now and then.
Sun May 08, 2011 4:16 am UTC
Forum: Mathematics
Topic: Four Color Theorem
Replies: 15
Views: 5954

### Re: Four Color Theorem

Someone has posted about this before, and my usual response is a link to a 14 page thread from another forum of non-mathematicians trying to come up with a counterexample to the 4-color theorem without knowing the impossibility of the task. Sadly the thread was archived and is no longer available. F...
Sun May 08, 2011 4:04 am UTC
Forum: Mathematics
Topic: Geometry/calculus (I think) goat problem.
Replies: 23
Views: 2930

### Re: Geometry/calculus (I think) goat problem.

Alternatively, think about the maximum distance that the goat can move from the barn in a certain direction. Assume that when viewing the barn from above, the goat is tied at the rightmost point. Then clearly the goat can stretch the rope to its full 10 feet so long as he doesn't walk to the left (e...
Wed Apr 13, 2011 2:38 pm UTC
Forum: Mathematics
Topic: 4+D rendering.
Replies: 19
Views: 3020

### Re: 4+D rendering.

As far as I can tell, 'elemental' line segments are shorter than 'aspectual' lines. I have nothing to validate this. I might be wrong, and all the lines might be of uniform length, or the elemental lines might be the longer. I have nothing to counter those possibilities, but I suspect the elemental...
Wed Apr 13, 2011 2:07 pm UTC
Forum: Mathematics
Topic: Random Integer
Replies: 18
Views: 2759

### Re: Random Integer

God A: "I created life on this planet. I still haven't thought of a name for it though." God B: "I just use numbers. I call that planet number..." With our current understanding of mathematics whatever number the second god mentions the first would have expected a higher one. Ho...
Wed Apr 13, 2011 4:34 am UTC
Forum: Mathematics
Topic: Beautiful mathematical pictures (large images!)
Replies: 10
Views: 3207

### Re: Beautiful mathematical pictures (large images!)

Sweet. I always liked http://math.ucr.edu/home/baez/roots/deg5.png , but I like your picture better! The other pictures on that page (http://math.ucr.edu/home/baez/roots/) are prettier than the one you linked to. Specifically the one of all roots of polynomial with coefficients in {-1,0,1} and degr...
Tue Apr 12, 2011 6:12 pm UTC
Forum: Mathematics
Topic: Table Seating Problem
Replies: 7
Views: 2597

### Re: Table Seating Problem

Unfortunately this doesn't work either, since there are duplicates at each jump. I'm tempted to conjecture that for composite n there's no solution for (n-1)/2 seatings and there's always one for (n+1)/2 as well, but I don't see an immediate proof. Since we've defined a "minimal solution"...
Tue Apr 12, 2011 2:15 am UTC
Forum: Mathematics
Topic: |i|
Replies: 34
Views: 5782

### Re: |i|

I provided a perfectly acceptable definition. "|z_n| goes to infinity as n goes to infinity" means exactly "given any bounded set S, there is some N for which n larger than N implies z_n does not lie in S". If the LHS is true and you give me a bounded set, I can choose some N fo...
Tue Apr 12, 2011 2:00 am UTC
Forum: Mathematics
Topic: 4+D rendering.
Replies: 19
Views: 3020

### Re: 4+D rendering.

Extending this pattern, you can see that if you have n points, the convex solid with edges between every pair of vertices exists in at least n-1 dimensions. So if I understand your shape correctly, your shape exists in 8 dimensions, and every face is a triangle. Sadly, my mind doesn't bend far enou...
Tue Apr 12, 2011 1:03 am UTC
Forum: Mathematics
Topic: Math discovered or invented?
Replies: 110
Views: 17871

### Re: Math discovered or invented?

I mostly agree with Mario Livio as he puts it in "Is God a Mathematician?" It's a mixture of the two. The axioms and definitions of mathematics are invented: we choose them because they conform to our intuition and because we find them useful in our work. The relationships between these in...
Tue Apr 12, 2011 12:39 am UTC
Forum: Mathematics
Topic: Table Seating Problem
Replies: 7
Views: 2597

### Re: Table Seating Problem

I just thought of a new way to look at this problem. Consider only odd N since, given an optimal set of arrangements, we can get an arrangement for N-1. Think of the people as N vertices in a graph. Then in each seating arrangement we add an edge between vertices if those two people haven't sat next...
Wed Apr 06, 2011 3:35 am UTC
Forum: Mathematics
Topic: |i|
Replies: 34
Views: 5782

### Re: |i|

The real numbers are not totally ordered by |.| either. Compare 1 and -1. Crap again. I was thinking the nonnegative real numbers, in which case everything I said actually makes sense. "Let |z| go to infinity" isn't even well-defined if z is real. z would need to be nonnegative or nonposi...
Wed Apr 06, 2011 3:32 am UTC
Forum: Mathematics
Topic: How do you interpret notation in pathfinding?
Replies: 2
Views: 495

### Re: How do you interpret notation in pathfinding?

The simplest way to understand big O is that it describes how quickly a function increases. In your specific case, it refers to how long it takes to find paths in terms of the size of the graph.
Mon Apr 04, 2011 4:56 pm UTC
Forum: Mathematics
Topic: |i|
Replies: 34
Views: 5782

### Re: |i|

Eh, if you were talking to me about complex numbers and mentioned that you wished to "let z get large", I would assume you meant "let |z| go to infinity". Once again, the meaning of that is not intuitively clear: "let |z| go to infinity" is not well-defined with regard...
Mon Apr 04, 2011 4:46 pm UTC
Forum: Mathematics
Topic: 4+D rendering.
Replies: 19
Views: 3020

### Re: 4+D rendering.

Being less vague would be helpful. When you say shape, what do you mean exactly? Do you mean that it is a higher dimensional polytope with 9 vertices? Or is it just a collection of 9 points in space?
Sun Feb 27, 2011 9:39 pm UTC
Forum: Mathematics
Topic: The Shortest String Containing all Permutations of n Symbols
Replies: 29
Views: 28592

### Re: The Shortest String Containing all Permutations of n Sym

There is a clear pattern here that is not difficult to generalize, but the difficulty is proving that this pattern is indeed optimal in general -- it could be the case (for large n) that if we increase one of the early numbers (i.e., we don't use the greedy algorithm but rather add some extra lengt...
Sun Feb 27, 2011 9:01 pm UTC
Forum: Mathematics
Topic: |i|
Replies: 34
Views: 5782

### Re: |i|

You can think of absolute value in the real numbers as the distance from 0. It's the same in the complex plane. I always like to go for "how 'big' a number is", which if you're thinking of complex numbers as vectors then that works quite neatly. Except that the imaginary numbers are not l...
Sun Feb 27, 2011 8:48 pm UTC
Forum: Mathematics
Topic: "Oh no! We forgot how to say... math... stuff!"
Replies: 294
Views: 92230

### Re: "Oh no! We forgot how to say... math... stuff!"

Why not short-dash short-dash short-dash done horizontally under where you'd usually write? The issue is that an ellipses is a common mathematical symbol (as evidence by it having its own symbol in latex) and yet it is written as three distinct symbols. Writing three dashes is just as bizarre as wr...