## Search found 423 matches

Tue Jun 10, 2008 10:56 am UTC
Forum: Mathematics
Topic: Infinite Dimensional Hypersphere
Replies: 26
Views: 3176

### Re: Infinite Dimensional Hypersphere

@Frimble: Just because the surface of the ball and its interior are both infinite dimensional in some sense does not make them the same. Is the surface of a 3-sphere the same as the interior of a 2-sphere? Yes? A flat 3-sphere can be seen as the interior of a flat 2-sphere with opposite points on t...
Tue Jun 10, 2008 10:13 am UTC
Forum: Mathematics
Topic: Infinite Dimensional Hypersphere
Replies: 26
Views: 3176

### Re: Infinite Dimensional Hypersphere

First, a technical note: the object you're describing should be called a hyperball. "Sphere" denotes the surface of such an object. In answer to your question, I'm not sure whether "uniform distribution" can be meaningfully applied to points in an infinite-dimensional hyperball,...
Tue Jun 10, 2008 9:35 am UTC
Forum: Mathematics
Topic: What else can we imagine?
Replies: 32
Views: 4268

### Re: What else can we imagine?

After a few years with it, I'm now happy with i . My question is: are there other imaginary/non-real numbers? That is, numbers that can be produced through standard operations that aren't real but have a singularly defined value. Obviously I don't mean numbers of the form x+iy . Also I don't think ...
Mon Jun 09, 2008 1:22 pm UTC
Forum: Mathematics
Topic: Theorems named after the wrong people
Replies: 21
Views: 8797

### Re: Theorems named after the wrong people

Not actually theorems as such but:

Student's t distribution was also named after a pseudonym. The discoverer's real was William Sealy Gosset.

I think that Einstein gets overdue credit for relativity, seeing as the equations were first derived by Lorentz (or however you spell his name).
Mon Jun 09, 2008 10:04 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0434: "xkcd Goes to the Airport"
Replies: 107
Views: 31432

### Re: xkcd Goes to the Airport Discussion

Are lock picks really illegal? You can buy them on the internet from locksmiths' suppliers easily.
Sun Jun 08, 2008 6:33 pm UTC
Forum: Mathematics
Topic: What else can we imagine?
Replies: 32
Views: 4268

### Re: What else can we imagine?

After a few years with it, I'm now happy with i . My question is: are there other imaginary/non-real numbers? That is, numbers that can be produced through standard operations that aren't real but have a singularly defined value. Obviously I don't mean numbers of the form x+iy . Also I don't think ...
Sun Jun 08, 2008 6:20 pm UTC
Forum: Mathematics
Topic: Quiz me on infinite series!
Replies: 16
Views: 2430

### Re: Quiz me on infinite series!

One of my favorites, not hard but interesting. Determine if the series: sin θ + sin 2 θ + sin 3 θ... is convergent or divergent for the following values of θ. Where the series converges, find the value of the limit: π/2 π/4 π 3π/2 Hence or otherwise find an expression for the limit valid for any rea...
Thu Jun 05, 2008 10:23 am UTC
Forum: Mathematics
Topic: Amusing answers to tests
Replies: 393
Views: 62179

### Re: Amusing answers to tests

It is also possible by using origami - in which case you don't even need a compass or a straightedge - if the angle provided is on a piece of paper. This sound interesting, but I can't see how it works, I take it the method is not trivial. What are the permitted operations for applying origami to g...
Fri May 23, 2008 6:03 pm UTC
Forum: Mathematics
Topic: new theory on numbers
Replies: 29
Views: 3536

### Re: new theory on numbers

The greeks, later the Arab/Persian mathematicians and a bit again the Europeans of 12th-17th century saw everything in geometry. So for example x 2 - 4x + 4=0, didn't mean anything to them, because there is a negative there. But, x 2 + 4 = 4x meant "There is a length, the area of a square with...
Fri May 23, 2008 2:33 pm UTC
Forum: Mathematics
Topic: new theory on numbers
Replies: 29
Views: 3536

### Re: new theory on numbers

It seems to me that the issue here is basically this: What are the consequences of giving real numbers a unit? This is important as the fact that real numbers are dimensionless is often used as an axiom. For arguments sake, let's give them a unit: ξ. The following four steps follow logically from th...
Fri May 16, 2008 9:06 pm UTC
Forum: Mathematics
Topic: Sphere -> Cartesian mapping
Replies: 16
Views: 2119

### Re: Sphere -> Cartesian mapping

I agree it probably wouldn't (I don't actually know anything much about it not having gone to university yet), I only mentioned it because from what I have read, using it negates the need for another spacial dimension (not that introducing curvature instead sounds any easier). I don't have a problem...
Fri May 16, 2008 9:15 am UTC
Forum: Mathematics
Topic: Sphere -> Cartesian mapping
Replies: 16
Views: 2119

### Re: Sphere -> Cartesian mapping

as far as I know, to find the length of the shortest path between two points on a curved surface (without defining another spacial dimension) basically requires an understanding of non-euclidean (in this case elliptical) geometry. Eh.... I wouldn't say that. Elliptical geometry might be the best wa...
Thu May 15, 2008 6:44 pm UTC
Forum: Mathematics
Topic: Sphere -> Cartesian mapping
Replies: 16
Views: 2119

### Re: Sphere -> Cartesian mapping

Robin S wrote:I have to ask: why can't you just solve your Travelling Salesman problem on a graph, without worrying about what space it's embedded in?

I assume it's because he has been given locations on the earth and needs to find the distances between them in order to find the graph.
Thu May 15, 2008 3:47 pm UTC
Forum: Mathematics
Topic: Sphere -> Cartesian mapping
Replies: 16
Views: 2119

### Re: Sphere -> Cartesian mapping

f[y], y is only one dimensional (I think). So I wouldn't have thought it's possible to use it as a coordinate system. The traveling salesman problem however only requires a graph with every node connected to every other node. If I have interpreted your question correctly you are basically asking for...
Thu May 15, 2008 2:47 pm UTC
Forum: Mathematics
Topic: How much of a math nerd are you?
Replies: 95
Views: 9937

### Re: How much of a math nerd are you?

I have decided to sit four maths exams surplus to those I need to go to university (to read maths). This includes one paper that only two people from my college have passed in the last decade. (AEA Maths, I will probably post some of the problems on this forum as my teachers don't seem keen on them)...
Mon May 12, 2008 6:19 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 0356: "Nerd Sniping"
Replies: 376
Views: 173467

### Re: "Nerd Sniping" Discussion

PvNP should do the trick.
Fri May 09, 2008 6:40 pm UTC
Forum: Mathematics
Topic: Fractals, baby! Vote now!
Replies: 45
Views: 8551

### Re: Fractals, baby! Vote now!

The Oxford Concise Dictionary of Mathematics defines a Julia set as: 'The boundary of the set of points z 0 in the complex plane for which the application of the function f(z)=z 2 +c repeatedly to the point z 0 produces a bounded sequence. The term may be used similarly for other functions as well....
Thu May 08, 2008 7:03 pm UTC
Forum: Mathematics
Topic: Fractals, baby! Vote now!
Replies: 45
Views: 8551

### Re: Fractals, baby! Vote now!

The Oxford Concise Dictionary of Mathematics defines a Julia set as: 'The boundary of the set of points z 0 in the complex plane for which the application of the function f(z)=z 2 +c repeatedly to the point z 0 produces a bounded sequence. The term may be used similarly for other functions as well.'...
Thu May 08, 2008 5:47 pm UTC
Forum: Mathematics
Topic: Fractals, baby! Vote now!
Replies: 45
Views: 8551

### Re: Fractals, baby! Vote now!

They're still Julia sets, just plotted over a larger domain. Larger domain? In what sense? There are the same number of points in a 4 dimensional space as there are in a 2 dimensional space. (I'm sorry I can't help it :) ) In any case doesn't the fact that their domain is a non-abelian (non-commuta...
Thu May 08, 2008 5:15 pm UTC
Forum: Mathematics
Topic: Fractals, baby! Vote now!
Replies: 45
Views: 8551

### Re: Fractals, baby! Vote now!

How about Quaternion Julia fractals? Hard to appreciate, as they have fractal dimensions between 3 and 4 but quite pretty anyway.

(please correct me if I have got my terminology wrong, I have had trouble finding good explanations on the subject)
Sun May 04, 2008 2:26 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 0415: "Restraining order"
Replies: 99
Views: 31285

### Re: "Restraining order" Discussion

If the distances were 500 yards and 500.3 yards, then by walking in a straight line she could force him to walk in a tractrix.
Thu Apr 10, 2008 7:39 pm UTC
Forum: Science
Topic: xkcd 356: Nerd Sniping
Replies: 3
Views: 3579

### Re: xkcd 356: Nerd Sniping

Very good, but what method should be used?
Thu Apr 10, 2008 7:13 pm UTC
Forum: Science
Topic: xkcd 356: Nerd Sniping
Replies: 3
Views: 3579

### xkcd 356: Nerd Sniping

There may already be a thread about this, but I can't find it. It seems to me that the best way to approach the puzzle in this thread is find the resistance of a number of finite networks formed by removing an infinite section of the network, and to form these values into an infinite series, the lim...

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