Search found 423 matches

by Frimble
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...
by Frimble
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,...
by Frimble
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 ...
by Frimble
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).
by Frimble
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.
by Frimble
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 ...
by Frimble
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...
by Frimble
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...
by Frimble
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...
by Frimble
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...
by Frimble
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...
by Frimble
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...
by Frimble
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.
by Frimble
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...
by Frimble
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)...
by Frimble
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.
by Frimble
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....
by Frimble
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.'...
by Frimble
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...
by Frimble
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)
by Frimble
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. :)
by Frimble
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?
by Frimble
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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