Search found 234 matches

by Giallo
Fri Aug 16, 2013 11:30 pm UTC
Forum: Mathematics
Topic: Area of a spherical triangle?
Replies: 11
Views: 4624

Re: Area of a spherical triangle?

The spherical equivalent of the straight lines in Euclidean space are the great circles (i.e. the geodesics of the sphere). You have to use those as edges of the triangle. Then you can find the angles by finding the vectors tangent to your two edges at the vertex and using the usual formula <a,b> = ...
by Giallo
Sat Jul 20, 2013 8:40 pm UTC
Forum: Mathematics
Topic: The difference betwen "find", "state", "give", etc.
Replies: 4
Views: 1689

Re: The difference betwen "find", "state", "give", etc.

In my experience, usually a statement beginning with "find" is a question which doesn't give away the final answer in the statement (as does a "show that..."), and which requires a formal proof of the results you find. IMO, those are probably the best question when you begin to h...
by Giallo
Fri Jul 19, 2013 1:08 pm UTC
Forum: Mathematics
Topic: Twin Prime Conjecture - A leap forward
Replies: 5
Views: 2872

Re: Twin Prime Conjecture - A leap forward

If you're interested, Polymath (an online project/group of mathematicians, comprehending among others Terrence Tao) attacked the problem massively, reducing the gap to around 12,000 for sure, and with results for a gap a little more than 5,000 to be checked. The link is the following: http://michael...
by Giallo
Thu May 16, 2013 9:38 pm UTC
Forum: Science
Topic: D-Wave Quantum Computer
Replies: 5
Views: 3486

Re: D-Wave Quantum Computer

Wait, weren't n qubits equivalent to 2n classical bits? That would mean 2*1025 bits!?

Or am I wrong in my first statement?
by Giallo
Thu May 16, 2013 7:54 pm UTC
Forum: Science
Topic: D-Wave Quantum Computer
Replies: 5
Views: 3486

D-Wave Quantum Computer

I stumbled upon this article: http://blog.physicsworld.com/2013/05/16/google-and-nasa-acquire-d-wave-quantum-computer/ It basically says that NASA, in collaboration with Google and USRA, bought a 512-qubit quantum computer. Now, as far as I know, the records for a quantum computer are around 2-3 qub...
by Giallo
Mon Apr 01, 2013 10:19 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1190: "Time"
Replies: 106138
Views: 37273836

Re: 1190: "Thing that keeps slipping into the future"

Wow. I have been away for something like 100 newpix, and there are 80 new pages to this thread. I will never be able to read it all... Can someone enlighten me on the current topics of discussion?
by Giallo
Thu Mar 28, 2013 11:01 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1190: "Time"
Replies: 106138
Views: 37273836

Re: 1190: "Time"

New pic. He's taking away a flag. I don't know why, but this makes me kinda sad... :(
by Giallo
Thu Mar 28, 2013 9:47 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1190: "Time"
Replies: 106138
Views: 37273836

Re: 1190: "Time"

My hypothesis on what happens next: Godzilla comes out of the water. Or Chtulhu. Or both.

Would be cool :D
by Giallo
Mon Feb 18, 2013 9:51 pm UTC
Forum: Science
Topic: Asteroid 2012 DA14
Replies: 33
Views: 4914

Re: Asteroid 2012 DA14

tomandlu wrote:Just out of curiosity, how much damage would DA14 do if it hit water rather than land? Would the damage be 'different'?


I've read somewhere that it would be like a little atomic bomb (around 3 megaton, maybe?), but I don't have the source, I'm sorry.
by Giallo
Fri Feb 08, 2013 10:52 pm UTC
Forum: Science
Topic: Four-body Celestial Mechanics Problem
Replies: 24
Views: 3742

Re: Four-body Celestial Mechanics Problem

You could take the known particular solutions for the 3-body problem (where the bodies would be your stars) and try to look for stable points for a fourth (negligible) mass and see if it would work. Else you could use more than three stars. For example you could have something like 8 stars orbiting ...
by Giallo
Sun Feb 03, 2013 12:05 pm UTC
Forum: Mathematics
Topic: Application of Krein-Milman's theorem
Replies: 4
Views: 2054

Re: Application of Krein-Milman's theorem

From what I found through a quick google search, Krein-Milman's theorem makes no mention of a norm. Wikipedia: "Let X be a locally convex topological vector space (assumed to be Hausdorff), and let K be a compact convex subset of X. Then, the theorem states that K is the closed convex hull of ...
by Giallo
Sat Feb 02, 2013 11:09 pm UTC
Forum: Mathematics
Topic: To fit an elephant
Replies: 2
Views: 3084

To fit an elephant

The following quote is attributed to John von Neumann: "With four parameters I can fit an elephant, and with five I can make him wiggle his trunk." How well can we fit an elephant using a minimum of parameters? How would you proceed? Here's an example: http://www.johndcook.com/blog/2011/06...
by Giallo
Sat Feb 02, 2013 8:30 pm UTC
Forum: Mathematics
Topic: Application of Krein-Milman's theorem
Replies: 4
Views: 2054

Re: Application of Krein-Milman's theorem

Ok, maybe I got something. Does any of you know if the weak* topology is at least T3 (regular)? If it is, probably I can make the separation theorem work. If anyone is interested in the details write down here or PM me, and I will elaborate on what is going on.
by Giallo
Sat Feb 02, 2013 7:41 pm UTC
Forum: Mathematics
Topic: Application of Krein-Milman's theorem
Replies: 4
Views: 2054

Re: Application of Krein-Milman's theorem

To be a little more precise on the problem: The fact is that when you prove Krein-Milman, you have to use convex separation between a closed convex set and a point (which forms a compact set). The question can thus be reduced to: what kind of topology is sufficient in order to have the possibility t...
by Giallo
Sat Feb 02, 2013 5:08 pm UTC
Forum: Mathematics
Topic: Application of Krein-Milman's theorem
Replies: 4
Views: 2054

Application of Krein-Milman's theorem

Looking around while studying for an exam in functional analysis, I found this interesting fact: There is no normed vector space X such that X* = C R [0,1] (the space of continuous, real-valued functions on [0,1]). The proof goes like this: Assume there was such an X. Then by Alaoglu's theorem the c...
by Giallo
Fri Feb 01, 2013 9:34 pm UTC
Forum: Mathematics
Topic: "fouriest" transformations
Replies: 9
Views: 2741

Re: "fouriest" transformations

Well, you can always write an integer greater than 810 in a base such that you have n10 = 14b. If I come up with something better I'll let you know.
by Giallo
Fri Feb 01, 2013 11:57 am UTC
Forum: Mathematics
Topic: (HW) Equicontinuous and pt-wise convergence implies uniform
Replies: 7
Views: 3492

Re: (HW) Equicontinuous and pt-wise convergence implies unif

Yeah, but personally I find it easier to think about it this way. I mean yes, if given compactness you either have to choose a sequence, or a set of open sets. But there's a difference in what sets you choose, there are usually many ways to do it. I don't think they are the same hint...but whatever...
by Giallo
Fri Feb 01, 2013 1:29 am UTC
Forum: Mathematics
Topic: (HW) Equicontinuous and pt-wise convergence implies uniform
Replies: 7
Views: 3492

Re: (HW) Equicontinuous and pt-wise convergence implies unif

I'll give a slightly different hint. For any x in K, equicontinuity can give us a ball around it on which none of the functions deviate from their value at x by more that some chosen buffer (epsilon/2) perhaps. Compactness allows us to choose a finite number of these neighborhoods that cove...
by Giallo
Thu Jan 31, 2013 8:18 pm UTC
Forum: Mathematics
Topic: (HW) Equicontinuous and pt-wise convergence implies uniform
Replies: 7
Views: 3492

Re: (HW) Equicontinuous and pt-wise convergence implies unif

Let f be the pointwise limit of the f k 's. My hint is: Let e > 0, consider the sets U k = {x in K: |f(x) - f n (x)| < e for every n > k}. Try to show that those sets are open (here you will most probably have to use equicontinuity) and that they cover K, then use compactness...
by Giallo
Wed Jan 23, 2013 9:16 pm UTC
Forum: Science
Topic: Noether's Theorem
Replies: 0
Views: 1062

Noether's Theorem

So I have this version of Noether's Theorem: Given a Lagrangian L(q,q') independent of time and a continuous symmetry f(a) : q -> q a , ie L is invariant under f(a) for all a in R, then the quantity p i v i is conserved (with Einstein summation convention, p i = dL/dq i ), where v i = dq a /da in a ...
by Giallo
Tue Jan 22, 2013 7:23 pm UTC
Forum: Mathematics
Topic: ISO giant tech tree of math
Replies: 14
Views: 3022

Re: ISO giant tech tree of math

Your requirements for topology are a great illustration of why this sort of project is a personal work of art rather than science. To me, learning topology only depends on a knowledge of set theory, although it was historically influenced by our intuition of several branches of elementary math. The...
by Giallo
Tue Jan 22, 2013 7:04 am UTC
Forum: Mathematics
Topic: ISO giant tech tree of math
Replies: 14
Views: 3022

Re: ISO giant tech tree of math

I am also interested. I study maths, but actually I wouldn't even be able to classify the biggest "realms" of maths... (algebra, analysis and geometry? What of topology? Is it a branch of algebra? And probability theory? Statistics? Should theoretical physics be included?) Anyway, they are...
by Giallo
Mon Jan 21, 2013 6:53 am UTC
Forum: Mathematics
Topic: Graphing conic sections from super-general form
Replies: 1
Views: 633

Re: Graphing conic sections from super-general form

Assume A is non-zero, then without loss of generality (dividing by A if necessary) we may assume A = 1. Let z = x + By/2, then z2 = x2 + Bxy + y2B2/4 and we can write the conic equation as z2 + (C - B2/4)y2 + Dz + (E - B/2)y + F = 0.
by Giallo
Sat Jan 19, 2013 12:55 pm UTC
Forum: Mathematics
Topic: Looking for a set of math problems from Discover magazine
Replies: 16
Views: 2371

Re: Looking for a set of math problems from Discover magazin

ConMan wrote:The question is worded enough that it mentions the "members" of the club, implying more than one. In the absense of any information to the contrary, I think you have to take that as your hint.


We are royality, we do not need other members than ourselves in our exclusive King's club.
by Giallo
Mon Jan 14, 2013 11:10 am UTC
Forum: Mathematics
Topic: Sine Derivative Proof?
Replies: 32
Views: 5975

Re: Sine Derivative Proof?

An easier way is to calculate it as the limit of (sin(x+h) - sin(x-h))/h for h->0. Trigonometric identities give you what you want (also using sin(h)/h=1 for h->1).
by Giallo
Fri Jan 11, 2013 2:17 pm UTC
Forum: Mathematics
Topic: Euler-Lagrange equations/geodesic equations
Replies: 1
Views: 1269

Euler-Lagrange equations/geodesic equations

So, we have the Euler-Lagrange equations that gives us differential equations to find a curve minimizing the functional S[q] = \int L(q,q',t) dt , namely: \frac{\partial L}{\partial q} - \frac{d}{dt}\frac{\partial L}{\partial q'} Now, given a simple smooth m-dimensional submanifold M...
by Giallo
Wed Jan 09, 2013 7:11 pm UTC
Forum: Science
Topic: Lunar soil as growth medium?
Replies: 32
Views: 4352

Re: Lunar soil as growth medium?

If really the Moon is a solidified glob of lava which separated from Earth in an early stage, I don't see why it shouldn't be (potentially) fertile. But maybe I'm overlooking some important factor. Any opinion?
by Giallo
Wed Jan 09, 2013 7:07 pm UTC
Forum: Mathematics
Topic: [Complex Analysis] Deforming a contour
Replies: 8
Views: 1959

Re: [Complex Analysis] Deforming a contour

It should, I haven't calculated the bounds. Pay attention that the integral goes to 0 because the bound for |f(z)| on the contour goes down faster than 1/N, while the length of the contour increases linearly with N. This is important.
by Giallo
Tue Jan 08, 2013 11:23 pm UTC
Forum: Books
Topic: Wheel of Time (Split from Geeky/Nerdy Kids Books)
Replies: 228
Views: 126273

Re: Wheel of Time (Split from Geeky/Nerdy Kids Books)

I thought about re-reading the series, but I have sooooo many other books to read. Got....9ish for Christmas, takes my 'to be read' pile to only abou 100 titles. Want to pace myself for 45-50 books this year. It will be hard if I do books like Malazan Book of the Fallen or GED. WoT is easier, even ...
by Giallo
Tue Jan 08, 2013 10:13 pm UTC
Forum: Books
Topic: Wheel of Time (Split from Geeky/Nerdy Kids Books)
Replies: 228
Views: 126273

Re: Wheel of Time (Split from Geeky/Nerdy Kids Books)

pseudoidiot wrote:Trying to decide if I'll:

1. Wait for the ebook version.
2. Order it from Amazon, but have to find something else to read for the next 2 days.
3. Just go buy it at Barnes & Noble and start reading tonight.


If I'm not mistaken, the ebook is not yet available. You'll have to do with 2 or 3...
by Giallo
Tue Jan 08, 2013 9:01 pm UTC
Forum: Books
Topic: Wheel of Time (Split from Geeky/Nerdy Kids Books)
Replies: 228
Views: 126273

Re: Wheel of Time (Split from Geeky/Nerdy Kids Books)

emceng wrote:It was out for delivery a few hours ago! I should have it waiting for me when I get home.


Good reading, then :D
by Giallo
Tue Jan 08, 2013 7:15 pm UTC
Forum: Mathematics
Topic: [Complex Analysis] Deforming a contour
Replies: 8
Views: 1959

Re: [Complex Analysis] Deforming a contour

By the residuum theorem, as long that your contour includes the same singularities with the same indexes (ie: you make the same number of turns around them) your integral is the same. Probably you can also prove that using Cauchy's theorem. You can try it, it shouldn't be too hard and it is a good ...
by Giallo
Tue Jan 08, 2013 5:59 pm UTC
Forum: Books
Topic: Wheel of Time (Split from Geeky/Nerdy Kids Books)
Replies: 228
Views: 126273

Re: Wheel of Time (Split from Geeky/Nerdy Kids Books)

emceng wrote:
Giallo wrote:The last book is coming out tomorrow :D
I don't know whether I should be happy or not... I have finals in 2 weeks.


I'm excited! Just need to check my Amazon order and make sure it is being delivered tomorrow!


I bought it! Ah, the smell of freshly printed pages!
Did you get it?
by Giallo
Tue Jan 08, 2013 10:54 am UTC
Forum: Mathematics
Topic: [Complex Analysis] Deforming a contour
Replies: 8
Views: 1959

Re: [Complex Analysis] Deforming a contour

By the residuum theorem, as long that your contour includes the same singularities with the same indexes (ie: you make the same number of turns around them) your integral is the same. Probably you can also prove that using Cauchy's theorem. You can try it, it shouldn't be too hard and it is a good e...
by Giallo
Mon Jan 07, 2013 10:50 pm UTC
Forum: Books
Topic: Wheel of Time (Split from Geeky/Nerdy Kids Books)
Replies: 228
Views: 126273

Re: Wheel of Time (Split from Geeky/Nerdy Kids Books)

The last book is coming out tomorrow :D
I don't know whether I should be happy or not... I have finals in 2 weeks.
by Giallo
Sun Jan 06, 2013 7:44 pm UTC
Forum: Mathematics
Topic: Proof that int y' dx = int y dy ?
Replies: 15
Views: 2883

Re: Proof that int y' dx = int y dy ?

Ok, here's a possible proof: Let f(y) = dF/dy. We write y = y(x). Then we have d/dx F(y) = dF/dy dy/dx = f(y) dy/dx, by chain rule. We get thus ∫ f(y) dy/dx dx = ∫ d/dx F(y) dx = F(y) = ∫ dF/dy dy = ∫ f(y) dy, where we the fund. thm of calculus twice. You get your case for F(y) = y 2 /2. By the way,...
by Giallo
Sat Jan 05, 2013 12:36 am UTC
Forum: Mathematics
Topic: C^k maps
Replies: 6
Views: 1137

Re: C^k maps

Sounds related to the Inverse Function Theorem Indeed, in fact I have said as much in my second post. Your condition for Det(Jf) to be non-zero everywhere is probably enough for C 1 functions, but I'm not sure if it's enough for C k , k>1 functions. It feels like you need to have some condition on ...
by Giallo
Fri Jan 04, 2013 10:43 pm UTC
Forum: Mathematics
Topic: C^k maps
Replies: 6
Views: 1137

Re: C^k maps

Lopsidation wrote:Is f(x)=x3 a counterexample at x=0, or am I missing something?


Df = 3x2, which gives 0 for x = 0, thus it doesn't satisfies the conditions. Good try, anyway. It shows that the derivative must probably have full rank to avoid similar cases...
by Giallo
Fri Jan 04, 2013 10:40 pm UTC
Forum: Mathematics
Topic: C^k maps
Replies: 6
Views: 1137

Re: C^k maps

By the way, what is actually done to show/circumvent that is: (we really want to show that f -1 composed with another function e in C k (U',R n ) is again C k , where U' is a subset of R r ) - fix x 0 in U - "restrict" f to a function g:U->R m by eliminating some components in the range su...
by Giallo
Fri Jan 04, 2013 10:27 pm UTC
Forum: Mathematics
Topic: C^k maps
Replies: 6
Views: 1137

C^k maps

I am studying for an exam, and in a proof of some lemma I am given a long and quite complicated argument which could be greatly reduced if the following fact is true: Say f:U->R n is a map which is k-times continuously differentiable (C k ) and an homeomorphism onto its image. Is the inverse map of ...

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