Search found 774 matches

by MartianInvader
Tue Oct 28, 2008 7:57 pm UTC
Forum: Logic Puzzles
Topic: Unusual Cake Slicing
Replies: 84
Views: 18152

Re: Unusual Cake Slicing

Ok, it's been a long time and no-one has gotten it. PaulT, do you know a solution? If so, perhaps it's time for a hint? This puzzle has been driving me crazy.
by MartianInvader
Tue Oct 28, 2008 2:42 am UTC
Forum: Mathematics
Topic: Topology?
Replies: 17
Views: 2343

Re: Topology?

The intro I like to talk about is gluing together edges of a square in order to make a sphere (all glued into a single point), a torus (opposite sides glued), a klein bottle (one pair of opposite sides glued with a flip), and real projective space (both opposite sides glued with flips).
by MartianInvader
Tue Oct 28, 2008 1:17 am UTC
Forum: News & Articles
Topic: U.S. Democratic Super Majority: Implications
Replies: 39
Views: 3000

Re: U.S. Democratic Super Majority: Implications

How are they not able to pass anything they want at all with a simple majority (51%) in both houses of Congress, though? Everybody's mentioned filibusters, but let's also remember the good ol' presidential veto. Doesn't that require 2/3 majority to overturn? And Bush has often flat-out stated "...
by MartianInvader
Mon Oct 27, 2008 1:03 am UTC
Forum: Mathematics
Topic: n-dimensional rotation matrix
Replies: 20
Views: 10988

Re: n-dimensional rotation matrix

So, just to make sure I'm understanding: If I have a set of points in the (n-1)-dimensional hyperplane plane through the origin given by x, and apply the rotation you have defined to them, their images will all be in the (n-1)-dimensional hyperplane through the origin defined by y? Yeah. You can se...
by MartianInvader
Sun Oct 26, 2008 7:05 pm UTC
Forum: Logic Puzzles
Topic: Unusual Cake Slicing
Replies: 84
Views: 18152

Re: Unusual Cake Slicing

Okay, so are you claiming this is a solution? I mean, if you slice the cake into two pieces and only one contains the center, then they're NOT congruent; this is easy to prove. I don't think you're allowed to cut up into lots of different pieces (since you did slice a couple of your congruent pieces...
by MartianInvader
Sun Oct 26, 2008 6:48 pm UTC
Forum: Mathematics
Topic: n-dimensional rotation matrix
Replies: 20
Views: 10988

Re: n-dimensional rotation matrix

To put it algorithmically, get an orthonormal basis for your vector space so that the first two basis vectors span the plane generated by your two normal vectors. Say your vectors are at angle \theta apart. Then write the 2-dimensional rotation-by-\theta matrix in the upper-left corner of your n-by-...
by MartianInvader
Sun Oct 26, 2008 6:14 pm UTC
Forum: News & Articles
Topic: The Completely Official Sarah Palin Thread
Replies: 408
Views: 26869

Re: John McCain's VP pick is Gov. Sarah Palin of Alaska

Hmm... Okay. There's something bothering me here. There's different standards being applied for what constitutes "sexist"... maybe not by the same person, but I thought it should be pointed out. The whole "bad mother" thing... this was being argued as sexist because one would nev...
by MartianInvader
Fri Oct 24, 2008 10:19 pm UTC
Forum: Logic Puzzles
Topic: Immortal monkey with a typewriter
Replies: 21
Views: 4689

Re: Immortal monkey with a typewriter

Yep, you're right, phlip. How about this? Let S_m be the number of sequences of length m so that no initial segment is repeated. Now we can obtain such a sequence of length m+1 by adding a new letter to such a sequence of length m. Then we have the following recurrence relations: If m is even, S_{m+...
by MartianInvader
Fri Oct 24, 2008 9:30 pm UTC
Forum: Mathematics
Topic: Infinite geometry, redundant concepts
Replies: 4
Views: 1291

Re: Infinite geometry, redundant concepts

http://en.wikipedia.org/wiki/Riemann_sphere I think you might enjoy reading that. The circles which pass through the "point at infinity" are exactly the lines in the standard complex plane. Mobius transformations also give a nice feel for the similarities between lines and "infinite ...
by MartianInvader
Fri Oct 24, 2008 2:08 am UTC
Forum: Logic Puzzles
Topic: Immortal monkey with a typewriter
Replies: 21
Views: 4689

Re: Immortal monkey with a typewriter

Isn't it as simple as (1/n) ^ x, where x ~ number of characters typed so far? Well, that's the chance of doing it on a certain step, but then you gotta sum it up. So you'd be looking at something like summing (1/n)^m from 1 to infinity, which would be 1/(n-1). Bu...
by MartianInvader
Fri Oct 24, 2008 2:01 am UTC
Forum: Mathematics
Topic: Advice on delta-epsilon proofs
Replies: 8
Views: 1787

Re: Advice on delta-epsilon proofs

That's a really nice development from the intuitive definition to the mathematical one.
by MartianInvader
Wed Oct 22, 2008 11:26 pm UTC
Forum: Logic Puzzles
Topic: Unusual Cake Slicing
Replies: 84
Views: 18152

Re: Unusual Cake Slicing

That proof strategy will probably work, though you have a few errors. You don't necessarily have a straight line to the center (maybe the pieces are all spiral-like), so you'll have to use a path. If you assume that all the "outer" edges correspond to each other, then you can assert that t...
by MartianInvader
Wed Oct 22, 2008 8:50 pm UTC
Forum: Mathematics
Topic: Questions about some weird intervals
Replies: 19
Views: 1817

Re: Questions about some weird intervals

I like to view things topologically, so I just use the word "closed interval" and forget about this "extended real line" nonsense.
by MartianInvader
Wed Oct 22, 2008 8:45 pm UTC
Forum: Mathematics
Topic: Little Challenge
Replies: 11
Views: 1524

Re: Little Challenge

Yeah, Token didn't subtract enough. I think we want {n \choose p}p^m - {n \choose p-1}(p-1)^m - {n \choose p-2}(p-2)^m - ... - {n \choose 1}(1)^m This might have some nice expression... I'm not sure. In the given case, that's the same as mine. I'm wrong because I missed some double counting, which ...
by MartianInvader
Wed Oct 22, 2008 8:38 pm UTC
Forum: News & Articles
Topic: Poor Joe. All he wanted was poopy pipes,
Replies: 132
Views: 6979

Re: Poor Joe. All he wanted was poopy pipes,

WOW, this thread has gotten real crazy real fast. I wanna join in! I can't believe nobody has responded to this little tidbit yet- The blame for high gas prices in Europe falls on the metric system. Our government adds maybe $1 in taxes to every gallon. Europe adds about $1 per litre. I think in Fra...
by MartianInvader
Wed Oct 22, 2008 5:14 pm UTC
Forum: News & Articles
Topic: You can't sue God..
Replies: 49
Views: 4423

Re: You can't sue God..

Man, reading that article just makes the lawsuit seem full of AWESOME. All the posts put in this thread talking about how this is wasting taxpayer money etc. are exactly the questions he was trying to get people to ask! If, as a result of this lawsuit, stricter measures get placed on what types of l...
by MartianInvader
Wed Oct 22, 2008 4:39 pm UTC
Forum: Mathematics
Topic: Little Challenge
Replies: 11
Views: 1524

Re: Little Challenge

Yeah, Token didn't subtract enough. I think we want

{n \choose p}p^m - {n \choose p-1}(p-1)^m - {n \choose p-2}(p-2)^m - ... - {n \choose 1}(1)^m

This might have some nice expression... I'm not sure.
by MartianInvader
Tue Oct 21, 2008 2:44 pm UTC
Forum: News & Articles
Topic: Obama cancels campaign events; grandma is dying
Replies: 44
Views: 4993

Re: Obama cancels campaign events; grandma is dying

Every time the McCain campaign has tried something like that, it's blown up in their face. I think they've learned their lesson by now.
by MartianInvader
Mon Oct 20, 2008 8:17 pm UTC
Forum: News & Articles
Topic: Makin' Diamonds
Replies: 25
Views: 2727

Re: Makin' Diamonds

If I recall correctly, diamonds are only expensive now because of hoarding from the diamond companies... artificial diamonds, while cool, aren't exactly necessary yet. Would artificial diamonds be cost effective if natural diamonds were priced normally? I think the point is the companies are drivin...
by MartianInvader
Fri Oct 17, 2008 5:17 pm UTC
Forum: News & Articles
Topic: Poor Joe. All he wanted was poopy pipes,
Replies: 132
Views: 6979

Re: Poor Joe. All he wanted was poopy pipes,

Belial wrote:The press's fabled "liberal bias" or "conservative bias" (depending on whom you ask) is extremely, ridiculously secondary to its laziness and sensationalism biases.


Oh man, I am so sigging that.
by MartianInvader
Thu Oct 16, 2008 5:13 pm UTC
Forum: News & Articles
Topic: Sarah Palin supporter wants to kill Obama
Replies: 107
Views: 7218

Re: Sarah Palin supporter wants to kill Obama

I don't think he's full of shit, but it's just not that surprising. I mean, if I was at a rally for a candidate I supported, and someone I knew in the crowd yelled something like that, I might not approve of it, but I certainly wouldn't give his name to the FBI, especially if I thought he wasn't ser...
by MartianInvader
Thu Oct 16, 2008 12:48 pm UTC
Forum: News & Articles
Topic: Another hexagonal vortex discovered on Saturn
Replies: 13
Views: 1993

Re: Another hexagonal vortex discovered on Saturn

Thanks for your input, weosdfl34! And thanks for those e-mails with the links to penis enlargement product sites! But seriously, we all know what this hexagon is. It's clearly some sort of underground alien complex, constructed by Saturnian life forms vastly different, and vastly superior to us. Our...
by MartianInvader
Wed Oct 15, 2008 11:04 pm UTC
Forum: News & Articles
Topic: Is it bad for a presidential candidate to be intelligent??
Replies: 63
Views: 5108

Re: Is it bad for a presidential candidate to be intelligent??

Aw c'mon, now you're splitting hairs. Your (22/7) question clearly was phrased to try to discredit his (GreaterSteven's) original point by making it sound nigh-impossible to accomplish; he responded to this point by citing an example where it had been done in less time with less resources. Now you'r...
by MartianInvader
Wed Oct 15, 2008 6:11 pm UTC
Forum: Mathematics
Topic: How important are the field/vector space axioms?
Replies: 6
Views: 1126

Re: How important are the field/vector space axioms?

I seem to recall that linear algebra works perfectly fine over division rings (i.e., fields without the communativity axiom for multiplication). So yeah, some of the axiomatic stuff is just thrown in there for comfort. But it probably wouldn't be a bad idea to just mentally note what axiom you're us...
by MartianInvader
Tue Oct 14, 2008 4:40 pm UTC
Forum: Mathematics
Topic: constant time fibonacci numbers?
Replies: 10
Views: 3195

Re: constant time fibonacci numbers?

Yup. That's also why I was careful to say "linear in the size of the input". The size of the input would be the number of bits used to store it.
by MartianInvader
Tue Oct 14, 2008 2:07 pm UTC
Forum: Mathematics
Topic: implicit differentiation
Replies: 14
Views: 1251

Re: implicit differentiation

Yeah, implicit and explicit differentiation are the same operation. The words "implicit" and "explicit" refer to what you're differentiating , not to how you're doing it. If you have a function defined explicitly, it means something like f(x) = x^3 +sin(x). A function defined imp...
by MartianInvader
Tue Oct 14, 2008 1:50 pm UTC
Forum: Mathematics
Topic: constant time fibonacci numbers?
Replies: 10
Views: 3195

Re: constant time fibonacci numbers?

But doesn't everything that uses arbitrarily large input take at least linear time in the size of the input? I mean, it takes that much time just to read in the data.
by MartianInvader
Tue Oct 14, 2008 1:30 am UTC
Forum: Mathematics
Topic: Implicit differentiation is a lie!
Replies: 39
Views: 4063

Re: Implicit differentiation is a lie!

The differentials dx and dy are smooth sections of the cotangent bundle of R 2 . In the case you have a function f: R -> R , the graph of f is a one-dimensional submanifold, and dx and dy restrict to smooth sections of the cotangent bundle of graph(f). They are (locally) related to each other by dy...
by MartianInvader
Sun Oct 12, 2008 3:14 pm UTC
Forum: Logic Puzzles
Topic: Mutual ignorance
Replies: 14
Views: 3052

Re: Mutual ignorance

I understand what the problem is intended to be (and I'm working on it), but you may want to alter its set-up a smidgen. As it is, there's no basis for saying "we'll never know them", since there's nothing keeping A from just telling B what the sum of the numbers are and B from telling A t...
by MartianInvader
Sun Oct 05, 2008 4:12 am UTC
Forum: Mathematics
Topic: Naughty Functions
Replies: 59
Views: 5190

Re: Naughty Functions

Even worse - The function which is zero for x \leq 0 and e^{-1/x} for x > 0 is continuous and differentiable, but isn't even equal to its Taylor expansion around zero (indeed, every derivative at zero is zero, so the Taylor expansion would be the zero polynomial). Also, plenty of functions are once-...
by MartianInvader
Thu Oct 02, 2008 11:43 pm UTC
Forum: Mathematics
Topic: One third Russian
Replies: 10
Views: 1286

Re: One third Russian

Sure! Your Russian-ness is just the average of the Russian-ness of all your ancestors at some fixed level (it's the average of your parents Russian-ness, which is the same as the average of your grandparents' Russian-ness, which is the same as the average of your great-grandparents Russian-ness, etc...
by MartianInvader
Thu Oct 02, 2008 11:24 pm UTC
Forum: Mathematics
Topic: Intersection of two spheres
Replies: 14
Views: 1930

Re: Intersection of two spheres

Indeed. I count that as "doing something tricky." I purposely used the word "typically" when I said you get a k+m-n sphere. How about I phrase it this way: The intersection is is a k+m-n sphere 100% of the time :D
by MartianInvader
Thu Oct 02, 2008 7:46 pm UTC
Forum: Mathematics
Topic: Intersection of two spheres
Replies: 14
Views: 1930

Re: Intersection of two spheres

What would one you get if you intersected two 3-spheres in a similar way? When intersecting spheres in this way, you should keep track of the ambient space. For examples, the intersection of two 1-spheres (a.k.a. circles) in two dimensions is a 0-sphere (a.k.a. two points), while their intersection...
by MartianInvader
Wed Oct 01, 2008 8:07 pm UTC
Forum: News & Articles
Topic: McCain: If I were dictator, which I always aspire to be...
Replies: 40
Views: 3757

Re: McCain: If I were dictator, which I always aspire to be...

Yeah... at best, you're taking issue with McCain because he made a joke in poor taste.

At worst, you might as well talk about how McCain said "I will... destroy... America."
by MartianInvader
Mon Sep 29, 2008 2:28 pm UTC
Forum: Mathematics
Topic: University Calculus Bonus Problem
Replies: 16
Views: 1913

Re: University Calculus Bonus Problem

You -could- do this in a calculus sort of way, but it seems like overkill: Let x be the amount of cake cut from the first cake (x in the interval [0, 1/2] ). Clearly, the cutter will want to cut the second cake either in half or into one big slice, depending on which cake the second person wants to ...
by MartianInvader
Mon Sep 29, 2008 1:23 am UTC
Forum: News & Articles
Topic: Media Bias
Replies: 26
Views: 2642

Re: Media Bias

No, it doesn't. Their result assumes that right-leaning members of Congress will use right-leaning sources and left-leaning members of Congress will use left-leaning sources. Well, I think it's possible to do a statistical study based on this assumption. If you were to take each source, look at the...
by MartianInvader
Sun Sep 28, 2008 4:04 pm UTC
Forum: News & Articles
Topic: Media Bias
Replies: 26
Views: 2642

Re: Media Bias

In the 109th Congress (2005-2007) there were 41 more Republicans than Democrats (about 7 1/2 % difference). If anything, this metric should lead to a right-leaning press (if the press truly were central) since the Republicans had more seats, and therefore had more ability to write/push through bill...
by MartianInvader
Sun Sep 28, 2008 3:32 pm UTC
Forum: Mathematics
Topic: Naughty Functions
Replies: 59
Views: 5190

Re: Naughty Functions

I can't think of a way to define it nicely in one equation, but I'll describe such a function for you: Let f(x) be zero for 0 <= x <= 1. Between x = 1 and x = 2, have it jump up and then down (in two straight lines if you don't mind it being nondifferentiable, or in a bump if you want it smooth), so...
by MartianInvader
Sun Sep 28, 2008 2:59 pm UTC
Forum: News & Articles
Topic: Media Bias
Replies: 26
Views: 2642

Re: Media Bias

Why is Congress considered to be the arbiter of the mean? Probably because with Congress you're guaranteed to have a good deal of citation on both sides. You've got people who are very specifically political on both the right and left side of the spectrum making the citations quite regularly. Seems...
by MartianInvader
Thu Sep 25, 2008 10:57 pm UTC
Forum: Mathematics
Topic: Basic terminology question
Replies: 5
Views: 1036

Re: Basic terminology question

Ordered pairs? Strings? Words?

I think maybe "Ordered n-tuple" is probably what you're looking for.

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