Search found 782 matches

by MartianInvader
Thu Oct 02, 2008 7:46 pm UTC
Forum: Mathematics
Topic: Intersection of two spheres
Replies: 14
Views: 1989

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: 3871

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: 1999

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: 2780

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: 2780

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: 5583

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: 2780

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: 1061

Re: Basic terminology question

Ordered pairs? Strings? Words?

I think maybe "Ordered n-tuple" is probably what you're looking for.
by MartianInvader
Wed Sep 24, 2008 6:44 pm UTC
Forum: Logic Puzzles
Topic: Unusual Cake Slicing
Replies: 84
Views: 18702

Re: Unusual Cake Slicing

Very interesting one. A question for clarification: Are we assuming that all the pieces must be connected? (i.e., if I divvied it up into 5 squares and 5 circles, could I claim 1 piece is a square + a circle?)
by MartianInvader
Tue Sep 23, 2008 2:40 pm UTC
Forum: Mathematics
Topic: Hyper bowls!
Replies: 18
Views: 2652

Re: Hyper bowls!

Yesila wrote:I like to put chips in them when I have a party.


Hyperbolic chips are low-calorie, their triangle shapes are thinner. :?
by MartianInvader
Tue Sep 23, 2008 2:24 pm UTC
Forum: Mathematics
Topic: d/dx (e^(x+1)+1) help please
Replies: 9
Views: 2582

Re: d/dx (e^(x+1)+1) help please

To do it without the chain rule, notice that e^{x+1} = e^{x}e. Then you're just multiplying by a constant (remember e is just a number, not a variable), so the derivative of this is e^{x}e since d/dx (e^x) = e^x. Also, you can't use the power rule like that. You can only use the nx^{n-1} rule when y...
by MartianInvader
Fri Sep 19, 2008 8:12 pm UTC
Forum: Mathematics
Topic: Fringe: Number Sequence. Spoilers inside.
Replies: 8
Views: 3496

Re: Fringe: Number Sequence. Spoilers inside.

It does have at least some sort of mathematical feel to it. All the numbers are products of the first 5 prime numbers (except 1), and except for the last one they're all products of exactly two of those primes (the last is 2*5*11).
by MartianInvader
Fri Sep 19, 2008 12:53 am UTC
Forum: Logic Puzzles
Topic: The Russian Postal Service Problem
Replies: 10
Views: 3441

Re: The Russian Postal Service Problem

Well, the answer I've heard to similar questions: -He puts the ring in the box, locks it, and sends it to her. -She puts a second lock on the box, to which she has the only key, and sends it back to him. -He unlocks and removes his lock, sends the box back to her. -She can now unlock the box and get...
by MartianInvader
Fri Sep 19, 2008 12:47 am UTC
Forum: Logic Puzzles
Topic: What question is its own answer?
Replies: 17
Views: 3828

Re: What question is its own answer?

Homer Simpson wrote:Do I know what rhetorical means?!
by MartianInvader
Wed Sep 17, 2008 6:40 pm UTC
Forum: Mathematics
Topic: i^i
Replies: 4
Views: 1232

Re: i^i

Raising complex numbers to imaginary powers is typically a multi-valued function. We define x^y as e^{y ln x}. e raised to powers is a genuine function, but ln isn't, exactly. ln(1) could be 0, but it could also be 2 \pi i, 4 \pi i, -2 \pi i, etc. In general, asking for the natural log of a number g...
by MartianInvader
Tue Sep 16, 2008 7:55 pm UTC
Forum: Mathematics
Topic: Bodybuilding forum + recurring decimal =
Replies: 24
Views: 3903

Re: Bodybuilding forum + recurring decimal =

After reading that thread I was so tempted to go to that forum and say, "Hey guys, I'm a mathematician, and some of my math buddies told me you can actually alter your appearance via diet and exercise. I think this is bullshit, there's no way to change the way you look." ...unless maybe yo...
by MartianInvader
Tue Sep 16, 2008 7:52 pm UTC
Forum: Mathematics
Topic: Divisibility rules
Replies: 6
Views: 2140

Re: Divisibility rules

By definition, z is a factor of z, so if x is divisible by all factors of z, it's divisible by z :P You probably want the rule to be divisible by all prime factors of z Except then it's not true (12 is divisible by all prime factors of 9). Maybe all powers of primes which are factors of z? But now ...
by MartianInvader
Tue Sep 16, 2008 7:38 pm UTC
Forum: News & Articles
Topic: A Very good documentury on how the global economy works...
Replies: 89
Views: 5910

Re: A Very good documentury on how the global economy works...

Ok, I have a quick question about this video that has more or less nothing to do with the fervent argument that's been going on in the last dozen or so posts. My question is this: Is the current European economy operating in this same way? The video says this exponentially growing debt system is the...
by MartianInvader
Fri Sep 12, 2008 4:58 pm UTC
Forum: Mathematics
Topic: Bodybuilding forum + recurring decimal =
Replies: 24
Views: 3903

Re: Bodybuilding forum + recurring decimal =

Post #132 in that thread is, if I'm not mistaken, a proof of Fermat's last theorem.
by MartianInvader
Fri Sep 12, 2008 2:13 pm UTC
Forum: General
Topic: Donating Blood
Replies: 43
Views: 3562

Re: Donating Blood

I once donated and played soccer that afternoon, without problem. That was back in high school, though; I wouldn't try it again today.
by MartianInvader
Tue Sep 09, 2008 2:52 am UTC
Forum: Mathematics
Topic: The U shaped things
Replies: 7
Views: 1263

Re: The U shaped things

To supplement, if A were an element of the sets and not a subset, you'd use the symbol \in

So if B = {1, 2, 3}, and A = {1, 2}, you'd say A \subset B, 1 \in B, etc.
by MartianInvader
Mon Sep 08, 2008 10:59 pm UTC
Forum: Mathematics
Topic: Forgive me, but I have a dumb question.
Replies: 16
Views: 1938

Re: Forgive me, but I have a dumb question.

Ah, but infinity is not a real number. "The limit exists" means the limit is a real number. "The limit doesn't exist" means the limit is not a real number. "The limit is infinity" is a slightly misleading statement, as it means that the limit does not exist, but it does...
by MartianInvader
Sat Sep 06, 2008 4:15 pm UTC
Forum: Mathematics
Topic: A remarkable fact (the finiteness of pi)
Replies: 19
Views: 2618

Re: A remarkable fact (the finiteness of pi)

Martian invader, your right about the center of mass. If you make a horn from 1 to a, a goes to infinity, then the moment-of-inertia is proportianol to ln(a), while the volume stays bounded, something like \pi-1/a . So if you divide them, the centre of 'mass' (volume really) goes to infinity if a d...
by MartianInvader
Fri Sep 05, 2008 9:47 pm UTC
Forum: Mathematics
Topic: A remarkable fact (the finiteness of pi)
Replies: 19
Views: 2618

Re: A remarkable fact (the finiteness of pi)

Isn't the volume of a solid of revolution the cross section times the distance the centre of mass moves? So is the centre of mass at the origin for a reciprocal curve? I'm not familiar with this method, but it sounds like something that maybe only works if the cross-sections have constant areas? Ho...
by MartianInvader
Sat Aug 30, 2008 4:54 pm UTC
Forum: Mathematics
Topic: Sine Derivative Proof?
Replies: 32
Views: 6102

Re: Sine Derivative Proof?

Well to be fair, often sin(x) and cos(x) are defined by their Taylor series expansions, and their geometric properties are shown later. In that case, using the Taylor series argument is fine.
by MartianInvader
Sat Aug 30, 2008 4:47 pm UTC
Forum: Mathematics
Topic: weird thing with exponents and factorials
Replies: 6
Views: 1994

Re: weird thing with exponents and factorials

If you've had calculus, the thing you should be thinking about is this:

The nth derivative of xn is the constant function n!.
by MartianInvader
Sat Aug 30, 2008 4:04 pm UTC
Forum: News & Articles
Topic: Georgia breaks ties with Russia
Replies: 12
Views: 1139

Re: Georgia breaks ties with Russia

I'm imagining myself as the Bush Administration. McCain's not doing as well as I'd like, and nothing gets the people on the side of the warmongers like a big, bad, foe that's already fighting. If I were the administration, there's nothing I'd love more than for Russia to invade Georgia (forced or no...
by MartianInvader
Tue Aug 26, 2008 5:02 pm UTC
Forum: Mathematics
Topic: Something I just Noticed
Replies: 15
Views: 1945

Re: Something I just Noticed

And all even numbers are exactly four less than a multiple of a square of a number twelve more than a multiple of ten, mod 2.
by MartianInvader
Mon Aug 25, 2008 3:43 pm UTC
Forum: Mathematics
Topic: What's the genus of this surface?
Replies: 6
Views: 1257

Re: What's the genus of this surface?

If I understand correctly, you started with a torus, cut two holes in the surface, then connected the two holes with a tube (or to be specific, a copy of circle x interval). That process gives you a surface of genus two.
by MartianInvader
Tue Aug 19, 2008 3:10 am UTC
Forum: Mathematics
Topic: Finite Difference Operator
Replies: 4
Views: 1141

Re: Finite Difference Operator

Derivatives?


Edit: Ohhh, for real n. Nevermind.
by MartianInvader
Tue Aug 19, 2008 2:25 am UTC
Forum: Mathematics
Topic: Algebraic Topology
Replies: 11
Views: 2259

Re: Algebraic Topology

Nah, you need cells in all kinds of dimensions. For example, you couldn't get a torus with only 0- and 2-cells; you need at least 2 1-cells. You can see this using fundamental group or homology, both of which are discussed in Hatcher's book. However, almost any manifold can be constructed as a cell ...
by MartianInvader
Sun Aug 17, 2008 10:07 pm UTC
Forum: Mathematics
Topic: Algebraic Topology
Replies: 11
Views: 2259

Re: Algebraic Topology

Topologically, an n-cell is just a closed, n-dimensional ball. That's it. Calling in an "n-cell" implies that you're going to glue it onto other cells in a certain way. The way you attach an n-cell to a space is by "gluing" its boundary. The boundary of an n-ball is an (n-1) sphe...
by MartianInvader
Sun Aug 10, 2008 6:21 am UTC
Forum: Mathematics
Topic: What does this mean?
Replies: 10
Views: 1662

Re: What does this mean?

There's definitely varying levels of not understanding the statement.

To understand it with minimal study, you probably don't need to know what the Hecke operators are.

You should, however, know what the heck operators are.
by MartianInvader
Sat Aug 09, 2008 6:37 pm UTC
Forum: Mathematics
Topic: What does this mean?
Replies: 10
Views: 1662

Re: What does this mean?

Well, since no one has said the words yet, SL(2,Z) stands for the Special Linear group. In this case, the special linear group of 2x2 matrices with integer entries. This means 2x2 matrices with integer entries that have determinant 1. That's probably the simplest term in that sentence, except maybe ...
by MartianInvader
Sat Aug 09, 2008 1:19 pm UTC
Forum: Mathematics
Topic: Math Research
Replies: 12
Views: 2041

Re: Math Research

Woohoo! Go geometric group theory! To answer the "what the heck is it?" question: Geometric group theory typically studies groups by studying their Cayley graphs. Unfortunately a group can have many different Cayley graphs (depending on what generating set you use), so you look for propert...
by MartianInvader
Sat Aug 09, 2008 1:24 am UTC
Forum: News & Articles
Topic: War in Georgia
Replies: 98
Views: 8408

Re: War in Georgia

I can't find any firm statement about who started the current set of aggressions (the first violence since 1992). Regardless of who sparked the violence, I have to agree with Mercurius: the Ossetians have a legitimate claim to independence and if the US is going to laud democracy, it should stop su...
by MartianInvader
Fri Aug 08, 2008 8:25 pm UTC
Forum: News & Articles
Topic: War in Georgia
Replies: 98
Views: 8408

Re: War in Georgia

I don't think we'll see any US arms going to Russia in this one. Georgia's allied with the west and applied for membership in NATO, and supported by Bush. Given the proximity to all the Middle-East stuff and Bush's rhetoric, I'd guess that we'd be sending troops in to help them against Russia if we ...
by MartianInvader
Thu Aug 07, 2008 1:35 pm UTC
Forum: News & Articles
Topic: Music taste linked to mental state
Replies: 27
Views: 3102

Re: Music taste linked to mental state

Oh good! In this modern, fast-paced world, who has time to actually TALK to their kids anymore? These handy correlations will make it much quicker to decide when something ain't right with your children.
by MartianInvader
Wed Aug 06, 2008 3:38 pm UTC
Forum: News & Articles
Topic: Pet Pitbull Cloned in Commercial First
Replies: 17
Views: 1681

Re: Pet Pitbull Cloned in Commercial First

Brought back a dog that looks like her dead pet but has a different personality? Pshh, she could have saved money and just buried it at the old Pet Sematary.
by MartianInvader
Mon Aug 04, 2008 2:08 pm UTC
Forum: News & Articles
Topic: Cops Shoot Family Pet, Mace Baby
Replies: 29
Views: 2853

Re: Cops Shoot Family Pet, Mace Baby

Is anyone else really annoyed by this article? I mean, they don't even tell you where this happened - it could have been in New York city or in rural Tibet for all they say, right? And what was the cause of the macing/shooting? All they seem to be doing is repeating names over and over to make you s...

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