## Search found 774 matches

- Wed Sep 24, 2008 6:44 pm UTC
- Forum: Logic Puzzles
- Topic: Unusual Cake Slicing
- Replies:
**84** - Views:
**18152**

### 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?)

- Tue Sep 23, 2008 2:40 pm UTC
- Forum: Mathematics
- Topic: Hyper bowls!
- Replies:
**18** - Views:
**2528**

### 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.

- Tue Sep 23, 2008 2:24 pm UTC
- Forum: Mathematics
- Topic: d/dx (e^(x+1)+1) help please
- Replies:
**9** - Views:
**2503**

### 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...

- Fri Sep 19, 2008 8:12 pm UTC
- Forum: Mathematics
- Topic: Fringe: Number Sequence. Spoilers inside.
- Replies:
**8** - Views:
**3330**

### 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).

- Fri Sep 19, 2008 12:53 am UTC
- Forum: Logic Puzzles
- Topic: The Russian Postal Service Problem
- Replies:
**10** - Views:
**3340**

### 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...

- Fri Sep 19, 2008 12:47 am UTC
- Forum: Logic Puzzles
- Topic: What question is its own answer?
- Replies:
**17** - Views:
**3766**

### Re: What question is its own answer?

Homer Simpson wrote:Do I know what rhetorical means?!

- Wed Sep 17, 2008 6:40 pm UTC
- Forum: Mathematics
- Topic: i^i
- Replies:
**4** - Views:
**1213**

### 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...

- Tue Sep 16, 2008 7:55 pm UTC
- Forum: Mathematics
- Topic: Bodybuilding forum + recurring decimal =
- Replies:
**24** - Views:
**3615**

### 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...

- Tue Sep 16, 2008 7:52 pm UTC
- Forum: Mathematics
- Topic: Divisibility rules
- Replies:
**6** - Views:
**2063**

### 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 ...

- 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:
**5599**

### 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...

- Fri Sep 12, 2008 4:58 pm UTC
- Forum: Mathematics
- Topic: Bodybuilding forum + recurring decimal =
- Replies:
**24** - Views:
**3615**

### Re: Bodybuilding forum + recurring decimal =

Post #132 in that thread is, if I'm not mistaken, a proof of Fermat's last theorem.

- Fri Sep 12, 2008 2:13 pm UTC
- Forum: General
- Topic: Donating Blood
- Replies:
**43** - Views:
**3422**

### 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.

- Tue Sep 09, 2008 2:52 am UTC
- Forum: Mathematics
- Topic: The U shaped things
- Replies:
**7** - Views:
**1218**

### 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.

So if B = {1, 2, 3}, and A = {1, 2}, you'd say A \subset B, 1 \in B, etc.

- Mon Sep 08, 2008 10:59 pm UTC
- Forum: Mathematics
- Topic: Forgive me, but I have a dumb question.
- Replies:
**16** - Views:
**1862**

### 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...

- Sat Sep 06, 2008 4:15 pm UTC
- Forum: Mathematics
- Topic: A remarkable fact (the finiteness of pi)
- Replies:
**19** - Views:
**2517**

### 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...

- Fri Sep 05, 2008 9:47 pm UTC
- Forum: Mathematics
- Topic: A remarkable fact (the finiteness of pi)
- Replies:
**19** - Views:
**2517**

### 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...

- Sat Aug 30, 2008 4:54 pm UTC
- Forum: Mathematics
- Topic: Sine Derivative Proof?
- Replies:
**32** - Views:
**5871**

### 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.

- Sat Aug 30, 2008 4:47 pm UTC
- Forum: Mathematics
- Topic: weird thing with exponents and factorials
- Replies:
**6** - Views:
**1923**

### Re: weird thing with exponents and factorials

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

The n

The n

^{th}derivative of x^{n}is the constant function n!.- Sat Aug 30, 2008 4:04 pm UTC
- Forum: News & Articles
- Topic: Georgia breaks ties with Russia
- Replies:
**12** - Views:
**1107**

### 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...

- Tue Aug 26, 2008 5:02 pm UTC
- Forum: Mathematics
- Topic: Something I just Noticed
- Replies:
**15** - Views:
**1898**

### 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.

- Mon Aug 25, 2008 3:43 pm UTC
- Forum: Mathematics
- Topic: What's the genus of this surface?
- Replies:
**6** - Views:
**1197**

### 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.

- Tue Aug 19, 2008 3:10 am UTC
- Forum: Mathematics
- Topic: Finite Difference Operator
- Replies:
**4** - Views:
**1117**

### Re: Finite Difference Operator

Derivatives?

Edit: Ohhh, for real n. Nevermind.

Edit: Ohhh, for real n. Nevermind.

- Tue Aug 19, 2008 2:25 am UTC
- Forum: Mathematics
- Topic: Algebraic Topology
- Replies:
**11** - Views:
**2200**

### 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 ...

- Sun Aug 17, 2008 10:07 pm UTC
- Forum: Mathematics
- Topic: Algebraic Topology
- Replies:
**11** - Views:
**2200**

### 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...

- Sun Aug 10, 2008 6:21 am UTC
- Forum: Mathematics
- Topic: What does this mean?
- Replies:
**10** - Views:
**1606**

### 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.

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.

- Sat Aug 09, 2008 6:37 pm UTC
- Forum: Mathematics
- Topic: What does this mean?
- Replies:
**10** - Views:
**1606**

### 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 ...

- Sat Aug 09, 2008 1:19 pm UTC
- Forum: Mathematics
- Topic: Math Research
- Replies:
**12** - Views:
**1969**

### 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...

- Sat Aug 09, 2008 1:24 am UTC
- Forum: News & Articles
- Topic: War in Georgia
- Replies:
**98** - Views:
**8095**

### 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...

- Fri Aug 08, 2008 8:25 pm UTC
- Forum: News & Articles
- Topic: War in Georgia
- Replies:
**98** - Views:
**8095**

### 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 ...

- Thu Aug 07, 2008 1:35 pm UTC
- Forum: News & Articles
- Topic: Music taste linked to mental state
- Replies:
**27** - Views:
**3000**

### 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.

- Wed Aug 06, 2008 3:38 pm UTC
- Forum: News & Articles
- Topic: Pet Pitbull Cloned in Commercial First
- Replies:
**17** - Views:
**1622**

### 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.

- Mon Aug 04, 2008 2:08 pm UTC
- Forum: News & Articles
- Topic: Cops Shoot Family Pet, Mace Baby
- Replies:
**29** - Views:
**2730**

### 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...

- Thu Jul 31, 2008 1:38 pm UTC
- Forum: Mathematics
- Topic: Sum of cosines
- Replies:
**19** - Views:
**1938**

### Re: Sum of cosines

Ah, well done CFT, I should have thought of using that formula for sin. But why would the sum be N+1 if x = 2k\pi? Isn't sin(2k\pi) = 0, so the sum will always be zero? Someone's going crazy here, and I'd sure like to know if it's me.

- Thu Jul 31, 2008 1:57 am UTC
- Forum: Mathematics
- Topic: Sum of cosines
- Replies:
**19** - Views:
**1938**

### Re: Sum of cosines

That series is always bounded, unless each term is 1 or each term is -1 (that is, the series is bounded as long as A is not an integer multiple of pi). Um, I think you made an error with that first statement. If each term is 1 or -1, won't the series always be bounded? (Seems as though the partial ...

- Wed Jul 30, 2008 9:15 pm UTC
- Forum: Mathematics
- Topic: Sum of cosines
- Replies:
**19** - Views:
**1938**

### Re: Sum of cosines

This thread made me think of a related question that's been bugging me for a while, so I'm just gonna post it here. Fix some constant A, and consider the series \sum_{n=0}^\infty sin(nA) . Then if A isn't an integer multiple of pi, the terms won't go to zero and the series will diverge. But ...

- Wed Jul 30, 2008 8:49 pm UTC
- Forum: Mathematics
- Topic: Percentage of numbers that are prime
- Replies:
**37** - Views:
**9882**

### Re: Percentage of numbers that are prime

To clarify: It is always the case that you CAN rearrange terms to make it go to infinity, which is what your particular arrangement did. Not every arrangement causes the series to go to infinity, obviously (e.g. the original convergent arrangement). I just meant to take the statement "you can m...

- Wed Jul 30, 2008 5:18 pm UTC
- Forum: Mathematics
- Topic: Percentage of numbers that are prime
- Replies:
**37** - Views:
**9882**

### Re: Percentage of numbers that are prime

The issue is what NathanielJ said: your series is at best conditionally convergent. That means that if it does indeed converge, then what it converges to depends on the order in which you add stuff, which you haven't clearly defined. By rearranging the order of the terms in a conditionally converge...

- Tue Jul 29, 2008 6:57 pm UTC
- Forum: News & Articles
- Topic: White House fed Fox News Talking Points
- Replies:
**66** - Views:
**3839**

### Re: White House fed Fox News Talking Points

F) On a day when several other New York newspapers made a story about a failed terror plot the most prominent story on their front page, the Times picked a story about peasants who hand make bricks in India their most prominent story and moved the terror plot story to page 37, and O'Reilly question...

- Tue Jul 29, 2008 3:03 pm UTC
- Forum: Mathematics
- Topic: most important languages for maths
- Replies:
**10** - Views:
**1726**

### Re: most important languages for maths

I seriously doubt that Princeton DOESN'T have a language requirement. I'm a grad student at a far less prestigious university and I had to pass an exam on one of French, German, and Russian (I chose French). This doesn't mean I speak French; I basically needed to learn enough key words so that I cou...

- Mon Jul 28, 2008 7:31 pm UTC
- Forum: News & Articles
- Topic: White House fed Fox News Talking Points
- Replies:
**66** - Views:
**3839**

### Re: White House fed Fox News Talking Points

This is one of the most idiotic things I have ever heard. Have you ever even seen a newspaper? How can you possible justify an argument that a 2600 word article with maybe the first 50 words on page 1 is as much a front page story as one with the first half of the story or more on the front. And ho...