## Search found 790 matches

- Tue Oct 14, 2008 4:40 pm UTC
- Forum: Mathematics
- Topic: constant time fibonacci numbers?
- Replies:
**10** - Views:
**3289**

### 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.

- Tue Oct 14, 2008 2:07 pm UTC
- Forum: Mathematics
- Topic: implicit differentiation
- Replies:
**14** - Views:
**1302**

### 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...

- Tue Oct 14, 2008 1:50 pm UTC
- Forum: Mathematics
- Topic: constant time fibonacci numbers?
- Replies:
**10** - Views:
**3289**

### 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.

- Tue Oct 14, 2008 1:30 am UTC
- Forum: Mathematics
- Topic: Implicit differentiation is a lie!
- Replies:
**39** - Views:
**4288**

### 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...

- Sun Oct 12, 2008 3:14 pm UTC
- Forum: Logic Puzzles
- Topic: Mutual ignorance
- Replies:
**14** - Views:
**3118**

### 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...

- Sun Oct 05, 2008 4:12 am UTC
- Forum: Mathematics
- Topic: Naughty Functions
- Replies:
**59** - Views:
**5766**

### 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-...

- Thu Oct 02, 2008 11:43 pm UTC
- Forum: Mathematics
- Topic: One third Russian
- Replies:
**10** - Views:
**1349**

### 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...

- Thu Oct 02, 2008 11:24 pm UTC
- Forum: Mathematics
- Topic: Intersection of two spheres
- Replies:
**14** - Views:
**2026**

### 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

- Thu Oct 02, 2008 7:46 pm UTC
- Forum: Mathematics
- Topic: Intersection of two spheres
- Replies:
**14** - Views:
**2026**

### 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...

- 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:
**3931**

### 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."

At worst, you might as well talk about how McCain said "I will... destroy... America."

- Mon Sep 29, 2008 2:28 pm UTC
- Forum: Mathematics
- Topic: University Calculus Bonus Problem
- Replies:
**16** - Views:
**2053**

### 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 ...

- Mon Sep 29, 2008 1:23 am UTC
- Forum: News & Articles
- Topic: Media Bias
- Replies:
**26** - Views:
**2832**

### 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...

- Sun Sep 28, 2008 4:04 pm UTC
- Forum: News & Articles
- Topic: Media Bias
- Replies:
**26** - Views:
**2832**

### 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...

- Sun Sep 28, 2008 3:32 pm UTC
- Forum: Mathematics
- Topic: Naughty Functions
- Replies:
**59** - Views:
**5766**

### 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...

- Sun Sep 28, 2008 2:59 pm UTC
- Forum: News & Articles
- Topic: Media Bias
- Replies:
**26** - Views:
**2832**

### 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...

- Thu Sep 25, 2008 10:57 pm UTC
- Forum: Mathematics
- Topic: Basic terminology question
- Replies:
**5** - Views:
**1065**

### Re: Basic terminology question

Ordered pairs? Strings? Words?

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

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

- Wed Sep 24, 2008 6:44 pm UTC
- Forum: Logic Puzzles
- Topic: Unusual Cake Slicing
- Replies:
**84** - Views:
**19083**

### 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:
**2729**

### 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:
**2661**

### 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:
**3586**

### 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:
**3521**

### 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:
**3870**

### 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:
**1251**

### 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:
**4070**

### 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:
**2232**

### 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:
**6022**

### 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:
**4070**

### 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:
**3702**

### 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:
**1287**

### 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:
**1987**

### 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:
**2690**

### 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:
**2690**

### 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:
**6249**

### 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:
**2032**

### 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:
**1185**

### 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:
**1992**

### 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:
**1275**

### 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:
**1167**

### 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:
**2313**

### 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:
**2313**

### 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...