Search found 209 matches

by aguacate
Sun Oct 14, 2007 9:57 pm UTC
Forum: Mathematics
Topic: Are there jordan curves with non-zero area?
Replies: 15
Views: 5536

Re: Are there jordan curves with non-zero area?

I have little knowledge in this area so forgive my misunderstandings. Isn't a hilbert curve non-overlapping?
by aguacate
Sun Oct 14, 2007 2:26 am UTC
Forum: Mathematics
Topic: Are there jordan curves with non-zero area?
Replies: 15
Views: 5536

Are there jordan curves with non-zero area?

When one of the professors who specializes in a math field (I can't remember which one) related to this question was asked, he said "I don't know."
by aguacate
Tue Oct 09, 2007 12:04 am UTC
Forum: Mathematics
Topic: (-1)^pi
Replies: 25
Views: 3288

Re: (-1)^pi

What can you say about negative numbers to powers of transcendental numbers? Mathematica, apparently, can't say anything. You may have to tell it to display the numerical result. Type (-1)^<ESC>pi<ESC> //N where <ESC> is the escape key. Nice, yes, thank you. OK, here are so more thoughts: -1 is rea...
by aguacate
Mon Oct 08, 2007 11:04 pm UTC
Forum: Mathematics
Topic: (-1)^pi
Replies: 25
Views: 3288

Re: (-1)^pi

Rilian wrote:my calculator won't do (-1)^(2/3)

But I know that the answer is 1!

And matlab gives a retarded answer.

>> (-1)^(2/3)

ans =

-0.5000 + 0.8660i


That's a valid answer.
by aguacate
Mon Oct 08, 2007 11:03 pm UTC
Forum: Mathematics
Topic: (-1)^pi
Replies: 25
Views: 3288

Re: (-1)^pi

Bluhhh, I feel retarded. -1 = e^(i*pi) so (-1)^pi = e^(i*pi^2)) = what you wrote. Why doesn't mathematica know this? For a second I thought I had stumbled upon something profound.
by aguacate
Mon Oct 08, 2007 10:54 pm UTC
Forum: Mathematics
Topic: (-1)^pi
Replies: 25
Views: 3288

(-1)^pi

What can you say about negative numbers to powers of transcendental numbers? Mathematica, apparently, can't say anything.
by aguacate
Thu Sep 27, 2007 2:35 pm UTC
Forum: Mathematics
Topic: Favorite Mathematical Equation
Replies: 87
Views: 21755

Re:

Sana wrote:Probably
Image

Not sure why. It's just interesting I guess.


Yes this one is a classic, although I think

e^(i*pi) + 1 = 0

is better.
by aguacate
Thu Sep 27, 2007 2:31 pm UTC
Forum: Mathematics
Topic: Graduate-Level Math Courses
Replies: 10
Views: 2655

Re: Graduate-Level Math Courses

I wouldn't really consider the monetary cost of the university. For every place I've checked out so far the math departments cover you 100% the whole way (or the first year for sure and after that depending on if you're making satisfactory progress).
by aguacate
Tue Sep 25, 2007 6:25 pm UTC
Forum: Mathematics
Topic: Monkeys and Shakespeare
Replies: 32
Views: 4345

Yakk wrote:That's it! We can start a Shakespeare monkey breeding program.

You stick a bunch of monkeys in front of typewriters. After a month, those whose typewriters contain the longest and most frequent subsets of Shakespeare are bred: those that do not are put down.


We have a winner
by aguacate
Sat Sep 22, 2007 6:27 pm UTC
Forum: Mathematics
Topic: When would you use the (various) canonical forms?
Replies: 11
Views: 2170

skeptical scientist wrote:I'm confused. Why would anyone care about anything other than proving theorems?


Seriously, go back to the physics forum
by aguacate
Fri Sep 21, 2007 3:57 pm UTC
Forum: Mathematics
Topic: Monkeys and Shakespeare
Replies: 32
Views: 4345

Let's say the monkeys are given a keyboard that randomly switches all the key assignments (drawing from the nomal and shifted keys) every time a key is presssed. That would make it pretty random I think.
by aguacate
Thu Sep 20, 2007 4:45 pm UTC
Forum: Mathematics
Topic: Word Numbers Puzzle
Replies: 33
Views: 4444

You don't include the "and" in the writing out of the number in this puzzle The 51 billionth letter also completes the spelling of an integer. Which one, and what is the sum of all the integers to that point? [1] For example, 911,610,034 is written "ninehundredelevenmillionsixhundred...
by aguacate
Wed Sep 19, 2007 7:20 am UTC
Forum: Mathematics
Topic: Basic/Self-Evident Truth in Mathematics
Replies: 53
Views: 11994

Vector discussion Although, to be able to apply all the logical consequences to the "real world vectors" you have to posit the axiom "real world vectors behave and will always behave like the mathematically defined vectors". You will never show this to be true through experiment...
by aguacate
Tue Sep 18, 2007 5:52 pm UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 494625

zenten wrote:Why is pi afraid of the 2501st digit of e?


http://www.qwantz.com/archive/001013.html
by aguacate
Mon Sep 17, 2007 12:55 am UTC
Forum: Mathematics
Topic: The 6 Ns puzzle
Replies: 40
Views: 5816

Did you read the previous replies? My first solution for 9 involved the explicit use of Pi and skeptical scientist made the same observation that you did; in my second solution for 9 I use no explicit constants. In the previous reply, I was not giving a solution for 9, I was explaining to someone e...
by aguacate
Thu Sep 13, 2007 10:00 pm UTC
Forum: Mathematics
Topic: Logarithms = ???
Replies: 21
Views: 3903

When you took the square out of the log in the left hand side, you should have taken the square root of everything, not just x^2. I.e., it should have been 3x, not 9x.

edit: one more clarification just to make sure you follow - log(9x^2) = log[(3x)^2] = 2log(3x)
by aguacate
Thu Sep 13, 2007 5:18 am UTC
Forum: Mathematics
Topic: What to do - Adventure or finish school faster (or $?)
Replies: 4
Views: 1490

What to do - Adventure or finish school faster (or $?)

Need to decide pretty soon... If I go to grad school in 2008 I have to apply by the end of this year. I still have no idea which school I want to go to. I don't really know any math professors to give me recommendations (just transferred in this year), and I have to take the GREs. I have the general...
by aguacate
Fri Sep 07, 2007 5:42 pm UTC
Forum: Science
Topic: Weird Science Teachers
Replies: 54
Views: 8256

My E&M physics professor had a reputation. On the first day of class he distributed the sylabuses by tossing the stack of paper in the air above our heads. Actually he distributed every handout that way. Every time he went on vacation he was always 'going to mars'. He pronounced robot funny. I t...
by aguacate
Fri Sep 07, 2007 5:18 pm UTC
Forum: Mathematics
Topic: Group table
Replies: 6
Views: 1351

Don't really want to start a new thread....

Would it be correct to say that

generating set: {a}, relation: a^n = e

is the freest cyclic group of order n? Because starting from here, any cyclic group can be formed by adding more equations (right?) Wait, are cyclic groups always finite?
by aguacate
Fri Sep 07, 2007 5:05 pm UTC
Forum: Mathematics
Topic: My mathematical speed bump
Replies: 36
Views: 6364

Nothing beats locking yourself in your room (preferrably on a saturday) and opening your book and working out all the problems until you figure it out. When you do figure something out and learn something new endorphins are released in your brain which provides motivation to learn more and work hard...
by aguacate
Thu Sep 06, 2007 11:16 pm UTC
Forum: Mathematics
Topic: Peer-review my mathy blog post!
Replies: 23
Views: 3914

Re: Peer-review my mathy blog post!

Really it's the idea of a circle that the elements are trying to fit, not the circle itself, that makes a circle part of the universe. Perhaps you could say that they are always within epsilon of a true circle (using whichever method you like to determine how it's 'within')? It is like the skeleton...
by aguacate
Thu Sep 06, 2007 8:20 pm UTC
Forum: Mathematics
Topic: Group table
Replies: 6
Views: 1351

Group table

I am learning about group tables. Let's take the additive group of integers mod 5. Here is the table. +_0 1 2 3 4 0_0 1 2 3 4 1_1 2 3 4 0 2_2 3 4 0 1 3_3 4 0 1 2 4_4 0 1 2 3 Using the table alone we can see what properties this structure has. It has closure, because only 0-4 appear in the body. It h...
by aguacate
Thu Sep 06, 2007 4:18 pm UTC
Forum: Mathematics
Topic: Peer-review my mathy blog post!
Replies: 23
Views: 3914

Re: Peer-review my mathy blog post!

The real question you need to ask yourself, is there anything nature which is circle like at all? The circle is an abstract geometrical construct, really quite different in many respects to what the universe is made up off. Plenty of things look like circles. http://farm1.static.flickr.com/92/25181...
by aguacate
Wed Sep 05, 2007 8:21 pm UTC
Forum: Language/Linguistics
Topic: Words you love.
Replies: 680
Views: 141749

Holocaust It puts pictures of empty fading ghosts in your face (enhanced by the sound 'hollow'), then you have 'cost' at the end, but it's got a 'au' in it so you also think of 'caught', and the gh in caught along with the H at the beginning bring you back to 'ghosts'. Gauze? Say the word out loud ...
by aguacate
Wed Sep 05, 2007 6:41 pm UTC
Forum: Mathematics
Topic: Peer-review my mathy blog post!
Replies: 23
Views: 3914

I do not know as much as I would like to about physics. Is there any compelling reason to believe that either the universe is or is not made up of simple geometric objects?
by aguacate
Tue Sep 04, 2007 3:40 pm UTC
Forum: Mathematics
Topic: Is 20 too old for a first real analysis course?
Replies: 32
Views: 7393

I'm 22 and I start my first real analysis course in a few weeks.
by aguacate
Fri Aug 31, 2007 9:02 pm UTC
Forum: Mathematics
Topic: Basic/Self-Evident Truth in Mathematics
Replies: 53
Views: 11994

zenten wrote:Isn't drawing links between math and nature the role of science, not math?



What do you think motivates the definitions?
by aguacate
Fri Aug 31, 2007 5:31 pm UTC
Forum: Mathematics
Topic: Basic/Self-Evident Truth in Mathematics
Replies: 53
Views: 11994

Yakk wrote:Like most things worth doing, Mathematics is both an art and a tool. Denigrating the art and praising the tool is not always best for the tool, even if you do not care for the art. :)


And praising the art while denigrating the tool is just silly.
by aguacate
Fri Aug 31, 2007 5:18 pm UTC
Forum: Mathematics
Topic: Fractional Calculus (and other fun with diff. operators)
Replies: 20
Views: 3696

This is going a little anayltic number theory-ish, but I was reading "On Prime Numbers Less than a give magnitude" and there was one integral that was evaluated from +\infty to +\infty. How is this possible? Also how can an integral be evaluated from c-i\infty to c+i\infty? Don't know abo...
by aguacate
Thu Aug 30, 2007 11:07 pm UTC
Forum: Mathematics
Topic: Basic/Self-Evident Truth in Mathematics
Replies: 53
Views: 11994

Why are you calling me a bot? I didn't know I had to post to any particular thread before I could participate in your forum. Some of the people here are just used to acting like weiners. In their defense, on the other hand, there is a rules thread (it's the first one) http://forums.xkcd.com/viewtop...
by aguacate
Wed Aug 29, 2007 10:58 pm UTC
Forum: Mathematics
Topic: Inexact graph search algorithms
Replies: 15
Views: 3297

Hmm, I should have said "that will probably give you a close answer" not the closest answer. My whole point that I want you to understand is that probability and accuracy are completely different ideas, and you need to specify what you want. I don't know anything about these functions you ...
by aguacate
Wed Aug 29, 2007 6:53 pm UTC
Forum: Mathematics
Topic: Inexact graph search algorithms
Replies: 15
Views: 3297

The more information you have about your function, the more efficient your algorithm can be. Without more information on the function, you need to at least search all of value 1s as has been said. The first question that needs answering is whether you can accept failures as long as they are unlikely...
by aguacate
Tue Aug 28, 2007 10:51 pm UTC
Forum: Mathematics
Topic: Inexact graph search algorithms
Replies: 15
Views: 3297

It seems to me that the goal in looking for an optimal algorithm would be not only to find the most accurate/quickest algorithm but to find the algorithm that is most probable to be most accurate/efficient. Without more information on your functions, no algorithm other than an exhaustive search of V...
by aguacate
Fri Aug 24, 2007 4:53 pm UTC
Forum: Mathematics
Topic: I wonder know how interesting these formulas are
Replies: 7
Views: 2124

gmalivuk wrote:It's only key of C inasmuch as the note numbers have C=0. But it's not like playing in a different key changes the frequency of any of the notes.


It doesn't change the frequency only if you're using equal temperament.
by aguacate
Wed Aug 22, 2007 11:33 pm UTC
Forum: Mathematics
Topic: "Chances Are... Adventures in Probability"
Replies: 1
Views: 1339

Yes! I do not believe I finished it before it was due back at the library. Interesting read. Seemed more about history than about math.
by aguacate
Mon Aug 20, 2007 7:24 pm UTC
Forum: Mathematics
Topic: What level of mathematics do people know on this forum?
Replies: 63
Views: 9622

I don't think you'll go over everyone's heads. There is a pretty wide spread of math knowledge around here.
by aguacate
Sun Aug 19, 2007 5:40 am UTC
Forum: Mathematics
Topic: Math Challenge - Irrational Numbers (make a proof)
Replies: 8
Views: 4453

All fractions containing two integers do not repeat in decimal form eventually. pi/4 is a fraction. All rational numbers (I think this is what you meant) on the other hand do not repeat in decimal form eventually, unless you count 000000... as a repeating decimal (ie 3.2 = 3.200000000...), then in t...
by aguacate
Thu Aug 16, 2007 5:57 am UTC
Forum: Mathematics
Topic: WLOG
Replies: 7
Views: 3089

WLOG

What does "without loss of generality" mean and when should it be used?
by aguacate
Thu Aug 16, 2007 5:56 am UTC
Forum: Mathematics
Topic: Help with this theorem - accumulation pts and cpt sets
Replies: 11
Views: 2572

No we didn't and later on he even taught us (in R) TFAE: 1) K closed and bounded 2) K compact 3) every infinite subset S of K has a limit point in K: S* intersect K is not empty This being specifically in R, I don't see why. I'd ask him but our next class is the final exam :( should have reviewed my...
by aguacate
Thu Aug 16, 2007 5:15 am UTC
Forum: Mathematics
Topic: Help with this theorem - accumulation pts and cpt sets
Replies: 11
Views: 2572

Not all compact spaces are closed. While it is true that a compact subspace of a hausdorff space is necessarily closed, it is not true that a compact subspace of an arbitrary topological space is closed. Take, for example, the indiscrete topology on R (the only open sets are the null set and all of...

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