Mathematics

I'm not sure, if it is a senceful question but... I always get angry when someone write something like [math] \lim_{x \rightarrow 2 }\left(\frac{x^2-4}{x-2} \right) =4 [/math] because it's not equal ,it approximates, it's "almost equal". I know, it's mathematicly correct, but something's telling me that the equality is not the best symbol for this. The question is if the "4" on the right represents number or constant function (and my opinion is it should end in this [math] \lim_{x \rightarrow 2 }\left(\frac{x^2-4}{x-2} \right) =\lim_{x \rightarrow 2 } (4) [/math] formula without other editing, if it is a function...) and if that "4" is a real number, why is there e…

Could some kind soul explain the simplification of the following sin(theta) + mucos(theta) = cos(theta) - musin(theta) tan(theta) + mu 1 - mutan(theta) I understand that sin(theta)/cos(theta) = tan(theta), but cannot work out how the 1 - the rest comes from. Thanks

Hi all, how would you find the kinetic energy of a sparrow of 28.6 g moving at a speed of 13 M S^-^1. Thanx.

Which of these relation on the set of all people are equivalence relation ? Determine the properties of an equivalence relation that the other lack. (1) {(a,b) | a and b are the same age} (2) {(a,b) | a and b have the same parents} (3) {(a,b) | a and b share a common parents} (4) {(a,b) | a and b have met} (5) {(a,b) | a and b speak common language} Appreciate your reply.

I dare anybody to try and disprove the fact that 0.9999999..... repeating doesn't equal 1. In particular, read some of the proofs on this website here: http://www.qntm.org/?pointnine Good luck

While thinking about random walk on a graph, standard approach is that every possible edge is equally probable - kind of maximizing local entropy. There is new approach (MERW) - which maximizes global entropy (of paths) - for each two vertexes, each path of given length is equally probable. For a regular graph it gives the same, but usually they are different - it MERW we get some localizations, not known in standard random walk. It was derived in http://www.arxiv.org/abs/0710.3861 in the context of optimal encoding. In http://www.arxiv.org/abs/0810.4113 are analyzed it's localization properties. It can also suggest the nature of quantum physics ( http://www.advanc…

I made a thread with general exploration of the concept of portals before but now I want to just explore this scenario. I was wondering where to put this but I think that it needs to be explored mathematically to be solved although I would be grateful if explanation would be given as well as mathematics. For this thread what I will be calling portals are 2D areas of space in a 3D environment, they behave physically like an other very thin thing would. They can't bend and are rectangular. They are one sided and the back side is solid, things cannot pass though the solid parts. There are thin edges around the front side much like the frame of a picture, they are also so…

Hey all, just a quick question, does anybody recognize a pattern in the following numbers...? 1, 2, 2, 3, 4, 3, 5, 4, 6, 7, 5, 3... I can post more if you need them. Cheers, Gabe

I know this is a stupid question but Im going to ask it anyway Ive written an iterative algorithm in C (programming language) and wondered how to represent this in maths. For example, int main(void) { int x; for(x=40; x>0; x/=2) { process(x); } return 0; } So each of the following is put into the equation... 40 20 10 5 2 1 Basically all I want to know is what do you use in maths to represent equating a formula with a range of input values?

Hi everyone, I want to find a function to fit a two arrays data (X,Y=f(X)) with high precision, but I am not succeed. Can any one help me. These are my data: X={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19 ,20,21,22,23,24,25,26,27,28,29,30,31,32, 33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49 ,50,51,52,53,54,55,56,57,58,59,60,61, 62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78 ,79,80,81,82,83,84,85,86,87,88,89,90, 91,92,93,94,95,96,97,98,99,100,101,102,103}; Y={-3.82047923,-4.78741509,-3.7235349,-3.83978508,-4.05577459,-4.30089612,-4.533835, -4.74829898,-4.94488133,-5.12552735,-4.85195336,-4.7612524,-4.68355948,-4.69161082, -4.73528276,-4.79596239,-4.…

Hey all, While this is a sort of computer oriented problem, I decided to put it in General Mathematics, because the answer to this question will be a math answer. So on we go. When you tell the computer to draw a circle with a diameter x on the screen, it won't draw a perfect circle. Why? Well, let's skip the "Pi is irrational part" for a second. The screen is made of pixels. Pixels are squares. So, ultimately, the shape we see is lots of tiny squares put together so as to form something resembling a circle. But it's not a circle. It's squares. Now here's what I need; how does a computer know, based on the diameter of the circle that we want it to draw, how many s…

Does an equation that describes a physical situation apply to a situation in which one of its parameters does not exist?

there is a triangle ABC.Find the locus of point X such that area of triangle ABX=area of triangle XAC.

Hey all, I was thinking the other day, I know it's possible to have, say, base [math]\pi[/math] number systems...but what about base one? Or base smaller-than-one, eg. [math]1/2[/math]? Or negative bases? Or fractional bases? How would one convert to and from those systems? Cheers, Gabe

I have got a quadratic form as following: F(w) = g^T * w + (1/2)* w^T * B * w Here T is the matrix transpose. Someone said the if p is a solution to this quadratic form then p is a solution to an equation of the form: (B + aI) * p = -g Here I is the identity matrix. May I ask why please? Thanks a lot!

hi all, can anyone please help. Im stuck on calculating the volume - If you had a mass of 1.028 x 10^26 kg and density of 1.61 x 10^3 kg m-3. I have come up with what i think is the answer that is 0.63850931677m^3 If this is correct, then how do i write this answer to the appropriate number of significant figures. Many thanks Carl1

Is it true what people say to me that maths s easy and all it is a logical puzzle because i am so bad at it?

Hi, does anyone have an "order" of maths? I know it sounds strange, but I need a list of different types of maths, and in which order they should be explored. I hope to be a mathematician or a physicist someday, but I'm still struggling with the 10th grade math that I'm doing now >.< so I'd like some type of list, so that I can first perfect the current math that I'm doing with online guides, then know where to move next. Also, this would help me ace a lot of my math tests. If anyone has any advice, or a link or anything of the sort, it'd be greatly appreciated. Thanks.

I was reading about the Arecibo message thingy, with the message being transmitted in 1679 bits because there's only two ways to lay out 1679 in a grid, one of which would make "sense" and one that wouldn't. Then I thought, this would only work if aliens used a square grid system (where information can have x & y co-ordinates) for their layouts, which there's no guarantee they would... What if alien visual representations or data were laid out on a hex grid? Maybe they would arrange them from the center spiraling outwards either clockwise or counter-clockwise. Maybe they would be arranged in rows and zigzag columns, or columns and zigzag rows, or maybe …

I am dealing with tomography inverse problem by using trust-region optimization now. I compared my result with other optimization algorithms found that trust-region results are much better. May I ask if the trust-region optimization subproblem contains a regularization already itself please? If it contains regularization itself and how does this related to Tikhonov regularization please? By the way, I am using Matlab fminunc to implement the large scale trust-region Newton algorithm. Thanks a lot and I am looking forward to your reply!

Hi, everyone. Hey, so I have a statistics project to do. I'm just trying to balance some ideas. I need to make a research question and eventually a hypothesis and alternative hypothesis that I will prove or disprove. I was thinking of doing something related to the NBA such as Home vs Away game success or something about the business world. We learned annova tables, two samples, one samples to prove or disprove hypothesis. Anyone got any ideas or recommendations on something that wouldn't be too tough to do?

Hey all, I was browsing through our math book the other day, and I came upon an interesting question. Say you have a table with a diameter of 0.6m, and on that table a square meter-by-meter tablecloth. One corner of the tablecloth is hanging over by half a meter, and another by 0.3 meters. By how much are the other corners hanging over? I came up with 0.5 and 0.3 meters, but I'm not sure I'm right. Can anyone verify? Thanks in advance, Gabe

Posted below is a link to an attempted proof of FLT that I haven't been able to find a flaw in: http://groups.google.com/group/fermats-last-theorem-flt-2008

So today I was bored in class so I started to think about polynomials, specifically parabolas. I know that it is possible to find imaginary roots of a parabola. My question is when you graph this parabola that has two imaginary roots the curve never hits the x-axis then were are the imaginary roots at? When I asked my instructor he said he had no idea. My only guess was that there was a z-axis there the appeared somewhere but I really have no ideas. So where are the imaginary roots on the graph?

Is the fact that a Minus x Minus = Positive an axiom or is there a [simple] mathematical proof?