Mathematics

Let's say we define a set [math]S[/math] in the following manner. [math] 0 < S_0 < 1 [/math] [math] S_n = (1-S_{n-1})^x[/math] If we take the example [math]S_0 = \frac{1}{2}[/math] and [math]x = 3[/math] then the set apears to not converge and to follow no set pateren, is this chaos?

What are people's opinions on which are the most important theorems in mathematics? By important I mean those with the most significant consequences both in pure and applied mathematics (not just obscure results that happen to be interesting to a few individuals). I would suggest the the Pythagoras Theorem should be up there. What else?

Hi all Have a quick question... I'm writing up my year's project work, and shockingly enough it involves a handful of straight line graphs. Excel kindly provides me with a line of best fit and its corresponding equation, along with a value called R-squared. (Mine is 0.537... not too good) I know this is a measure of how good the fit is, but I'm not sure how to explain this in my write-up. I won't need detail on it, just a brief statement to the tune of "The correlation isn't very good". How should I refer to this R-squared value? I know very little about statistics. Cheers Kaeroll

I am amused to consider that I find nothing in nature that exists as a negative quantity, for example, a tree cannot have a minus quantity of leaves, if it started with 3000 leaves and now has 2000 it does not have -1000 leaves it has 2000 leaves. leaving aside 'debt' which is a man made concept/quantity, where if anywhere does negative exist in nature, such things as 'negative voltage' is merely a reversal of polarity or direction. Travelling at -3mph is actually travelling at 3 miles per hour in a different direction, negative is an opposite direction and not an opposite to positive in any true sense. In the sum 5-3=2 there is no negative quantity, there is …

Is there a name for a family of parametric curves [math] x(t) , y(t) [/math]where... [math](\frac{dx}{dt})^2+(\frac{dy}{dt})^2=1[/math]? If possible, generalized to multiple dimensions... [math](\frac{dx_1}{dt})^2+(\frac{dx_1}{dt})^2+...+(\frac{dx_n}{dt})^2=1[/math]

I have a surface Z, which is a function of the variables x1,x2,x3... etc. ie. Z(x1,x2,x3...) I have a point Z0 and a point Z1 which corresponds to some point on this surface. There is some line M that connects Z0 and Z1 on the Z surface, note that M does NOT have to be the shortest distance. However, M must be bound to the surface Z. How do I find the length of the line M on this surface? Ideally the expression would be somehow linked to the directional derivative, IE. I've been thinking of slicing the line M into tiny little components, and taking the directional directive at each point of M, the integrating with respect to.. something (maybe dx1, dx2, dx3... …

An open interval is an interval that does not include its end points. http://mathworld.wolfram.com/OpenInterval.html What I don't understand is why is it called an open interval?

Hello, I have a question about the change of radix, for example: Convert 1020304 base 10 into base 7: 1020304 / 7 = 145757 r 5 145757 / 7 = 20822 r 3 20822 / 7 = 2974 r 4 2974 / 7 = 424 r 6 424 / 7 = 60 r 4 60 / 7 = 8 r 4 8 / 7 = 1 r 1 1 / 7 = 0 r 1 => 11446435 There is a tip to divide a big number with a little number?, is posible with a simple calculator get the remainders from a divition like that?

Hey all, so, I was at this math contest last Tuesday. The contest consisted of 4 question, of which one was geometry. I had absolutely no clue on how to solve it, so I was wondering if anybody here could help me. We have a triangle [math]ABC[/math], which is not isosceles. Let [math]x[/math] be a line that bisects the angle [math]ACB[/math], [math]y[/math] be the perpendicular bisector of [math]AB[/math], [math]h_a[/math] be a line perpendicular to [math]BC[/math] and passing through [math]A[/math] and finally [math]h_b[/math] be a line perpendicular to [math]AC[/math] and passing through [math]B[/math]. Let [math]K \in x \cap y[/math], [math]P \in KC \cap h_a[/ma…

Would You mind telling me how to install plugin vbLatex for vBulletin? Could you tell... step to step. Thanhs a lot. K19:embarass:

Anybody want to try this problem? I know the answer and how to do it, I'll tell you later. Anyways... You have a random number generator, that generates the numbers 1-5 randomly (equal probability of each). You need to make a random number generator out of it that generates the numbers 1-7 randomly (equal probability of each). How do you make it out of the first generator? For example, you can take a number from the first one, and run it through the first one 5 more times, and say if you get some answers tell the generator to start over again, etc.

i know this is a reall general and broad question{and stupid/new to this world sounding}, im just wondering what kind of answers ill get. i love math, but when i ask myself this question, i seem to lack the answer.

Hey to everyone here in this forum. I'm new here and I have got a question concerning the exterior derivative and the Lie derivative. I have to show the following: (I searched for them for four hours on the net but no site is giving me a proof of it) These two I have to show for all p-form (p is between 0 and m if M is a manifold of dimension m) This is the formula for the exterior derivative which I have to show: Sorry I don't know why the picture are not shown here. Hope someone can help me!!! Any help is appreciated! If you have a book or a site where you have found one of these proofs let me know! Thanks

How is it a paradox? Is it just seems to be parsing the model of reality incorrectly? Or what?

i = [math]\sqrt{-1}[/math] i[math]^{4}[/math] = [math]\sqrt{-1}[/math][math]^{4}[/math] = 1 [math]\sqrt[4]{1}[/math] = i = 1 Therefore [math]\sqrt{-1}[/math] = 1, but that would mean that 1*1 = -1 Which is impossible. How is this? Did I make a miscalculation? Or is this really a paradox?

I keep doing the problem like the formula says but I keep getting the wrong answer The problem is m^2-3=-m 21. m^2 -3=-m m^2 +m-3=0 m^2/1 +m/1=3/1 m^2+(m/2)^2=3 m^2 +m+0.25=3 + 0.25 m^2 + m +0.25=3.25 (m+0.5)^2= square root of 3.25 m+0.5= square root of 3.25 and thats where I get stuck because when I look in the back I see im way off. Can someone explain what im doing wrong. It would be a big help.

Does anybody have any ideas on how to work out [imath]\sqrt{0.9}[/imath] without a calculator (to approx 10 d.p.)? I know there are a few methods for working out for working out square roots by hand, but i was wondering if there was a cleverer/easier way of doing it.

could this be a typo? in a question sheet? 2cosecx-1=0???

I have no clue how to do this one... let a= -1+i, b=-2-i, solve for z. b*=complex conjugate of b z-b*=Im(a^2/(2b+i))

can someone explain how it expands or contracts on a complex plane? The first time i tried to see how it works, i used real numbers, but is there a difference or am i doing something wrong because the triangles as a result are not similar.

What do you think about this podcast from the American Military university?

hey, im a freshman in highschool, so im barely educated in too much complex math, but i want to learn it all{ i know, big statement}. im in an algebra 1 class right now. any good book suggestions teaching this to calculas math? or anything higher than calculas? thanks.

Let us work in the [math]\mathbb{Z}_{2}[/math] graded category. A Loday algebra is a "crippled" or "wonky" Lie algebra. That is it satisfies the bracket satisfies the Jacobi identity, but is not skew symmetric. An interesting question is if there exists a homotopy version. I suspect that one can consider "crippled" [math]L_{\infty}[/math] -algebras. So, a series of brackets that satisfy higher Jacobi identities, but do not have a symmetry property. Any body seen anything like that? A differential over such an algebra would also be straight forward to define. I myself have defined notions of a differential [math]L_{\infty}[/math]-algebra and a differen…

first of this is part of my assignment , secondly please forgive me if i posted this in the wrong place.... this just seemd like the place to post this. i have 2 curved graphs S and V..... and one is increasing more rapidly than the other over a distance at one points in the graph and the other after a few values starts to increase faster than the other one. how would i find the values for the distance where S Gradient is ascending faster than V, and when V Gradient is ascending faster than S...... i only need a push in the right direction please.... i hope i said that coherently . my teacher said to use change in y/ change in x or something but im lost really..…

Hey all, The title's a little misleading, what I'm really wondering about is, can a cube and a cuboid have the same areas AND volumes, without the trivial solution of a=b=c=s, where s is the side of the cube. I did some calculations, however I have absolutely no idea if they're right, and to be quite honest I sort of doubt it. If a, b and c are the sides of a cuboid, and s is the side of a cube, this is what I came up with: http://i44.tinypic.com/oi9e75.jpg Cheers, Gabe