Mathematics

Hi, all! Google's turned up nothing relevant (except my post of the same thing on another non-SFN forum) to help me with this problem. I'm at a bit of a loss as to how to do the following elegantly—I've had some success with a slow, "nested" optimisation for what I'm trying to do, but I'm not happy with the results. I have a trajectory described by: [math]\frac{{dx}}{{d\tau}} = f(x,y,a,b,c)[/math] [math]\frac{{dy}}{{d\tau}} = g(x,y,a,b,c)[/math] where [math]a[/math], [math]b[/math], and [math]c[/math] are parameters. The functions [math]f[/math] and [math]g[/math] cannot be calculated analytically (iteration is required), but what happens internall…

Hello! I have recently ran into a productivity wall with my Pentium M 1,7 GHz Sony laptop, that I bought 3 years ago. I am working on a model of one process in Excel and the current version of the file is 200 Mbs comprised of 10 sheets filled to the brim with interrelated formulas (the final version is going to be close to 500 Mbs). Understandably my laptop is refusing to show any speed at all and takes minutes – and sometimes tens of minutes – to recalculate the workbook. I wonder if someone here is a power user of the Excel and can recommend to me a work station that can handle such files with ease? I am working in Excel 2003. Here are the specs of one PC that the loc…

Hello, In Wasserman & Faust's "Social Network Analysis" I read about the following problem with the n-clique concept: They give some references (Alba & Moore 1978, Mokken 1979) which I can't access. I've been drawing lots of graphs to find an example of the above but can't find any. Anyone knows? Thanks! For those not in the know: a geodesic is the shortest path between two nodes; an n-clique is "a maximal subgraph in which the largest geodesic distance between any two nodes is no greater than n".

I'm learning College Algebra. I'm wondering how to solve Exponential Equations, such as 8^(X^2 - 2X) = 1/2 8 to the [X squared minus 2X]th power = 1/2 and other equations of that nature.

Hello, I am studying for examinations and encountered a problem I do not know how to solve: Let w (omega) be a solution of the equation x^2 + x + 1 = 0 Then w^10 + w^5 + 3 = ? I first replaced x with w (omega) which yields w^2 + w + 1 = 0 What I actually tried to do is solve the actual value of "w" using the quadratic equation. However, when I plug this into the 2nd equation, this yields "3", when the answer is 2. Also, no calculators are allowed on the exam, so I can't be using the quadratic equation. Any help is appreciated. Thanks.

Is it true that if something is possible mathmatically it also possible in reality? If so what is this concept called?

I have a funny problem here... Solve for X: (sinX)/X = 0.5

As in the subject Pre-Algebra Pre-Calculus Calculus I Geometry etc. I will order them as a part of the Demystified series (with quizzes and tests) I really wanna get good at Maths Thanks

May algebra isn't that good, but I have a problem I would like to solve. If Mars' tectonics lasted only 800 million years and Venus' plate tectonics lasted for about three billion years and Earth's plate tectonics should shut down in about 2 billion years from now, then, I should be able to estimate when plate tectonics ceases on worlds, given their mass to Earth. 0.3 = 0.8 0.4 = A 0.5 = B 0.6 = C 0.7 = D 0.8 = E 0.9 = 3 1.0 = 6 1.1 = F 1.2 = G 1.3 = H Etc. How can I find the values of A though H and beyond? If I know that 0.3 is 0.8 and 1.0 is 6, then I should be able to solve this, but I can't figure it out.

Hi, I would like to know whether there exist two shapes A and B (in 2D plane) that are equal (ie. equal transformation between A and B exists) but A is proper subset of B. The definition of "being equal" (equal transformation preseves lengths - eg. rotation, traslation etc.) and "proper subset" (the sets are not equal) are I think commonly known. For infinite shapes these shapes A and B exist: eg. half-line, half-plane and so on but what about shapes that are bounded by say circle with the radius of 1? Does some examples exist (maybe some fractals) or can be proven that it is not possible? Thank you in any thoughts. Honzik

I am interested in the ontological status of mathematical entities and statements, and the place for mathematics in a reductive, materialistic universe. The mathematician Kronecker is supposed to have said 'God gave us the integers, all else is the work of man.' Translated into a secular form, this statement is the claim that the integers are somehow part of the 'ultimate furniture' of the universe. However, when we see two chairs, we will find on closer inspection that they are in fact not the same. I think that however natural it may seem to do so, and however ubiquitously it is done amongst many animal species, grouping objects with 'family resemblances' into cate…

Lorentz Contraction of a Moving Parabola http://mypeoplepc.com/members/jon8338/math/id42.html

Hey all, say we have N points in Cartesian space, and we are to find a nth degree polynomial that goes through all those points. How would you symbolically describe the solutions for the coefficients? Just to make my question clear, here's an example: N=2: we have two points, W and Z. So in this case we're looking for a linear equation in the form [math]y=ax+b[/math]. We get two equations, and solve for a and b. If we had three points, we would be looking for a quadratic function in the form [math]y=ax^2+bx+c[/math]. We get three equations, solve for a, b and c. Now what I'm looking for is a way to tell a computer how to get the coefficients given N points. Chee…

Hey all, this will sound like a pretty stupid questions, but given a set of N real numbers numbers, is there any operation that can be performed on them that would output a result unique only to that set of numbers, in that specific order? This question has been bugging me for some time, so I was wondering if there was some kind of proof or something that makes this impossible. If there is nothing to dispute the possibility of there being such an operation, can you think of one? Cheers, Gabe

I saw this game played first in the classic 1960's French film 'Last Year in Marienbad'. I learnt how to play it to always win, by trial and error. I believe there is also a simple maths algorithm for winning play but I have neither the skill nor patience to figure it out. Can anyone help? The game: For two players. Lay four rows of mathsticks: 1, 3, 5, 7. I III IIIII IIIIIII The play: A player can take any number of sticks from any one row at a time. The one who has to take the last match loses. Its always fun to play this a few times and let the patsy win, then offer to bet a couple of beers that you can win the next three games straight out. W…

Intersting... http://www.scribd.com/doc/14599592/A-Beleza-Na-Matematica

Suppose I have a function [math]f(x,y)[/math], along with a gradient at some arbitrary point [math](x_0, y_0)[/math] The surface is smooth and [math]C^1[/math], there thus also exists some gradient vector: [math]<\frac{df}{dx}(x_0, y_0) , \frac{df}{dy}(x_0, y_0)>[/math] I want to "follow" this vector to the next point [math](x_1, y_1)[/math], here there is another gradient vector [math]<\frac{df}{dx}(x_1, y_1) , \frac{df}{dy}(x_1, y_1)>[/math], I repeat this process for up to [math](x_n, y_n)[/math]. How do I write an expression for the curve? It seems like I would have to integrate along a vector somehow?

Is there a way to convert irrational numbers from decimal to binary? Has it already been done?

Hey all, I have two 2D vectors, [math]\vec{s}[/math] and [math]\vec{p}[/math], both starting at [math][0, 0][/math] and ending in the points [math]S[/math] and [math]P[/math] respectively. I'm looking for a vector [math]\vec{x}[/math](starting at [math][0, 0][/math] and ending in the point [math]X[/math]) that satisfies the equation [math]|\vec{s}-\vec{x}| = z \cdot |\vec{s} - \vec{p}|[/math], and that [math]X \in \; \rightarrow SP[/math] (I hope that's the proper syntax for a ray begining in S and going through P). In layman's terms, I'm trying to "zoom in" on [math]S[/math]. Now, the obvious way to solve the problem is find the equation for the ray (or line to be pe…

Hey guys, I've never got problem with solving quadratic, logarithmic or goniometric equations, but I don't know how to solve them when they are all together. The most simple example is: [math] \textup{log}(x)+\textup{sin}(x)+x^2+x+1=0 [/math] Is there any way to solve them without "computer help"? Thanks, pq

Hi I have a function f: [math]f(x(t))=\frac{d(x(t))}{dt}+x(t)[/math] Now how would I differentiate f with respect to x

does (x+h)log(x+h) = xlog(x+h) + hlog(x+h) ?

Hi, Suppose I have two points A, and B in some N-dimensional manifold. I would like to define distance (or metric) between A and B as follows: [math]d(A,B)=min | \int_\gamma f(s) ds | [/math] along some curve [math]\gamma[/math] In my head, it seems to be possible to evaluate a line integral without precisely defining distance. (ie. we just take tiny little points along this line, and evaluate f(s) at each tiny little point). However, all equations I've seen uses something like: [math]ds=\sqrt{{dx}^2+{dy^2}}[/math] which seems like a euclidean metric. So here are my ultimate questions, 1) is it possible to evaluate such a line integral withou…

Hey all, I was wondering, if one were to define a number r, for which [math]|r|=-1[/math], would it be possible to logically deduce it's behavior in mathematical operations? I know that the very concept is unimaginable and I also know it would be useless. But if we can have square roots of negative numbers, why not numbers denoting negative length? I'd be interested to know what [math]r^r[/math] would be, for example. Cheers, Gabe

Often I speak about how it is impossible ever to know anything as a true and unassailable fact, that assumptions are required in all things (even the scientific method, which attempts to be as objective as possible, operates on the unknowable assumption that observations of the material world can inform of its workings). Invariably, I am rejoined with: "But we know 2+2=4! That is irrefutable and unassailable, and requires no assumptions." This disturbed me, because it seemed to violate my previously stated ideology, so I thought deeply on it, and I came to the conclusion that mathematical statements like that are actually tautologies -- that four is defined as the…