Mathematics

A quick question about Bachman's A Geometric Approach to Differential Forms. I've read: 1. [imath]T_{p}\mathbb{R}^n[/imath] to mean "the tangent space of some path/surface in [imath]\mathbb{R}^n[/imath]" and, 2. [imath]T_{p}\mathbb{R}^n \times \mathbb{R}^m[/imath] to mean "some (n-1)*m dimensional space of real numbers." I haven't run into any problems using this definition but I think it would make the text easier to read if I actually understood what was going on (especially in the second example. Rev Prez

tommarrow, i am going to order some books and i need some information: i already have a background in differentiation and integration. what do i need to know before topology? is differential geometry before or after or the same as topology? any reccomendations on books would be nice as well.

Does it make sense to say that two points is a zero-sphere? I read that an n-spehere is the structure made from all the points being exactly the same radius from a single point in (n+1) dimensions (thats of the top of my head). But also shouldnt the resulting structure be of n-dimensions itself? I'm not sure whether two points would be called 0 dimensional would it? Also, could one visualise a 3-sphere (picturing it with 3 spatial dimensions and the fourth as time) as a point that grows to a sphere and then shrinks back down?

Suppose i have the following function of the variable z: [math] f(z) = \frac{z^2-1}{z-1} [/math] Is it true or false that f(1) = 2 ?

Hello, Suppose we have a truncated taylor series for exp(x), truncated at the term, just beyond the N-th power. Let's call these truncated series trunc(N, x). Some examples: trunc(0, x) = 1 trunc(1, x) = 1 + x trunc(2, x) = 1 + x + x^2/2 ... trunc(N, x) = 1 + x + x^2/2! + .... x^N/N! Here N! means the factorial of the integer N. Here, trunc(N, x) is an N-th degree polynomial over the complex numbers with variable x. The zeros of trunc(N, x) are on a very regularly shaped curve. The shape of the curve hardly depends on N. As an example I'll show the zeros for trunc(400, x) as a gif image, computed by means of my polynomial so…

how do you find the integral of x^x from some given negative number to 0? I can't even see the graph of x^x from -something to 0

Hi guys I'm on my vectors again. Last time you really helped me understand what i was doing! Refered to a fixed origin A=(5i-j-k) B=(i-5j+7k) Find the position vector of the point D, where Dis not A on AB such that |OD|=|OA| i did OD= xi+yj+zk from r=a+t(B-A) x=5-4t y=-1-4t z=-1+8t |AD|^2=(x-5)^2+(y+1)^2+(z+1)^2 |AD|^2=(5-4t-5)^2+(-1-4t+1)^2+(-1+8t+1)^2 d(|AD|^2)/dt=(32+32+128)t am i using the right method? i also did Cos(OAOD) but got silly decimals. for the vector eq. Thanks in advance!

How much information is stored in the wolfram maths website? It seems like alot to me. But do you reckon that it would be hard to create a system like wikipedia but dedicated to maths? How much effort would be involved, and would anybody here be willing to contribute if I started a website like that?

Let's consider the inscribed square of the circle such that its vertices describe the chords to its 4 quadrants and where area of the circle is, say, 64 units. Area of the inscribed square is given as 64/0.5 pi = 40.5 square units and where each line of the square defines the chord length to a quadrant of the circle. That chord length is given by the trianglature formulae of r*sqrt 2 = chord length; chord length*pi/4*sqrt 2 = quadrant arc length. The trianglature formulae derives from aeronautics engineer and writer E.P. LeRoy.

I can see how the idea of “nothing” or “0”, evolved from a hole or empty hand ..meaning that relative to objects (or contextual reality), there was a lack thereof. But what on earth were they thinking when they went past nothing to create -1?

I have a question about the following article: Hamiltonian Quaternions In the article you will see the following quote: My question is this: If you look up you will see w,x,y,z expressed for the product of two quaternions. There are 12 components. does anyone understand how you go from those 12 components, to a rotation of a sphere?

I’m trying to get some sort of intuitive grasp if imaginary numbers.. Does anyone have any inkling whatsoever as what they might be like or any analogy that might give me some point to start from. Or do we just send off our equations into the unknown and be happy when they return still making sense in the real world?

The Least Angle topic opened a rather heated debate 'mongst work associates, most of whom have a strong background in acadenics.....I do not! The question evolved to : What formula gives the distance between each adjacent angular degree on circumference of the circle? In a foregoing thread I gave the formula for describing the least possible distance between 2 adjacent degrees as pi/40. From that I now deduce that the distance between 2 adjacent degrees of any circumference is given as radius/radian. I think it stands, but before taking it to the others thought I might try for an outside opinion. What say you?

Guys, How do you solve this one? z^3 + Az^2 + Bz + C = 0 ; So far I have reached this solution ( resources from web of course ) w = (-f +- sqrt ( 27f^2 + 4e^3 )/ 27 ) / 2 * Substitution : z = y - b/3; y = x + s/x; s = -e/3; w = x^3; e = (c - b^2)/3 f = d + (2b^3/27) - (bc)/3;

Im sorry everyone, but I just had a brain fart and I cant seem to find this anywhere, so what is the equation for a circle? Basically, if I had an equation like x(squared) + y(squared) = 10x-8y+6 what would the center and the radius of that circle be? Im very confused at this point, because Im not a big fan of geometry, but any and all help is appreciated Thanks, Alex

I cannot believe that http://www.scienceforums.net/forums/showthread.php?t=11607 was closed! I just read it and was enjoying the discussion and was going to contribute to it until I noticed it being shut by (presumabley) dave. This is an outrage! I cannot see which rule was being violated. I am new here and was enjoying this place until I saw the brutality under which these mods enforce their powers! Dave just because you do not find something interesting doesnt mean it should not be discussed. Please dont close this thread. Ok now onto the discussion. If zero was the reciprocal of infinity then zero would be the reciprocal of negative infinity also which is ridiculou…

Hey guys, my first post here. I hope this turns out to be some descent forums. Does anybody know the name of the curve that is represented by: x + 1 y =... ------------ ...= y (x + 2)(x - 1) It creates a curve like this. Thanks alot!

Hi, I am creating a computer program that graphically draws mathematical functions, later I will make it do other curves as well but for now I need to solve something. How it works is by testing 0, then 0.01 and drawing a line between the two etc, sometimes it will jump from a very large number to a very small number when it reaches an assymptope, often the assymtopte is between the two test numbers so it is not detected. In that case a vertical line is drawn on the page. I know how to find assymtoptes myself, usually just by looking for zeros in denominators but the computer doesnt know that. How would I find these assymptopes? Is there a simple way of knowing…

In my upcoming maths GCSE, I know that I'm likely to get a question asking me to give a number as a product of it's prime factors. For instance, writing 50 as:[math]2\times 5\times 5[/math] wich is pretty easy, but what's the point? How could this be useful? Does it lead on to something that I might look at at a later stage or something?

how bout -49.5? do you round to -50 or -49 or is "rounding up" an improper term.

How do you find the vertex of a parabola using the calculator?

Ok im going to have a go at holding a quiz........ Q: Factorise completely the expression: f(x) = 3x^2 + x^2 - 12X -4, and hence solve the equation f(x) = 0. Ok try and solve the question, and gl to you all.... Winners will be announced in 2 days.

Hi, All!....my first posting here. I Find the Pythagorean Triples mentioned in one of the threads and curious to know what they are....if you will, please.

You have 50 coins totaling one dollar. One falls in a gopher hole while tossing the coins in your hand. What is the chance that a quarter fell into a gopher hole?

What exactly is pie and what does it do?