Geometric Definition and 813 Threads

What is the Alexandrov compactification of the following set and give the geometric interpretation of it: [(x,y): x^2-y^2>=1, x>0] that is, the right part of the hyperbola along with the point in it. This is a question from my todays exam in topology. I wrote that the given set is...

Hello, Suppose that I have a cell complex and I want to define it's geometric realization, I can do it via mapping such that assign coordinates to 0-cells. however how can i do that for edges, faces and volumes. is there is ageneral formulas for lines, faces and volumes. Regards

when I first learned about homeomorphic sets, I was given the example of a doughnut and a coffee cup as being homeomorphic since they could be continuously deformed into each other. fair enough. Recently I heard another such example being given about diffeomorphisms: "Take a rubber cube...

I am currently reading the special relativity section in Goldstein's Classical, and there is an optional section on 1-Forms and tensors. However i am having a lot of trouble understanding the geometric interpretation of a 1-form. Here is what I do understand: You take a regular vector...

Homework Statement find the sum for \sum_{k=1}^{\infty} kx^{k} Homework Equations \sum_{k=0}^{\infty} x^{k} = \frac{1}{1-x}; -1 < x < 1 The Attempt at a Solution \sum_{k=1}^{\infty} kx^{k} = \sum_{n=0}^{\infty}(n+1)x^{n+1} = x\sum_{n=0}^{\infty} (n+1)x^{n} = x \frac{d}{dx}...

\sum_{k=0}^{\infty} ar^k = \frac{a}{1-r} This equation isn't valid, for real numbers, unless \left | r \right | \leq 1. I can see that if r = 1 the denominator is be zero, but what about the other cases? The derivation I've seen is \sum_{k=0}^{\infty} ar^k = \sum_{k=0}^{\infty} ar^k \cdot...

Can anyone solve this for me? I think it is geometric distribution. Tom, Dick and Harry play .the following game. They toss a fair coin in turns. First Tom tosses, then Harry, then Dick, then Tom again and so on until one of them gets a Head and so becomes the winner. What is the...

Homework Statement Let X1,..,Xn be a random sample of size n from a geometric distribution with pmf P(x; \theta) = (1-\theta)^x\theta. Show that Y = \prod X_i is a sufficient estimator of theta. Homework Equations The Attempt at a Solution So \prod P(x_i, \theta) =...

I don't quite understand a few details here. First, What is the difference between geometric series and laurent series? Than, how do I multiply/divide 2 series with each other? Finally, I have this problem, and I'm really clueless as of what to do. Turn 1/(1-cos(z)) into a laurent series.

Hi. I've been learning how to use geometric algebra and I've been stumbling when I apply it to E&M. I am hoping someone here can point out what I am doing wrong. The problem comes when trying to represent the field tensor in terms of the 4-potential. Here is the standard form: F^{\mu\nu}...

I have to find the sum of \sum9(2/3)^n and I get a/1-r where a=9 and r=2/3...but I know a=6 and not 9. Can someone point out to me what I am doing wrong? The sum is from n=1 to infinity. Thanks! EDIT: I am thinking I take a(1) which is 6 as the a in a/(1-r), is this correct?

Homework Statement http://img264.imageshack.us/img264/7505/math.png Homework Equations AM = arithmetic mean = (a+b)/2 GM = geometric mean = sqrt(ab) The Attempt at a Solution I'm totally stuck on this, substituting does not help at all.

Hello, I am having hard time giving a geometric interpretation for the virtual velocity in classical mechanics, defined as: \delta \dot{x} = \frac{d}{dt} \delta x where \delta is the virtual differential operator, and \delta \dot{x} denotes the virtual velocity of x. I think having a...

Homework Statement We return to the example concerning the number of menstrual cycles up to pregnancy, where the number of cycles was modeled by a geometric random variable. The original data concerned 100 smoking and 486 nonsmoking women. For 7 smokers and 12 nonsmokers, the exact number of...

What is the algebra required to rewrite the nth term of: (sum from n=0 to infinity) of (pi^n)/(3^n+1) in geometric form?

Homework Statement general form of solutions to Ax=b Consider matrix A= {[ 2 -10 6 ] [ 4 -20 12 ] [ 1 -5 3 ]} Find a basis for the nullspace of A. Give a geometric description of the nullspace of A. The Attempt at a Solution I found the...

A romantic, lighted candle is placed 39 cm in front of a diverging lens. The light passes through the diverging lens and on to a converging lens of focal length 10 cm that is 5 cm from the diverging lens. The final image is real, inverted, and 21 cm beyond the converging lens. Find the focal...

Geometric vectors theory question :( Homework Statement Last question of the night: A=(-2,1,-2), B=(-3,-5,-7) and C=(1,-1,-3) are the vertices of a triangle. Which of the following points is true? A. ||AB||2+||BC||2= ||AC||2 B. ||CA||2+||AB||2=||CB||2 C. The triangle is a right...

Homework Statement Find a and b such that the point (a,-5,b) lies on the line passing through (-3,-1,3) and (3,-4,9)Homework Equations (maybe?) Component = P1P2 = (x2 - x1, y2 - y1)The Attempt at a Solution Since it's a line passing through, I thought I could just add the two points together...

Homework Statement 1)A hard rubber ball is dropped from a moving truck with a height of 5 m. The ball rises of the height from which it fell after each bounce. the total vertical distance the ball has traveled at the moment it hits the ground for the eighth time, to the nearest tenth of a...

Hi everybody: does anyone know of a good book on special relativity that takes a geometric approach? I'm doing research that requires that I know special relativity, and, while working problems out for personal-practice, all I do is either: 1) make gamma-messes 2) clumsily-use invariants...

Homework Statement Chose a point at random in a square with sides 0<x<1 and 0<y<1. Let X be the x coordinate and Y be the y coordinate of the point chosen. Find the conditional probability P(y<1/2 / y>x). Homework Equations No clue. The Attempt at a Solution Apparently, according...

Hi, can someone just confirm that to get the GSD of a distribution, I simply take the natural log (or log 10?) of all the numbers then find the arithmetic standard deviation of that? Thanks :)

Homework Statement If the ph of battery acid should be 0.8, what is the pH of the acid in a battery that is one-fifth as acidic as it should be? Homework Equations The Attempt at a Solution We just learned how to comparing pH in Geometric unit, using the formula 10^(ph1-ph2). But...

Homework Statement hi guys, i'm having trouble applying Kirchhoff's laws to determine the equivalent resistance of this symmetrical array of resistors (see attachment); i think there is a quick trick, using 4 current loops, but i can't remember it... nor find relevant documentation – this is...

Homework Statement Given matrix A: a 1 1 ... 1 1 a 1 ... 1 1 1 a ... 1 .. . .. ... 1 1 1 1 ... a Show there is an eigenvalue of A whose geometric multiplicity is n-1. Express its value in terms of a. Homework Equations general eigenvalue/vector equations The Attempt at a Solution My...

Homework Statement The experiment was changing dimethyl maleate into dimethyl fumerate, with the intent of being analogous to changing maleic acid into fumeric acid. In the experiment, we added 1 M Bromine in dimethylchlorine to our dimethyl fumerate, put the mixture in a hot water bath and...

I recently found out how to calculate the potential energy of a charged insulated sphere of radius R and charge density rho. I would like to know how to calculate the potential energy for other geometric objects, such as a line of charges, a sheet of charges, or a pyramid of charges. I don't...

Hi. Tried solving, but no idea how. At the end of 1995, the population of Ubris was 46650 and by the end of 2000 it had risen to 54200. On the assumption that the population at the end of each year form a g.p. find a) The population at the end of 2006, leaving your answer in 3 s.f. b)...

Homework Statement Let X be a random variable with distribution function px(x) defined by: px(0) = a and px(x) = Px(-x) = ((1-a)/2)*p*(1-p)^(x-1), x = 1,2... where a and p are two constants between 0 and 1, and px(0) is meant to be the probability that X=0 a) What is the mean of X...

Homework Statement Hi, there are two questions that I'm quite stuck with. 1.Find the number of terms in each of these geometric sequences. a) 1,-2,4...1024 b) 54,18,6...2/27 Homework Equations ar^n-1 The Attempt at a Solution 1. a) r= -2 1x-2^n-1 ? b)...

Homework Statement Hi, I was trying to work out this question, but i kinda got stuck. Can anyone help me please? Thanks 4. Find the number of terms in each of these geometric sequences. 2,10,50...1250 Homework Equations ar^n-1 The Attempt at a Solution 1250=2x5^n-1

A matrix is diagonalizable when algebraic and geometric multiplicities are equal. My professor proved this in class today, but I did not fully understand his explanation and proof. Can someone please help?

A matrix is diagonalizable when algebraic and geometric multiplicities are equal. I know this is true, and my professor proved it, but I did not understand him fully. Can someone please explain?

Homework Statement A beam of light in air makes an incident angle with the normal at 53 with an unknown substance. Part of the light is relected and part is refracted into the substance. The reflected ray and the refracted ray make an angle of 90 degrees. a) What is the refracted angle...

1. 1. Find the exact(no approximations)sum for the finite series S sub n= (2 + 2 + 2(2+...+64 i used the parentheses to represent a radical sign 2. Show that the sum of the first 10 terms of the geometric series 1 + 1/3 + 1/9 + 1/27+... is twice the sum of the first 10 terms of...

Homework Statement A ball is dropped vertically from height h onto a flat surface, after the nth bounce it returns to high h / 3^n. Find the total distance traveled by the ball. Homework Equations Sum (infinity) = \frac{a}{1 - r} The Attempt at a Solution I don't see the...

Is there a geometric interpretation of any n*n matrix?

ok so i know how to calculate the partial sum of a geometric series. But let's say i only want to calculate the sum of every other term, how would i do this? example: .5^0+.5^1+.5^2+...+.5^n = (.5^(n+1) - 1)/(.5-1) but what equation can i use to get the sum of only these terms...

given: ln (x) = integral 1/t dt from 1 to x and x=30 Without a calculator and only a graph of y=1/x How could you show that this geometric area under this curve (with any type of unit) is equal to 3.4 area units, the ln (30) not homework, I am looking for a tangible/physical...

Not homework but this is probably the best suited place for a puzzle: A large rectangle in the plane is partitioned into smaller rectangles, each of which has either integer height or integer width (or both). Prove that the large rectangle also has this property. I've given this several...

Is there a point to geometric proofs? The ones that I have encountered are so obvious that it almost seems useless to have to use them for anything.

Some years ago I used the device of representing composite numbers by rectangular forms to demonstrate the structure of numbers to third grade students. Primes were represented by lines of various lengths. Number 10 would be a 2x5 rectangle and 20 a 2x2x5 rectangular solid. (I used various...

I'm taking a class in abstract algebra this summer, so I thought I'd get ahead by reading the book before class starts. This is from a book called "Abstract Algebra: A Geometric Approach", chapter 1: Applying the Principle of Mathematical Induction with a slight modification. If S' \subset \{n...

Homework Statement \int 1/(1-xyz)dxdydz = \sum1/n3 from n = 1 to infiniti dx 0 to 1 dy 0 to 1 dz 0 to 1 Homework Equations The Attempt at a Solution Not sure how to relate the two of them

Homework Statement In a Geometric Sequence find t10. t3 = 4 and t6= 4/27 Give a recursive definition for the sequence: 1, 4, 13, 40... Homework Equations I know that a Geometric sequence is: tn=t1(r)n-1 And that a recursive formula starts off with tn-1 I'm not sure where to go...

Homework Statement Show that the ratio of areas is proportional to the sides squared: \frac{[ACD]}_{[CDB]} is proportional to \frac{AC^2}_{CB^2} Please, see the picture: http://dl.getdropbox.com/u/175564/geo_henry.JPG . Homework Equations AC = 2 * CB \frac{AD}_{DB} is propotional to...

Geometric Distribution? Geometric Distribution: In an experiment, a die is rolled repeatedly until all six faces have finally shown.? What is the probability that it only takes six rolls for this event to occur? ANSWER = 0.0007716 What is the expected waiting time for this event to occur...

Sorry, the title should be: geometric intepretation of moments My question is: does the formula of the moments have a geometrical interpreation? It is defined as: m(p) = \int{x^{p}f(x)dx} If you can't see the formula it is here too: http://en.wikipedia.org/wiki/Moment_(mathematics) with c=0...

Hello everyone, I am studying for an upcoming exam and have become somewhat confused as to exactly what geometric and material buckling represent. Are they representative of the shape of the neutron flux distribution in the reactor? Are these quantities related to the structural deformation...