Geometric Definition and 790 Threads

Hi could someone please explain what Geometric/berry phase is I've had a look and there seems to be several ways to interpret the physics. My understanding is that it occurs when your quantum state traces out a closed path in some parameter space, which is some how related to degeneracies in a...

Homework Statement Find the first three terms of a geometric sequence given that the sum of the first four terms is 65/3 and the sum to infinity is 27. Homework Equations \begin{array}{1} S_n = \frac{a(1 - r^n)}{1 - r}\\ S_n = \frac{a(r^n - 1}{r - 1} \end{array} The Attempt...

Homework Statement If 1 + 2x + 4x^2 + ... = \frac{3}{4} find the value of x. [Edit: Forgot to ask the question] Homework Equations S_n = \frac{a(1 - r^n)}{1 - r} t_n = ar^{n-1} The Attempt at a Solution a = 1 r = 2x I try to solve S_n and end up with 2x^n = \frac{6x - 7}{4}...

A dog is running around in a fenced-off rectangular field with dimensions of 40ft by 50ft. If the position of the dog is uniformly random throughout the field, what is the probability that the dog is 10 feet or more away from the fence at any given time? In know that since the dog is...

Homework Statement Find the sum of 9 terms of the series 3 + 3^(4/3) + 3^(5/3) + ... Homework Equations I'm just learning sequences and series and senior high school level. I'm finding it hard to apply a, ar, ar^(n-1), ... to this. a = 3. I don't know how to find common...

b1,b2,b3,... In the geometric sequence above, b1=1000 and bn=(2/3)bn-1 for all n\geq2. What is the least value of k for which bk<0.001? The Attempt at a Solution What I did first was I found what b0 is since we are given b1 and that is 1500. But I do not understand where the k is...

IMPORTANT! ---- what is the geometric intepretation of the gradient vector? Assume the situation in which I have a slope, a component of a function dependent on x and y, which is at an angle to the xy plane. The gradient vector would be perpendicular to the tangent plane at the point in which i...

Hi there, I have a question about photography. We know that in geometric optics, a bunch of parallel rays which going into the len will focus on the focus (a point). But as we see, the image is a set of points on a 2 dimensional plane. It is quite confusing that a focus is only a point...

I'm learning about special relativity in its differential geometry formulation. I don't understand how special relativistic effects can be derived from the Minkowski metric. It isn't obvious to me where relative velocity comes in, or why this makes things look different. Can somebody explain how...

They aren't equivalent in general, but do they ever coincide, and, if so, under what conditions? I've seen both denoted by juxtaposition. Is there a way to tell, in such cases, which is meant, or is it necessary to always use a different notation for the tensor product when the geometric product...

Homework Statement Let a1, a2, a3 denote the first three terms of a geometrical sequence, for which a1 + a2 + a3 = 26. a1 + 3, a2 + 4, a3 - 3 are the first three terms of an arithmetical sequence. Find the first term and the common quotient (ratio) of the geometrical sequence...

Hello all, the picture i have attached is the question. http://img842.imageshack.us/img842/8921/geometricproof.png I've concluded that there are two i isosceles triangles in this one triangle. \anglePSQ + \angleQSR = 90degrees Finding the angle in one of the isosceles triangles...

An infinite geometric progression has a finite sum. Given that the sum of the first two terms is 9 and the third term is 12. 1/ Find the value of the first term and the common ration r.

This looks almost like a geometric series; 1, 2, 5, 14, 41, 122, 365, ... but each term is one less than three times the preceeding one. So is this a sequence or a series? What is a formula for the value of the nth term in terms of n?

Homework Statement Given a convex lens of focal length of (x+5) cm and a concave lens of focal length x cm. The 2 lenses are placed 30 cm apart coaxially i.e along the same axis with the convex lens on the left while the concave lens is on the right. A light bulb is placed to the left of the...

Homework Statement The sum of the first six terms in a geometric sequence of real numbers is 252. Find the sum of the first four terms when the sum of the first two terms is 12. Homework Equations Sn = A1 - A1Rn divided by 1 - R R \neq 1 (I can't figured out how to make the...

Homework Statement I am having trouble following what is going on in this solution. We are looking to find the expectation value of: f(x,y)=\frac{1}{4^{x+y}}\cdot\frac{9}{16} I have gotten it down to: E(X) = \frac{3}{4}\sum_{x=0}^\infty x\cdot\left(\frac{1}{4}\right)^x\qquad(1) We know...

find the number of terms in 0.03+0.06+0.12+...+ar^n-1

Question: If Y has a geometric distribution with success probability .3, what is the largest value, y0, such that P(Y > y0) ≥ .1? Attempt: So i represented the probability of the random variable as a summation Sum from y0= y0+1 to infinity q^(yo+1)-1 p ≥ .1 using a change of variables...

the questions is The left end of a long glass rod in diameter has a convex hemispherical surface in radius. The refractive index of the glass is . Distances are measured from the vertex of the hemispherical surface (to the right is positive for image distances). Determine the position of...

Hi everyone, I've browsed around the forum a bit and found that others have had the same problem as me, however, none of the answers help me a lot, so I thought to post a more specific question, I hope you don't mind. I'm having a problem with the surface area of a sphere, probably because...

I ran across a paper today that I found rather interesting. The idea is that "there exists a geometry description other than the conventional description in a Hilbert space...". The gist of the paper is that the quantum phase space can be viewed as a complex projective space if the dimensions of...

Homework Statement http://bit.ly/9N9iLZ Evaluate: lim n-> infinity of Sum (from k = 1 to n) of sqrt(k/n) * 1/n Homework Equations taylor series? The Attempt at a Solution the above = lim n->infinity of Sum (from k = 1 to n) of k^1/2 / n^3/2 k approaches n so n^1/2 / n^3/2 ->...

Geometric Constructible Numbers... Hi, everyone. I have a question about geometric constructible numbers. I know that "if 'a' is constructible then [Q(a):Q]=2^n." But I heard that its inverse is not true. I want some counter examples about the inverse statement. (I have checked by googling 'i'...

Homework Statement Let an (read 'a sub n') be the nth digit after the decimal point in 2pi+2e. Evaluate SUM (n=1 to inf) an(.1)^n (here, again, an is meant to be 'a sub n') Homework Equations As far as I can see, this is a partial sum of a geometric series. To find the nth...

Homework Statement 1. Evaluate 4^1/3 . 4^-1/9 . 4^1/27 2. express 0.85555 ... as a farction . ( hint: write 0.85555= 0.8+0.05(1+0.1+0.01+...)) The Attempt at a Solution 1. well in this question i think the " r " is in the power ,,, and it's -1/3 but how to complete it ,,, what...

Hi, everyone: I am trying to understand the geometric interpretation of two simplicial cycles being homologous to each other. Let C_k(X) be the k-th chain group in the simplicial complex X, and let c_k be a chain in C_k(X) The algebraic definition is clear: two...

What is the difference between Diastereomers and Geometric Stereomers? Im a little confused on this one as I thought they were the same thing? Stevo1925

A couple friends worked on this problem (for a week now...) Trying to show that a conformal bijective map that sends vertices of one rectangle to vertices of another rectangle on the complex plane has to be linear. I would appreciate any help, Thank you.

a ball is dropped from a height of 10 feet, each bounce is 3/4 of the height of the bounce before a)find an expression for the height hn to which the ball rises after it hits the floor for the nth time so hn= 10(3/4)n b) find an expression for the vertical distance Di the ball has...

{sigma} 2*(-1/4)^(n-1) Could i treat this as a geometric series? i know geometric is in the form of ar^n but the n is (n-1) my A=2 my r= -1/4

Homework Statement They were asking for the geometric interpretation and the says its triangular prism with infinite right angles. I don't understand what they mean by that. Homework Equations The Attempt at a Solution

Homework Statement Prove that if two matrices are similar then they have the same eigenvalues with the same algebraic and geometric multiplicity. Homework Equations Matrices A,B are similar if A = C\breve{}BC for some invertible C (and C inverse is denoted C\breve{} because I tried for a...

I have the following mapping (generalized geometric mean): y(i)=exp\left[{\sum_j p(j|i)\log x(j)}\right]\\ ,\ i,j=1..N where p(j|i) is a normalized conditional probability. my question is - is this a contraction mapping? in other words, does the following equation have a unique...

Hello, I am having difficulty approaching this problem: Assume that K, Z_1, Z_2, ... are independent. Let K be geometrically distributed with parameter success = p, failure = q. P(K = k) = q^(k-1) * p , k >= 1 Let Z_1, Z_2, ... be iid exponentially distributed random variables with...

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...

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.

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...

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...