Geometric Definition and 790 Threads

1.Determine the magnification of a 5cm object that has been placed 20 cm in front of a lens with a power of -2.5 d? 2. Light strikes a rectangular piece of crown glass with an angle of incidence of 30 degrees. If the block of glass is 10cm, determine the measure of lateral displacement. Can...

For this problem i am given two complex numbers Z_1 , Z_2 and then a third which is the sum of the first two complex numbers Z_3 . I am then asked to find the geometric interpetation of these numbers in \mathbb{R}^2 . I am fine when graphing them in the complex plane but unsure of what they...

Light which are electromagnetic waves have an electric field component and magnetic field component. The electric field can be phase shifted but the magnetic field never does. In geometric optics, light is modeled as a straight line and its rules upon reflection and refraction are according...

I've read (and I've been told in lectures) that each graph (let's just say a combinatorial graph) corresponds to a topological space called the geometric realization - in this space the vertices are distinct points and the edges are subspaces homeomorphic to [0,1]. My question is this: Is this...

I am learning vectors in which there is a section in which geometric theorems are proved with the help of vectors. However while solving problems I often face difficulty on how to proceed ,where to use dot product, cross and etc.Is there any systematic manner on how to prove these ? Please...

Hi there everyone! Have a quick question for you. The question is: The sum to infinity of a geometric series is 9/2 The second term of the series is -2 Find the value of r, the common ratio of the series. I understand that we have to use the sum to infinity of a geometric series...

We're going to be starting them in a day or two, and I just wanted to know ahead of time what you guys might think we'll be learning with them, like formulae and that kind of stuff..

Find the sum of the series: \sum\limits_{n = 1}^\infty {nx^n } if \left| x \right| < 1 I thought maybe with the geometric form, but I am not sure.

Hi Folks, I have this here geometric series which I'm supposed to find the sum of: Given \sum_{n=0} ^{\infty} \frac{2n+1}{2^n} I the sum into sub-sums \sum_{n=0} ^{\infty} 2^{-n} + \sum_{n=0} ^{\infty} \frac{1}{2}^{n-1} taking 2^{-n} Since x^n converges towards 1/1+x therefore I...

Please help me to solve the following question : ABCD is a parallelogram .BA is procude to X and BA=AX . Prove that angle of XCB is 90 degree.

Hey guys i was having trouble on this question so i was wondering if someone could help me :) In a geometric series, (x-2),(x+5), and (4x-8) are consecutive terms. Determine all possible values of x. :confused:

Hi Can I claim that in order to find the sum of the series: \sum_{n = 0} ^{\infty} 2^{- n} \sum_{n = 0} ^{\infty} 2^{- n} = \sum_{n = 0} ^{\infty} x^n = \frac{1}{1-x} ? Sincerely Yours Fred

I've been looking into Geometric Algebra approaches to linear transformations and have found it to be MUCH nicer than the conventional matrix approaches for certain kinds of transformations. Moreover, I find it much more intuitive, particularly in its way of dealing with complex numbers. For...

I am trying to derive the geometric series for the following given identities, \begin{array}{l} \frac{1}{{0.99}} = 1.0101010101... \; \; \; {\rm{ (1)}} \\ \frac{1}{{0.98}} = 1.0204081632... \; \; \; {\rm{ (2)}} \\ \end{array} Here is my answer for (1), \sum\limits_{n = 1}^\infty...

Hi I have the following problem: show that 1/(1+x^2)) = 1-x^2 + x^4 + (-1)^n*(x^2n-2) + (-1)^n * (x^2n)/(1+x^2) I that know this arctan function can be expanded as a geometric series by using: 1 + q + q^2 + q^3 + ... + = 1/(1-q) Then by putting q = -x^2. I get...

A gravity graph is a kind of art "tool" that let's you draw nice geometric shapes. It has a board the size of a piece of paper that is weighted in the middle, each of the corners is connected to a piece of string and the strings are tied to a small rectangle (paralell to the board) about 1.5...

GEOMETRICAL STUDY OF SCHROEDINGER'S FORMULA If we take a look on previous expression, we could continue with the importance of complex numbers. The complex numbers are very important to represent points or vectors in plane, and can be expressed this way: a = b·x+c·y If we choose...

Question, in order to produce a 270 degree geometric rotation of the complex number (a + bi), would this be correct: (a + bi) * (-i) It seems logical since a 90 degree rotation results from (a + bi) * (i) Next question. What would be the equations for rotation of (a + bi) by 45 degrees, 135...

The Geometric Heat Equation--WTF?? I need some help getting from point A to B. Let's say we have the plain ol' heat equation u_t=\Delta u where the u=u\left(x,t\right), and that's all good. Then, we also have the so-called geometric heat equation \dfrac{\partial F}{\partial t}=kN where...

A Geometric Approach to the Standard Model Greg Trayling, Dept of Phys, U. Windsor, Windsor, Ontario A geometric approach to the standard model of the Clifford algebra \mathcal{CL}_7 is advanced. The gauge symmetries and charge assignments of the fundamental fermions are seen to arise from a...

aristarchus was the greek astronomer who was the first to find out the distance between the Earth and the sun. he observed that when the moon was exactly half full; the Earth (E), moon (M), and sun (S) formed a right triangle with the right angle at the moon. then how did he found out that the...

I hope you have fun with these... OK, so you know the geometric series, right? It goes like this: \sum_{k=0}^{\infty} z^k = \frac{1}{1-z},\forall z\in\mathbb{C}\mbox{ such that }\left| z\right|<1 How about this one? Call it, say, the geometric product: \prod_{k=0}^{\infty} \left( 1+...

This has been bothering me for a while. I've seen many different versions of this and I'd just like to get the following cleared up. Is the following true? \sum\limits_{k = 0}^N {r^k } = \frac{{1 - r^{N + 1} }}{{1 - r}} There are other related things I am slightly worried about but I...

If you have a geometric random variable with probability mass function: P(X=n) = p(1-p)^n n = 0,1,2,3... Find the Mean and the Variance. ---------------------------- Okay, I've looked everywhere and tried everything, however, i just cannot get it. i think that your supposed...

Consider the dihedral group D/o, generated by x and y where o(x)=2 and o(y)=5 What is the geometric significance of D/o? Which of G/<x> and G/<y> are well defined groups? Give reasons?

Why don't we discuss the Geometric algebra and how it differs from other Clifford algebras? For introduction, here's Hestenes' home page on Geometric calculus: http://modelingnts.la.asu.edu/ This is an easy reading introduction: (1) GA seamlessly integrates the properties of vectors...

In my first two of weeks we covered most of the light unit, and i was sick(in class, but coulnd't focus or abosrb information) and now i am at the end of the unit with this due tomoro and i do not understand how to do any, I need to learn how to do this, I can't understand most of it right...

I am doing a assingment for my classical mechanics class that requires the proof of: The dot product of |A dot B| <= (less than or equeal to) |A| |B| . I did the algebraic proof fine but we are required to do a geometic proof as well. This leaves me with the question what is the geometic...

geometric proof for vector relation-please help! hi there... i am trying to prove the following relation from vectors geometrically however nothing comes to my mind..i have succeeded in proving it algebraically. CAN ANYONE help me as to how do i prove this relation geometrically. The...

Here's a question that everyone in my class that I talked to couldn't find an answer to. "Suppose that you focus a camera direclty down on a printed letter on this page. The letter is then covered with a 1.00mm thick microscope slide (n = 1.55). How high must the camera be raised in order to...

Has anyone derived the Lorentz-transforms by using 'simple' geometrics? If so, could I get a link for the paper please. I tried to google for one but couldn't find.

Hi everyone, I'm new to these forums, so I've only just realized how much help they can be... I have some questions so please, don't hesitate to aid me in my time of need. These are regarding geometric sequences and series. I'm supposed to be using S=a+ar^n/1-r where s=the sum of the...

I was reading through various books about black holes, time warps, and multiple dimensions, and now I am simply asking for clarification on a few things, and previous discoveries on something I noticed while looking at geometric patterns via different dimensions. Last part first. Let me...

The problem is the following; N has a geometric distribution with Pr(N=0)>0. M has a Poisson distribution. You are given: E(N) = E(M); Var(N) = 2Var(M) Calculate Pr (M>1). From general knowledge we know that the expected value of a variable in a geometric distribution E(N) =...

i am given a set of amounts R(1+i)^(n-1)+R(1+i)^(n-2)+... R(1+i)^1,R and so on it has to do with compound interest. how do i prove this is a geometric series?

What is Minkowski's geometric when talking about relativity?

I don't know why I can't figure this one out tonight. I just can't think straight and I am hoping someone can help ASAP. Here is the question: In 1998 revenue from gambling was $651 million. In 2001 the revenue increased to $2.4 billion. What is the geometric mean annual increase for the period?

I've got a problem here... A geometric series has first term 1,the sum of the first 5 terms is twice that of the sum of the 6th to 15th term inclusive. Prove that r^5= \frac{1}{2} \sqrt {3-1} What i did was... 2s_5=s_{15}-s_5 using the formula for the sum of a GS, i got...

I'm given the sequence t(n) = 3 (-1)^n (0.5)^n ; n >= 1 It first asks for the sum of the terms t(1) + t(2) + ... + t(99) which is fine, but it follows up by asking the sum of t(1) + t(3) + t(5) + ... + t(99). Would i be using partial sums to solve this? If so, i don't know how to find...

I'm not to sure how to do this question. Q. A 4MBq gamma source emitting 5 KeV photons is held at a distance of 5 cm from the end window of a detector. The diameter of the detector window is 3.5 cm, and the quantum detection efficiency of the detector is 15%. i)What is the geometric...

Evaluate \Sigma 2(1/10)^n or explain why it diverges. (Infinity is on the top of the sum and n=1 on the bottom, I just didn't know how to put it in latex) This was a test question that I got wrong. I thought that it was a geometric series with r= 1/10. This would mean that r is less than 1...

Hi everyone... can anyone help me out? I am not sure if i am on the rigth track. Why do geometric isomers exist in alkenes, but not in alkynes? Does it have something to do with the that alkenes have a double bond and alkynes have a triple bond? Also the pi bond restricts the rotational...

Hello! I'm having difficulty answering the following question: Camera A has a lens with an aperture diameter of 8.50 mm. It photographs an object using the correct exposure time of 3.33×10−2 s. What exposure time should be used with camera B in photographing the same object with the...

Does anybody knows where can I find the resolution of the geometrical product of abc?

Can someone tell me (or help me find) the derivation of the pythagorean theorem, and the laws of sin,cos, and tangent. I know the first is a derivation of the low of cosins, but I'd like to know if there's a writeout as to how he actually came up with those results.

Classical Systems With Variable Mass And Other Geometric Systems 1. INTRODUCTION 1a) The material particle/system The fundamental object in classical mechanics is the material particle. A material particle has a position and a mass, and can be subject to forces. A material system is a...

I need a little help with this problem. In a geometric progession, the first term is 12 and the fourth term is -3/2. Find the sum to n terms and the sum to infinity. Find also, the least value of n for which the magnitude of the difference between the sum to infinity and to n terms are less...

Dear Friends I'd like to know if anybody has the solution of the aplication of nabla's operator to geometrical product: ab=a·b+a^b (inner and outer product) And if it's possible to apply a operator like this: d/dt + d/dx i + d/dy j + d/dz k. and the rules to operate. My...

Two lenses, one converging with focal length 20cm and one diverging with focal length -10cm, are placed 25cm apart. An object is placed 60cm in front of the converging lens. Determine (a) the position and (b) the magnification of the final image formed. I have a problem with this becasue...

Hey guys! I need some helps on an optics problem. It is from Giancoli Chapter 23, question 41: Question: A beam of light enters the end of an optic fiber (attachment B). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of...