Geometric Definition and 790 Threads

Hey! :o What is the geometric meaning of the following mappings, that are written in cylindrical coordinates?? (Wondering) The mappings are: $$(r, \theta, z) \rightarrow(r, \theta , -z) \\ (r, \theta , z) \rightarrow (r, \theta +\pi , -z)$$ And what is the geometric meaning of the following...

I was given the following as a proof that the inertial tensor was symmetric. I won't write the tensor itself but I will write the form of it below in the proof. I am confused about the steps taken in the proof. It involves grade projections. A \cdot (x \wedge (x \cdot B)) = \langle Ax(x...

Homework Statement Given an integer n and an angle θ let Sn(θ) = ∑(eikθ) from k=-n to k=n And show that this sum = sinα / sinβ Homework Equations Sum from 0 to n of xk is (xk+1-1)/(x-1) The Attempt at a Solution The series can be rewritten by taking out a factor of e-iθ as e-iθ∑(eiθ)k from...

Trying to solve a drawing task. The following has to be achieved: - Produce a Square (vertices of ABCD) - Cut line BC into two equal parts, label the point in between as M. - Draw a line between point M and A. - Divide angle of BMA into two equal parts. Label the location where the bisector...

Homework Statement Prove that for any a, b ∈ ℂ, |a - b|2 + |a + b|2 = 2(|a|2 + |b|2). Homework Equations |a|2 = aa* (a - b)* = (a* - b*) (a + b)* = (a* + b*) * = complex conjugate The Attempt at a Solution I've already shown that the relation is true. I'm not quite sure what the...

Homework Statement First, thanks in advace. Let us consider a microscope where the objective L1 has f1=20mm and magnification 10x. In the image plane is located a diafragm M with diameter 19mm (see fig). The size of the CCD is 4,8mm (vertical) x 5,6mm (horizontal). 20mm before of the CCD...

Homework Statement A ball is dropped from one yard and come backs up ##\dfrac{2}{3}## of the way up and then back down. It comes back and ##\dfrac{4}{9}## of the way. It continues this such that the sum of the vertical distance traveled by the ball is is given by the series...

Homework Statement Find the sum of the following series: Σ n*(1/2)^n (from n = 1 to n = inf). Homework Equations I know that Σ r^n (from n = 0 to n = inf) = 1 / (1 - r) if |r| < 1. The Attempt at a Solution [/B] I began by rescaling the sum, i.e. Σ (n+1)*(1/2)^(n+1) (from n = 0 to n =...

Homework Statement Let ## S_k , k = 1,2,3,…,100 ## denote the sum of the infinite geometric series whose first term is ## \frac{k-1}{k!} ## and the common ratio is ##\frac {1}{k}##. Then value of ##\frac {100^2}{100!} + \sum\limits_{k=1}^{100} | (k^2 - 3k + 1)S_k | ## is Homework Equations...

Hello everyone, I have another question mark buzzing inside my head. After the elimination steps of a matrix, I'm having some problems about imagining in 3D. For example, x=t , y=2t, z=3t what it shows us? Or, x=t+2, y=t,,z=t ? Or another examples you can think of. ( Complicated ones of...

I'm struggling with question 10. I'm not sure how to account for the different time? I'm probably just overthinking it. I have attached a picture of the answer as well. Again, trying to figure out question #10

Homework Statement Sorry if this is a dumb question, but say you have 1/(1-x) This is the form of the geometric series, and is simply, sum of, from n = 0 to infiniti, X^n. I am also trying to think in terms of Binomial Series (i.e. 1 + px + p(p-1)x/2!...p(p-1)(p-2)(p-(n-1) / n!). 1/(1-x) is...

Homework Statement Find the Geometric image of; 1. ## | z - 2 | - | z + 2| < 2; ## 2. ## 0 < Re(iz) < 1 ## Homework EquationsThe Attempt at a Solution In both cases i really am struggling to begin these questions, complex numbers are not my best field. There are problems before this one...

The article below is an excerpt from Discover magazine. What I don’t understand is the difference between the geometric magnetic and the magnetic north poles. From the article the North and South magnetic poles dips are not opposite of each other, so how is the geomagnetic pole calculated? Is...

Homework Statement I am giving the sum: k=1 to infinity Σ(n(-1)^n)/(2^(n+1)Homework Equations first term/(1-r) = sum for a geometric series The Attempt at a Solution [/B] With some manipulation of the denominator 2^(n+1) = 2*2^n I get the common ratio to be (-1/2)^n while the coefficient is...

I have seen the following said on a forum: This makes good sense to me. To me, as a programmer, this sounds like he is asking for a better API to look up the coordinate at runtime; perhaps that would force the engine to evaluate expressions in a particular order, but then that's what functional...

Homework Statement Hello! Revising geometric series, I have understood that I have the following issue - I have read again about these series and, please, take a look at what I have gotten as a result (picture attached). If I calculate a future cash flow, that is I take, for example, a = 0,5...

Homework Statement a man draws balls from an infinitely large box containing either white and black balls , assume statistical independence. the man draws 1 ball each time and stops once he has at least 1 ball of each color . if the probability of drawing a white ball is p , and and q=1-p is...

Hi all, I am reading through Riley, Hobson, and Bence's Mathematical Methods for Phyisics and Engineering, and on page 854 of my edition they describe (I am replacing variables for ease of typing) "expanding 1/(a-z) in (z-z0)/(a-z0) as a geometric series 1/(a-z0)*Sum[((z-z0)/(a-z0))^n] for n...

I seem to recall reading a geometry method that showed zero to be the inverse of infinity. Can you give me a reference for that?

Homework Statement A concave mirror forms an image on a screen twice as large as an object. Both object and mirror are then moved such that the new image is 3x the size of the object. If the screen is moved 75cm, how far did the object move? Homework Equations m = image distance / object...

Homework Statement An infinite geometric progression is such that the sum of all the terms after the nth is equal to twice the nth term. Show that the sum to infinity of the whole progression is three times the first term. Homework Equations [/B] S_{n} = \frac{a(1-r^n)}{1-r}\\ S_{\infty} =...

Verify, by a geometric argument, that the largest possible choice of $\delta$ for showing that $\lim_{{x}\to{3}}x^2=9$ is $\delta = \sqrt{9+\epsilon}-3$ I have no clue, hints?

Hi, I want to calculate a rotation of a vector GA style with this formula e^{-B \frac{\pi}{2}}(2e_{1}+3e_{2}+e_{3})e^{B\frac{\pi}{2}}. Now since no book/pdf on GA exists where a calculation is explicitly done with numbers, I wounder how to calculate this. Should I substitude e^{-B...

Can someone guide me with the steps to differentiate a geometric sum, x? ^{n}_{i=0}\sumx^{i}=\frac{1-x^{n+i}}{1-x} If I'm not wrong, the summation means: = x^0 + x^1 + x^2 + x^3 + ... + n^i Problem is: I have basic knowledge on differentiating a normal numbers but how do I apply...

Hi, I just want to see if I understood this. Since the geometric product is associative and so on we can write for two multivectors A and B given by A= \alpha_{0}+\alpha_{1}e_{1}+\alpha_{2}e_{2}+\alpha_{3}e_{1}\wedge e_{2} B= \beta_{0}+ \beta_{1}e_{1}+\beta_{2}e_{2}+\beta_{3}e_{1}\wedge e_{2}...

Homework Statement Find D2/D1. See attachment. Homework Equations The Attempt at a Solution Ans: D2/D1 = 0.68 I can't figure this one out. Any special trigonometric identities that might help here? Thanks.

Hey JO, I'm reading a book on geometric algebra and in the beginning (there was light, jk) a simple calculation is shown: Geometric product is defined as: ab = a \cdot b + a \wedge b or ba = a \cdot b - a\wedge b Now (a\wedge b)(a \wedge b)=(ab-a \cdot b)(a\cdot b - ba) =-ab^{2}a-(a...

Hey, Sorry if I am in the wrong part of the forums not sure where this question goes. I am having trouble with a geometric series that has letters involved. I understand the forumla for finding the sum of first n elements with just numbers. However the series i have is .. a1 = -5, a2 = -5x, a3...

Hi, I'm trying to calculate the position of the points from a struture like the picture attached. This is a mechanic structure that consist on 3 triangles (blue, orange and green), i know all the triangles sides lengths and also their angles (and some more colored in green). My objective is...

I am trying to derive the Probability distribution of Geometric Brownian motion, and I don't know how to find the variance. start with geometric brownian motion dX=\mu X dt + \sigma X dB I use ito's lemma working towards the solution, and I get this. \ln X = (\mu - \frac{\sigma...

I've been doing some light reading on Geometric Graph Theory, and it seem interesting to me. However, at the moment I've only managed to find a few Wikipedia articles and one .PDF of lecture notes. I'm looking for something which is more complete, such as a book or a website for example...

I'm working with some old software to optimize antenna networks, and I've come across some stuff that I don't understand. For the software to run, all impedence values entered must be normalized to 1 ohm. What does it mean to normalize an impedence and how do I do it? Also, the manual for the...

Take the case for the mean: \bar{x} = \frac{1}{N} \Big( \sum_{i=1}^Ni \Big) If we simply use the formula for the sum of a geometric series, we get \bar{x} = \frac{N}{2} (2a + (N - 1)d) where a and d both equal 1, so we simply get the result \bar{x} = \frac{1}{2} (N + 1)...

If the following integral: $$\\ \iint\limits_{a\;c}^{b\;d} f(x,y) dxdy$$ represents: So which is the geometric interpretation for ##f_{xy}(x_0, y_0)## ?

Hello, I need help. I do not know what to give values of the geometrical tolerance for Concentricity. They are two parts connected by a pin. Both parts are moving relative to each. Thanks for any advice.

I'm going through the Degroot book on probability and statistics for the Nth time and I always have trouble 'getting it'. I guess I would feel much better if I understood how the various distribution arose to begin with rather than being presented with them in all there dryness without context...

Homework Statement Calculate ##\sum\frac{4^{n+1}}{5^n}## (where n begins at 0 and approaches infinity). Homework Equations The Attempt at a Solution I could easily solve this if the numerator were just ##4^n## instead of ##4^{n+1}##, because then it would be a geometric series with...

So here's the deal guys: I have a bachelor's in physics and have gotten an A in an undergraduate special relativity course but I do not feel that I fully understand the subject. I can do the problems in special relativity which require the various formulas involved in the subject and I even...

For the question, shouldn't the sum be a(1/1-r) since we know lrl < 1 then that rn → 0 as n → ∞? I just don't quite understand why they wrote the sum is a(r/1-r). Is there a specific reason they did this? This is just a regular geometric series right? Is there any difference since the sum starts...

Homework Statement GMR_{hollow cylinder}=Re^{-Kμ} where K=\frac{AR^4-R^2r^2+Br^4+r^4ln(R/r)}{(R^2-r^2)^2}, where R is the outer radius and r is the inner radius, and mu is the relative permeability. We are to determine the numerical values of A and B. I am stumped on how to begin attempting...

"Geometric absolute" If exist a function called absolute that ensures that the result have always the posite sign, so, exist some function that ensures that the sign of the result is always ×? ##f(x) = x## ##f(\frac{1}{x}) = x##

This picture from https://www.amazon.com/dp/0198534469/?tag=pfamazon01-20 is all you need to derive the Cauchy-Riemann equations, i.e. from the picture we see i \frac{\partial f}{\partial x} = \frac{\partial f}{\partial y} should hold so we have i \frac{\partial f}{\partial x} = i...

Homework Statement This problem is from Mary Boas' "Mathematical Methods in the Physical Sciences" 3rd Ed. Capter 3 Section 4 Problem 3 Use vectors to prove the the following theorems from geometry: 3. The diagonals of a parallelogram bisect each other. Homework Equations Just...

Homework Statement (a) At the start of the competition, Shirley has 20 arrows in her quiver (a quiver is a container which holds arrows). 13 of Shirley’s arrows have red feathers, and 7 have green feathers. Arrows are not replaced when they are shot at the target. (i) At the end of the...

I am making a Geometric model for VESPR theory, which states that valence electron pairs are mutually repulsive, and therefore adopt a position which minimizes this, which is the position at which they are farthest apart, still in their orbitals. For example, the 2 electron pairs on either side...

The interpretation of the vector product is the area of the parallelogram with sides made up of a and b and the scalar triple product is the volume of the parallelpiped with sides a, b, and c, but what is the interpretation of the vector triple product. Is it just simply the area of the...

Homework Statement Explain the physical principle of total internal reflection used by optical cables. Calculate the critical angle of incidence that corresponds to a refracted angle θair = 90 Next, calculate the critical angle for a bare glass fiber submerged in water nH2O = 1.33...

Homework Statement Patients with certain heart problems are often treated with digitoxin, a derivative of the digitalis plant. The rate at which a person's body eliminates digitoxin is proportional to the amount present. In 1 day, about 10% of any given amount of the drug will be eliminated...

Homework Statement A ray is deflected by 2.37cm by a piece of acrylic. Find the thickness t of the acrylic if the incident angle is 50.5 degrees. http://imgur.com/kx2VT5c Homework Equations n1sinΘ1 = n2sinΘ2 The Attempt at a Solution n of acrylic is 1.5. Therefore, the refracted...