Geometry Definition and 999 Threads

Hello everyone! I just wanted to ask a question about how I should study for differential geometry. Now, as I have it, I've got a few suggestions for books, of which two stand out prominently: 1. John Lee's Introduction to smooth manifolds 2. De Carmo Which one would be best for self study...

Homework Statement I am given the following vectors : p = 3 q = 2 r = 5 2 4 3 -4 -3 -1 They ask to find these: 1. a normal to the plane containing p, q and r. 2. the distance from the origin to the plane...

Homework Statement #1 Given that the angle between the vectors a and b is 2Pi/3 and |a|=3 and |b|=4 calculate: (axb)^2 [(2a+b)x(a+2b)]^2 #2 Given three unit vectors, a, b, c such that a+b+c=0 find (a dot b) + (b dot c) + (c dot a) #3 Given AB=a+2b BC=-4a-b CD= -5a-3b...

Hi, I was wondering if someone wouldn't mind breaking down the geometrical differences between the Riemann, Ricci, and Weyl tensor. My current understanding is that the Ricci tensor describes the change in volume of a n-dimensional object in curved space from flat Euclidean space and that if we...

Geometry Question? A triangle has vertices, A(1,-1) , B(0,5) and C(-3,0). Find the length of the altitude from A to BC. You must find the POI of the altitude and BC: that's the hint So basically i have no idea how to do this... i got 4.3... but its wrong

Homework Statement A rectangle is 2 metres longer than it is wide. On the other hand, if each side of the rectangle is increased by 2 metres, then the area increases by 24 square metres. Find the side-lengths of the rectangle. Homework Equations The Attempt at a Solution So my...

I have read many threads concerning many excellent books on calculus but not for analytical geometry. I can't seem to find any thread about good references for analytical geometry. I am taking the course analytical geometry and calculus in college and I need good book in both fields. I have...

Hi friends . is there anybody here who can give me a fortran code for describing fcc lattice and give us the neighbours of each site and also which pay attention to periodic condition ? thank you for your help my friends.

I am not currently taking a Geometry class, but I've always been interested in Geometry and I'm now looking for a good College-Level Geometry book. All the ones I have checked out from my school's library claim to be College-Level, but mostly talk about subjects I remember learning about in High...

I'm to work out the internal forces in this truss. I know to get the reaction forces first, so I take the moment at the pin support to find the reaction at the roller support. I can't get my head around at how to find x through the geometry to add that force to the moment though. Is there not...

I need help with Part (b). I finished part (a) and attached it as well. My issue comes from how to apply the definition of connection forms to compute them. The definition states: Let E_1, E_2, E_3 be a frame field on R^3. For each tangent vector v at R^3 at the point p let \omega_{ij}(v )=...

Suppose I'm given a random function: (-8+5 z+4 z^2)\text{}+(7 z+6 z^4-7 z^5)w+(3 z^2-z^3)w^2+(-8 z-2 z^4-2 z^5)w^3+(3-4 z+4 z^2+7 z^3+6 z^4-8 z^5)w^4+(-6 z+4 z^4)w^5=0 Is there no way to determine it's ramification geometry at each singular (critical) point algebraically? I'm pretty sure...

Homework Statement Consider the points P = (1/2, √3/2) and Q = (1,1). They lie on the half circle of radius one centered at (1,0). a) Use the deifnition and properites of the hyperbolic distance (and length) to compute dH(P,Q). b) Compute the coordinates of the images of Pa nd Q...

Hello, I have been trying to help a friend of mine some descriptive geometry like orthographic projection of planes etc . . . I was wondering if someone can recommend a simple software that has the very basic construction tools like a ruler, compass, protractor etc so as to record some of the...

A quick novice question. What sort of shape would project a holographic reality (Kind of like water spraying from the inside walls of a sphere) from the boundaries of the universe and at the same time contain drains (black holes) that feed the shower?

I was just wondering they have a course at my university and I am trying to figure out what exactly it covers. Most people learn basic geometry in high-school so I was surprised to find a course for mathematics majors that is an upper division course in geometry at the college level. The course...

As the title says. Can anyone recommend me some good books for differential geometry(preferably ones with proofs and examples/exercises)?

Q. If a regular polygon has n number of sides, what will be the angles between the sides ? i tried to do this by taking ratios of figures and angles , such as 180/3 , 360/4 and so on , but the progression is not uniform so i am clueless right now. the answer is in terms of n and pi

The interest of this article was first pointed out by Tom Stoer in biblio thread comment. The idea is to take seriously the quantum nature of geometry and its interaction with fermions at the quantum level. The idea is even that geometry might be as we experience it BECAUSE her little triads...

Homework Statement Given: AB \coprod CD ; \angleA \cong \angleC Proof: AD \coprod BCHomework Equations Idk how to necessary finish it...The Attempt at a Solution Statement -------------- Proof 1. AB \coprod CD ; \angleA \cong \angleC ----------- 1. Given 2. I say \angleA is supp. \angleD and...

hey all, in this book ; https://www.amazon.com/Geometry-Riemannian-Spaces-Lie-Groups/dp/0915692341/ref=sr_1_1?ie=UTF8&qid=1348590926&sr=8-1&keywords=geometry+of+riemannian+++spaces++cartan On page 178 ( which I attach a snapshot of it) Cartan had introduced a formula (see in the snapshot...

Hi Guys, I have an query. I would like to know the best tool for Simulation, Geomtry and Mesh creation. I want to simulate a duct with a turbine in it as a Part of my research project. I am beginner for the simualtion field so please suggest accordingly the appropriate software. Also please...

Hi everyone, I was wondering if I could some advice from anyone who has some experience with higher level general relativity. Any help would be greatly appreciated! Some background: I'm currently working through Robert Wald's General Relativity and am struggling a lot with the "advanced...

How much energy is necessary to place three charges, each of 2.0 μC, at the corners of an equilateral triangle of side 2.0 cm? This is in the chapter all about electric potential so I think I have to use the voltage equations in some way. V = Kq/r u= qV I am honestly unsure of...

Hi guys, i was wondering how you calculate how fast a bullet would have to travel to 'overcome' gravity, i.e if it didn't hit anything (and discluding air resistance for now). Mapping the Earth as a circle and knowing things such as the radius of the Earth and gravity acts on the bullet at...

My teacher has defined U_1 = \langle1, 0, 0\rangle, U_2 = \langle0, 1, 0\rangle, and U_3 = \langle0, 0, 1\rangle. So it seems like the function maps L(\langle1, 0, 0\rangle, \langle0, 1, 0\rangle) = a, L(\langle1, 0, 0\rangle, \langle0, 0, 1\rangle) = b,, and L(\langle0, 1, 0\rangle...

find the equation of a circle whose center falls ont he line y=6-2x and which passes through the points A(-2,0) and B(4,0). poor in circles. how to even start?

Find the equation of the circle whose centre is (-3,4) and which touches the y-axis. how do i even begin?

Well, I found this challenge in another forum (not about math) on the internet, and, originally, there were no 'w', 'z' or 'y' drawn on the pic, it was just "find the x", but I put them on because I know you guys probably would create other variables to solve the problem. Another problem I had...

I am a physicist trying to understand the notion of holonomy in principal bundles. I am reading about the horizontal lift of a curve in the base manifold of a principal bundle (or just fiber bundle) to the total space and would like to relate it to the "classic" parallel transport one comes...

Basically, I want a trigonometry textbook, but a lot of the texts on trigonometry use theorems in geometry as though you are already familiar with them and simply skip proofs for these theorems (such as Pythagoras theorem, some properties of triangles, properties of quadrilaterals and triangles...

I know UC San Diego is good, Rothschild and Ebenfelt are there, but are there any other ones that stand out in these and related fields? Thanks a bunch

I was watching a Horizon program the other night on the BBC and was interested that they were able to repeat the "triangle on the surface of a sphere" experiment on the universe as a whole. When this experiment is performed on the surface of the Earth on a large enough scale the angles of...

Hi all, I have a heat sink for which I know the exact geometry (have the CAD model). This heat sink was custom designed and machined from a hunk of aluminum, though it is very basic and I have a hunch I can find an extrusion or OTS part that will match its performance. Rather than trying to...

Hi, I am new to the study of special relativity but think I understand it pretty well from the common circular geometrical framework. How important is it that I also understand it from the hyperbolic perspective and what would I gain over my current circular understanding?

Some Background I am working on a soccer robotics project called RoboCup (perhaps people here have heard of it), which revolves around building a fleet of autonomous soccer robots that play against each other (league website - http://small-size.informatik.uni-bremen.de/ ). The kicking...

What do you make of this recent paper of Chamseddine and Connes? Resilience of the Spectral Standard Model The version of the Standard Model based on a product of the spacetime manifold with a finite noncommutative space had previously predicted a Higgs mass of 170 GeV. Supposedly this paper...

say I have a circle with a diameter of d and there is a point at the top of the circle, p. I want to know the distance from point p to any other point on the perimeter and the angle θ from the tangent line of p. is there a function that will describe this? I will try to put up a picture to...

http://memorial.jacksonsd.org/www/jacksonsd_memorial/site/hosting/Summer_Math_11/GeometryHonorsSummerAssignment.pdf But it's the summer and I haven't done this in a couple of months. I need pages 10-16 done, I have already finished them but I know most of it isn't correct. I also know math...

The title says everything. Can a mathematician do fruitful research in general relativity if he masters differential geometry and manifolds?

Are there any good papers or books that go over our current understanding of differential geometry for 2-dimensional complex spaces? Hermitian vs anti-symmetric metric tensors, dealing with complex conjugates, and defining affine connections? Yes, I've already hit up Google, so I was hoping...

Working on another problem here with varying results. I have three line segments in 3D and am looking to find what would be a projected intersection between two. This projected intersection is defined by a ray that is perpendicular to the axis a and passes through both segments f and s. f...

Hi I am new to the forum and I'm looking for help for a math problem I was given in my linear algebra class... Here its goes: Geometrically, a 1-dimensional subspace of C^2 is what kind of object? De- scribe the intersection of two such subspaces. Translate these geometric no- tions into...

I'm trying to help a friend but I don't remember any of this, so it'd help us both. Book recommendations are also welcomed. Given the vector equations $$r: \begin{cases} x = 2 - \lambda, \\ y = 1 + 3 \lambda, \\ z = 1 + \lambda, \end{cases} \text{ and } s: \begin{cases} x = 1+t, \\ y = 3+4t, \\...

Homework Statement Find the equation of the circle whose centre lies on the x-axis and which passes through points A (6,0) and B (0,10). Homework Equations The Attempt at a Solution I drew a diagram of the circle and determined that the line AB has gradient 5/3. Its perpendicular bisector...

"A" starts a journey from a massive body in Schwarzschild geometry in a radial path and returns back to the starting point while "B" stays at rest. Please explain how to find the proper time of "A".

This is the course description: I want to take this class because the professor comes highly recommended, but I'm a little worried that I won't be entirely prepared for it. Normally this class requires Real Analysis as a prerequisite, and even though the professor explicitly states that...

Homework Statement 1. What is the molecular shape of Hydrazine N2H4 w.r.t. N atom? 2. H2S and H2O, which one has a larger bond angle? 2. The attempt at a solution 1. Trigonal Pyramidal is the answer given. But Hydrazine has 5 atoms around its central atom and I'm unable to fathom...

The question is "Is it ever correct to write \stackrel{\Large\leftrightarrow}{AB} = \stackrel{\Large\leftrightarrow}{CD}. If so, what does that imply about A, B, C, and D. I feel like this statement of equivalency would only be true in the circumstance that A and C were two different names...

Homework Statement In triangle ABC, the median from C meets AB at D. Through M, the midpoint of CD, line AM is drawn meeting CB at P. If CP=4, find CB. Homework Equations The Attempt at a Solution I constructed this drawing on GSP and found CB to be 12. I'm trying to show...