Geometry Definition and 999 Threads

Hey Everyone, I just wanted to ask for a bit of help on this research assignment I have to do. I have to show how Fractal Geometry contributes to the theory that Mathematics was invented. I have been looking into fractal dimensions and the fact that the dimensions we have labelled (1,2 and 3)...

Homework Statement Homework Equations L[c]:=\int_{a}^{b}(\sum_{i,j=1}^{2}g_{ij}(c(t))c_{i}'(t)c_{j}'(t))^{1/2}dt The Attempt at a Solution So g_{ij}(x,y)=0 for i{\neq}j, c_{1}'(t)=-Rsin(t), c_{2}'(t)=Rcos(t) so...

The stress-energy tensor is associated to a volume density and flux in 4-spacetime and the Einstein tensor seems to represent a three-dimensional curvature (being a one-form with vector values) that acts on and is acted by the stress-energy source. If this is correct, I'm not sure what is this...

String field from Loop SpinfoamQG:how to build SM matter on discrete quantum geometry note: EPRL is the current standard spinfoam formulation of Loop Quantum Gravity. http://arxiv.org/abs/1201.0525 String Field Theory from Quantum Gravity Louis Crane (Submitted on 2 Jan 2012) Recent work...

Homework Statement Given that P,Q and R lie on the hyperbola xy=c2, prove that if PQ and PR inclined equally to the coordinate axes, then QR passes through O. Homework Equations The Attempt at a Solution I don't understand what does ''PQ and PR are inclined equally to the...

Homework Statement (E) is a group of points M from a level/plane MA^{2}-MB^{2}=-4 And I is the center of [AB] Homework Equations show that IM*AB=-2 ( IM and AB have arrows on top) The Attempt at a Solution Well i split MA^{2}-MB^{2}=(MA-MB)(MA+MB) then i got ...

Homework Statement 2 circles have the equation x2+y2-2x-2y+1=0 and x2+y2-12x-12y+36=0 respectively. Both circle touches the x-axis, y-axis and the line 3x + 4y = 12. Find the fourth tangent of the 2 circles. Homework Equations The Attempt at a Solution This is second part of the...

Homework Statement A variable point P lies on the curve y2 = x3 and is joined to a fixed point A with coordinate (2,0). Prove that the locus of the mid-point of AP is y2= 2(x-1)3. Homework Equations The Attempt at a Solution According to what i know, I need to know the...

Astronomers say that there is neither an edge or center to the universe, yet we live in a finite universe. I understand how our universe can be finite yet have no edges due to the curvature of the universe, but I can't understand how it doesn't have a center. Space must be being curved around...

Homework Statement Disparity is defined as \delta = \alpha - \beta. Find \delta in terms of interocular distance a, viewing distance D and d, e and f. http://img220.imageshack.us/img220/7576/43519392.jpg The Attempt at a Solution I'm not getting anywhere. Any tips to get me started?

So I took an analysis class which covered chapters 9 and 10 of Rudin's PMA, for those of you who don't know that's multivariable analysis and differential forms, and I have taken a course in vector calculus but never a proper course on differential geometry. Thus my introduction to the subject...

Hi, given the algebraic function: f(z,w)=a_n(z)w^n+a_{n-1}(z)w^{n-1}+\cdots+a_0(z)=0 how can I determine the geometry of it's underlying Riemann surfaces? For example, here's a contrived example: f(z,w)=(w-1)(w-2)^2(w-3)^3-z=0 That one has a single sheet manifold, a double-sheet...

Homework Statement There are three problems based on the following diagram. You have a triangle on the cartesian plane with each corner having the coordinates (-a, 0) (a,0) (b,c) Find the coordinates (in terms of a,b,c) of the point where all three perpendicular bisectors of the...

Can anyone recommend a good geometry book?

This is a Lagrangian problem, I am posting it here in introductory physics because what I need help with isn't in Lagrangian mechanics, but rather geometry. http://img97.imageshack.us/img97/7504/what3.png I am confused as how they got those relations for x and y. I have tried to make...

Suppose you have the simplest type of black hole - time independent, no angular momentum or charge, Schwarzschild solution, then you modify the situation by adding a stationary mass outside the event horizon (I imagined lowering this slowly on an idealised string). The question is, does this...

Hi all , How can I find lecture notes on ArXiv ? I was looking for lecture notes on Yang-mills theories treated in the language of differential geometry but didn't succeed till now . Can some one recommend me some good resource for it?

[/itex][/itex]Homework Statement A battery consists of a cube of side L filled with fluid of conductivity s. The electrodes in the battery consist of two plates on the base at y = 0, one grounded and one at potential V = 12 Volts. The other sides of the battery casing are not conductive...

Homework Statement I have this arrow head geometry question (Please see diagram). I know L1, L2 and L3, angle B and the constant k (notice how the corner angle is equal to k * t2). I don't know t1 and t2. I'm pretty sure I have enough constraints, I'm just having trouble finding the right...

Homework Statement Please see below... Homework Equations Please see below... The Attempt at a Solution Hi. This question is on geometry with circle and triangle. I am stuck only on 2 parts of the solution and not the whole solution... Thank you...

I have a three link revolute manipulator at the origin. I know all the link lengths. The joint angle for the third link is coupled to the second such that Theta3 = k*Theta2. I want to determine the joint angles (thetas) of the manipulator given that the third link should lie on a line an angle...

Recently, I bought a book and found a strange question : In the given figure, PQRS is a quadrilateral. PO and QO are bisectors of angle P and angle Q respectively, then prove that angle QOP = 1/2 (angle R + angle S) I made several attempts to get the solution but failed. I guess, we need...

Homework Statement http://184.154.165.18/~devilthe/uploads/1321855187.pngHomework Equations No idea.The Attempt at a Solution Alright...so really no idea what to do here...never did any examples like this in class and have scoured over my notes for 2 hours now trying to figure this out...and...

I did bad in geometry my sophomore yr of high school. Sr. Year I plan on taking physics. How much of physics math deals with geometry?

Homework Statement (z' represent conjugate of complex number z,i is iota =sqrt(-1)) (1)find the locus of z. |z|2+4z'=0 (2)|z1|=1, |z2|=2, then find the value of |z1-z2|2+|z1+z2|2 (3)z=(k+3)+i[sqrt(3-k2)] for all real k. find locus of z Homework Equations |z|2=z.z' The Attempt at a...

Hello, After reading both How to Prove It: A Structured Approach - By Daniel J Velleman, and one of the Lost Feynman Lectures on Planetary Orbits, I'm wondering if anyone could suggest to me any good books they've read (or heard about) pertaining to logic (paired with analysis), or plane...

Hi, recently I've tried to find a good sintetic geometry book with both theory and exercises. Many people said well about this one https://www.amazon.com/dp/0486458059/?tag=pfamazon01-20 College Geometry. I've bought it and I've got so disappointed. I want a book that has exercises...

The concept of describing something in layman's terms has come into wide use in the English speaking world. To put something in layman's terms is to describe a complex or technical issue using words and terms that the average individual (someone without professional training in the subject area)...

Homework Statement I am asking about part iv). [PLAIN]http://img715.imageshack.us/img715/7977/113ivb.jpg Homework Equations I guess they would be the ones in the earlier parts... The Attempt at a Solution In the given fact, I think x^3 - x - m(x - a) distance from the...

I'm trying to create some kind of demo that rushes through a tunnel. I have made a random path generator that creates smooth looking paths in 3D space (just some 3D points) Now I would like to create polies that form a tunnel around that path. To give an example, let us assume that the path...

Hello , I have something called Asperger's Syndrome and I would like to find a narrow topic or highly specialized field to study in the future as an Aspiring pure mathematician. But I have little or no experience in Mathematics , that's why I'm asking this question. I obsess about geometrical...

Line 1 and line 2 are given by equation 1 and 2. Point A has coordinates (xo, yo, zo). Find the equation of line 3 which goes through A and crosses L1 and L2.

Homework Statement Given a triangle ABC with BC = 2AB. D and E are the midpoints of BC and BD respectively. Show that AD bisects angle CAE. Homework Equations The Attempt at a Solution Let AB= x, so DC= AB= x and ED = x/2. If AD bisects angle CAE, then AC/AE = DC/DE...

The very first time I ever heard about fractals was in my junior year in high school in my Algebra II class when we were studying complex numbers. I was fascinated by these wonderous objects and I've had many questions about them ever since. Though two of my main questions have always been...

Homework Statement This is part from a larger construction, but I realized if i can construct this, i can do the larger construction. All ofcourse with ruler and compass. I have been given an angle with its bisector and a point on that bisector. I have to construct a circle trough that point...

The co-ordinates of a point P on the line 2x - y + 5 = 0 such that |PA - PB| is maximum, where A is (4,-2) and B is (2, -4) will be: A) (11, 27) B) (-11, -17) (Answer) C) (-11, 17) (Eliminated since it does not lie on the given line) D) (0, 5) Honest speaking, I don't know what to do in...

Hi, I am currently studying for a one year postgrad MSc in Theoretical Physics. In my undergraduate physics degree, my dissertation was on general relativity, so I got a taste of differential geometry and manifolds which I really enjoyed. At the moment I'm currently attending lectures...

Hey all. At my school we have these things called "Real Problems" that we get every 3-4 weeks. This time it's about proofs. I have an A- in the class, so I got the difficult one with 4 very difficult (IMO) proofs. I have NO idea where to start on this..I have drawn it out for you. All help is...

Hey all, BACKGROUND: (please note that knowledge of this is not necessary): I'm currently writing a javascript application using vectors (with jquery and raphaeljs) that enables me to rotate custom text (using font.js file, not normal fonts). However, due to a bug in the new version of raphael...

Homework Statement Let ABC be an equilateral triangle with side 10 cm and let P be a point inside the triangle at a distance of 2 cm from the side AB. Given --> AB = BC = CA = 10cm and PD = 2 cm. If PD, PE, PF are the perpendiculars to the three sides, find out the sum, PD + PE + PF. Here is...

I was wondering if the common chord of two intersecting circles subtends an equal angle in both circles at the circumference (in no special cases i.e different radii circles etc) If not, are there any special case(s) where this would work, making these two triangles similar or ABDC is a...

Hello everyone, I was wondering if I could get some advice for the following problem: I have two algebraic sets X, X', i.e. X = V(J), Y = V(J'), and let I(X),I(Y) be the ideals of these sets, i.e. I(X) ={x \in X | f(x) = 0 for all x \in X}. I am trying to show that I(X \cap Y) is not always...

Okay so I am reading a book on analytic geometry because my algebra class is starting to really bore me, and I ran across this: slope = m = -1/2 (easy enouph) but then it states "since the slope is the tangent of the angle of inclination θ, we have: tan θ = -1/2 okay so I guess my...

Hello. I'm new here and I'm not sure if I should post this topic here or in general math, or anywhere else. Feel free to move the topic elsewhere if needed. Just a bit of explanation first. I'm not from USA (so forgive any grammar errors) and I don't understand completely your academic...

My university is offering a Differential Geometry course next semester and while I am interested in the subject, I do not plan to take the class unless it has practical use for me. I have no interest in doing theoretical work. Does differential geometry serve any use to applied physics/engineering?

Homework Statement Show the principal curvatures on x sin z - y cos z = 0 are +-1/(1 + x^2 + y^2)

Homework Statement Sphere with P as centre has equation (x-5)^2 + (y-9)^2 + z^2 -100 = 0 Sphere with Q as centre has equation (x-1)^2 + (y+3)^2 + (z-3)^2 -49 =0 These spheres intervine with each other. Find the surface area of the object limited by the two spheres. The Attempt at a Solution...

Okay, I'm not asking how to find the solution to this problem. I already found the solution they were looking for. The thing that confuses me is that I got two different solutions using two methods that should have given me the same answer. Could someone show me what I did wrong? Homework...

nevermind i figured it out