Geometry Definition and 999 Threads

Homework Statement Prove that a line in 3D space is imaged to a line on the image plane in a pinhole camera model. Homework Equations A 3D point give by (X,Y,Z) will be imaged on the image plane at x = f(\frac{X}{Z}) and y = f(\frac{Y}{Z}) where f is the focal point. The Attempt at...

Hello Everyone, I am just wondering what the difference in these is. Could someone please give a brief example of non-coordinate based differential geometry vs the equivalent in coordinate based, or explain the difference (whichever is easier)? Also, what advantages does one have over the...

Hi, I was wondering how to calculate, mathematically, the number of vertices on a cube, rather than just count them? Also, in a cube, how many edges are shared by a face? By counting the number of edges, there comes out to be 24, but since it face shares four edges, shouldn't there be 6 edges...

I read somewhere that a Geometry is a non Empty set and a subset of its power set which has subsets with at least two elements.The elements of the first set are called points and the elements of the second set are called lines.With specifying these two sets and considering some axioms,you will...

Okay so I am given a 3D figure with 5 points. Keep in mind this model has the hyperbolic parallel property and satisfies the incidence axioms. The question is to construct the dual geometry and then to prove or disprove that it is an incidence geometry. My question is how do I go about...

Can someone please describe to me how Euclidean Geometry is connected to the complex plane? Angles preservations, distance, Mobius Transformations, isometries, anything would be nice. Also, how can hyperbolic geometry be described with complex numbers?

Geometry Triangle Congruence - **Edited to include diagram** Homework Statement Hi! The three simple geometry problems are in the attached photo. Sorry if they're difficult to read. I haven't seen this information in so long, and could use some help. :D Can you use the given information...

Hi folks, I have a basic question I would like to ask. I ll start from the Euclidean analogue to try to explain what I want. Suppose we have a smooth function (real valued scalar field) F(x,y)=x^2+y^2, with x,y \in ℝ. We also have the gradient \nabla F=\left( \frac{\partial F}{\partial...

Homework Statement Determine the electron geometry and molecular geometry or the underlined carbon in CH3CN. A) tetrahedral/tetrahedral B) linear/trigonal planar C) trigonal planar/bent D)linear/linear E)trigonal planar/trigonal planar I'm not really sure how to structure this...

So I'm studying projective geometry and I'm confused about duality. In particular, I'm confused about drawing dual pictures. If you look at Menelaus's Theorem and Ceva's Theorem, they are supposedly dual diagrams. http://en.wikipedia.org/wiki/Menelaus'_theorem...

I am an Astrophysics undergrad, and will be taking Classical Differential Geometry I & II. Are there any classes that will make understanding Differential Geometry easier. I can chose from: -Introduction To Abstract Algebra -Introduction To Mathematical Analysis -Introduction To Real...

http://digi-area.com/DifferentialGeometryLibrary/ includes over 580 objects for differential geometry and its applications. Moreover here is 380 Exact Solutions of Einstein's Field Equations. The formulas are represented in different forms: metric from, Contravariant Newman–Penrose Tetrad...

Homework Statement Prove that the equations x=acos(\theta) and y=bcos(\theta +\delta ) is the equation of an ellipse and what angle does this ellipse's major axis make with the x axis? Homework Equations Equation of an ellipse is x=acos\theta, y=asin\theta Rotation matrix is for a rotation...

Identify one (1) lesson on circles that could integrate the Seed of Life in the delivery of the lesson. I need help on this urgently

Hi all, The question i have may not be best suited for this forum but i always seem to get sensible answers here! I have not found an answer too this after searching and searching... If my Rear geometry provides better performance in roll than in bump in comparison to my front axle...

Homework Statement If u is a unit vector, find u.v and u.wHomework Equations I assumed that unit vector means u=<1,1,1> u.v=|u||v|cos60 My knowledge of unit vectors is very limited. I know that a unit vector is i=<1,0,0> j=<0,1,0> k=<0,0,1> The Attempt at a Solution Since the triangle is...

I'm currently studying abstract algebra from Herstein's interesting book "Topics in algebra", I've learned different definitions so far and I've solved most of the problems covered in the book. I've so far studied groups, subgroups of them, normal subgroups, quotient groups, isomorphism...

Homework Statement Ok I'm able to track one star in the sky, over a period of one hour. We use three measurements to find the angle of the arc traced by the star. The three measurements also constitute two vectors. We can take the cross product of those vectors and it will give us a vector...

I'm working with 3D geometry, and I've been at this for days. I'm beating my head against a wall, because I'm nearly done with the project. There's only one glitch in my system. The Situation: I have a 3D cartesian coordinate system with a Spherical system overlaid over it (the "poles"...

Homework Statement a. Suppose you do not know your location (on Earth) or the direction of north. Now suppose you track one particular star in the sky. You measure its exact position in the sky and record the exact time of the measurement. How many such measurements are necessary to deduce...

I have decided to attempt to pick up some differential geometry on my own, and I am trying to get some traction on the subject which I do by trying to reduce it to familiar and simple cases. This is a trivial case, I know, but it will go a long way in advancing my understanding. Suppose the...

Homework Statement then points are uniformly spaced on a circle. Each of the points is connected by a segment to exactly one of the other points for a total of five segments. Some pairs of the segments may intersect and some may not. What is the maximum possible number of distinct intersection...

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...

Homework Statement 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...

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...

Homework Statement Show that if M is a surface such that every geodesic is a plane curve, then M is a part of a plane or a sphere. Homework Equations - If a geodesic, \alpha, on M is contained in a plane, then \alpha is also a line of curvature. - Let p be any point on a surface M and...