Geometry Definition and 999 Threads

As I understand it, a Cartesian coordinate map (a coordinate map for which the line element takes the simple form ##ds^{2}=(dx^{1})^{2}+ (dx^{2})^{2}+\cdots +(dx^{n})^{2}##, and for which the coordinate basis ##\lbrace\frac{\partial}{\partial x^{\mu}}\rbrace## is orthonormal) can only be...

Hello! I started recently to use ANSYS Workbench 15 to solve a stiffness problem of a three parts assembly. I have a general knowledge about FEM. I create the geometry in the Design Modeler by inserting the assembly from Solidworks 2010. It is a three parts assembly like a bicycle's wheel. Two...

Hi everyone, I have recently installed ANSYS 14.5. But after opening workbench, while trying to open Fluent I am getting problems like "Unable to start the geometry editor." and "Unable to start the Meshing editor." I have attached the error screen shot. Please help me out in this. Thanks a lot.

Homework Statement If two vertex of a square of the side AB is A(1,2) and B(2,4) find other two vertex C and D? Homework Equations 1. y-y1 = m ( x-x1) 2. m=y1-y2 / x1-x2 3. m1*m2= -1 4. (x-x1) / (x1-x2) =(y-y1)/(y1-y2) 5. m=tanA 6. If ax+by+c=0 then its parallel line is ax+by+k=0 The Attempt...

Hi, I am just about to finish working through the integration chapter of calculus on manifolds, and I am wondering whether it would be better to get spivaks first volume of differential geometry (or another book, recommendations?) and start on that, or to finish calculus on manifolds first...

Simple and basic question(maybe not). How are rotations performed in differential geometry ? What does the rotation matrix look like in differential geometry? Let us assume we have orthogonal set of basis vectors initially. I am looking to calculate the angle between two geodesics. Can this...

I am taking my bachelor in geometric quantization but I have no real experience in differential geometry ( a part of my project is to learn that). So I find myself in need of some good books that cover that the basics and a bit more in depth about symplectic manifolds. If you have any...

On the one hand there are Differential Geometry, Algebraic Geometry On the other there are Euclidean geometry, Hyperbolic geometry and elliptical geometry On the other there are Affine geometry, projective geometry. How do they all link up? Or are they all a bit different.

I'm trying to get an intuitive feel for Minkowski space in the context of Special Relativity. I should mention that I have not studied (but hope to) the mathematics of topology, manifolds, curved spaced etc., but I'm loosely familiar with some of the basic concepts. I understand that spacetime...

Hey! :o In what jobs is differential geometry applied and needed?

Separate questions: 1. What is the mathematical formalism where one can transform between field and geometry or they both being emergence? 2. What is the mathematical formalism that can describe QFT but not using the concept of fields nor particles. What are they called and current attempts at...

Let $A,\,B$ and $C$ be three angles of a triangle $ABC$. Prove that $(1-\cos A)(1-\cos B)(1-\cos C)\ge \cos A\cos B \cos C$

How, if at all, would differential geometry differ between the opposite "sides" of the surface in question. Simplest example: suppose you look at vectors etc on the outside of a sphere as opposed to the inside. Or a flat plane? Wouldn't one of the coordinates be essentially a mirror while...

Homework Statement Volume of tetrahedron T.ABC = V Point P is on the middle of TA, Q is on the expansion of AB making AQ = 2AB A shape is made through PQ which is parallel to BC so that it cuts the tetahedron into 2 pieces. What is the volume of the biggest piece? The Attempt at a Solution I...

have you encountered it and/or solved it? what did you think?

It is well known that: The shortest distance from a point to a line is the length of the line segment which is perpendicular to the line and joins to the point. Who first proved this? How far back in time does it go?

Homework Statement How do I find the surface area of a sphere (r=15) with integrals. Homework Equations Surface area for cylinder and sphere A=4*pi*r2. The Attempt at a Solution I draw the graph for y=f(x)=√(152-x2). A circle for for positive y values which I rotate. I will create infinite...

Homework Statement A short paper 12-16 pages I'm also fairly new to this topic Homework EquationsThe Attempt at a Solution I tried to ecplain it's application using the Robertson walker mrttuc but it ended upmlooking too much like a physics psper:/

I'm in 11th grade right now, and I would like to know whether or not I should spend my time learning geometry as my high-school education system places zero emphasis on geometry. If so, what type of geometry should I start with? (euclidean, analytic, differential, non euclidean?) by the time...

Homework Statement Problem statement uploaded as image. Homework Equations Arc-length function The Attempt at a Solution Tangent vector: r=-sinh(t), cosh(t), 3 Now, I just need to reparameterize it using arclength and verify my work is unit-speed. Will someone give me a hint? Should I use...

I have a certain Ansatz for a gravitational wave perturbation of the metric h_{\mu \nu} that is nonzero near an axis of background flat Minkowski spacetime The Ansatz has the following form: g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu} = \begin{bmatrix} -1 & 0 & 0 & 0 \\ 0 &...

ive been reading about people thinking sub Planck scale spacetime is "non commutative". i have a vague idea of non commutative geometry mathematically, but there's no "space" in non commutative geometry so how can SPACEtime be a non commutative ring? i thought non commutative geometry was just...

Hello, i am Ali doing PhD studies i am working on Activation Analysis of Hybrid reactor but i just stat studying this geometry but i am not able to understand this geometry for MCNPX modeling, so i need some help in modelling this geometry in MCNPX. please guide me in this regard

I was lying awake the other night and thinking about Pi and flatlanders. I haven't done a lot of topology reading, so forgive my naivete. Pi on a flat surface is a number we know well, but what happens to the ratio of a circle's diameter to its circumference on curved surfaces? First question...

I'm seeing a presentation of Euclidean geometry that isn't hand-holdy. I've looked at some textbooks used in high schools these days, and it's hard to find the axioms and theorems in the midst of all the condescension. I just want something that states the definitions, axioms and basic...

I am in need of a spherical geometry book.can some one suggest a good one?

Homework Statement Requirements: http://i.imgur.com/2WKyhto.png Homework Equations 2(L * W + L * H + W * H) SA = (2 * pi * radius * height + 2 * pi * radius^2) height = (volume)/(pi * radius^2) The Attempt at a Solution Code link: http://pastebin.com/sKFEGN0C

I am studying spherical astronomy can some suggest good books on spherical geometry.

In the figure, ABCD is a square of side 1 cm. ABFE and CDFG are trapeziums(/trapeziods?). The Area of CDFG is twice the Area of ABFE. Let x cm be the length of AE. (a) Express the length of FG in terms of x. (b) Find the value of x, correct to 2 decimal places. Thanks! :D

Hey, I am struggling to understand what the following is in terms of the mathematics (see Nakahara page 193 at the bottom...

Hello 1. Homework Statement We define the Dupin indicatrix to be the conic in TPM defined by the equation IIP(v)=1 If P is a hyperbolic point show: a. That he Dupin indicatrix is a hyperbola b/ That the asymptotes of the Dupin indicatrix are given by IIP(v)=1 , i.e., the set of asymptotic...

Hey JO, You all know the binomic formulas I guess. Let's look at the first: (a+b)^2=a^2+2ab+b^2 Now this can be interpretet as the area of a square with the sides (a+b). And that means the area of the square is decomposed into the components a^2,2ab and b^2. And this can also be done for a cube...

Crossing over the following paragraph: There are three types of special manifolds which we shall discuss, related to the real scalars of gauge multiplets in D = 5, the complex scalars of D = 4 gauge multiplets and the quaternionic scalars of hypermultiplets. Since there are no scalars in the...

I am currently in year 9 (9 grade for those in US) and I have a really rusty and a weak math background. I have 2 months of summer holidays coming up. I should be done with pre algebra in mid December. During my summer holidays I have more than 50 hours a week avalible for study and I was just...

Hi, This is also a sort of geometry question. My textbook gives a proof of the relation: sin(θ + Φ) = cosθsinΦ + sinθcosΦ. It uses a diagram to do so: http://imgur.com/gLnE2Fn sin (θ + Φ) = PQ/(OP) = (PT + RS)/(OP) = PT/(OP) + RS/(OP) = PT/(PR) * PR/(OP) + RS/(OR) * OR/(OP) = cosθsinΦ +...

Homework Statement Consider a universe described by the Friedmann-Robertson-Walker metric which describes an open, closed, or at universe, depending on the value of k: $$ds^2=a^2(t)[\frac{dr^2}{1-kr^2}+r^2(d\theta^2+sin^2\theta d\phi^2)]$$ This problem will involve only the geometry of space at...

In triangle ABC, $\angle ACB=\angle ABC=80^\circ$ and $P$ is on the line segment $AB$ such that $BC=AP$. Find $\angle BPC$.

Urs Schreiber submitted a new PF Insights post Higher Prequantum Geometry V: The Local Observables - Lie Theoretically Continue reading the Original PF Insights Post.

Urs Schreiber submitted a new PF Insights post Higher Prequantum Geometry IV: The Covariant Phase Space - Transgressively Continue reading the Original PF Insights Post.

I had geometry quite a while ago and I wonder if anyone has any idea how to tackle this problem: Is there any ABCDS pyramid (where ABCD is a rectangle) in which each 2 edges have different lengths and |AS|+|CS|=|BS|+|DS| Thanks

Urs Schreiber submitted a new PF Insights post Higher Prequantum Geometry III: The Global Action Functional - Cohomologically Continue reading the Original PF Insights Post.

Urs Schreiber submitted a new PF Insights post Higher Prequantum Geometry II: The Principle of Extremal Action - Comonadically Continue reading the Original PF Insights Post.

Homework Statement The moment of the couple is 600k (N-m). What is the angle A? F = 100N located at (5,0)m and pointed in the positive x and positive y direction -F = 100N located at (0,4)m and pointed in the negative x and negative y direction Homework Equations M = rxF M = DThe Attempt at a...

Urs Schreiber submitted a new PF Insights post Higher Prequantum Geometry I: The Need for Prequantum Geometry Continue reading the Original PF Insights Post.

Dear all I am studying general relativity and i have a question as follow. We have the 2- sphere can be scanned totally by a coordinate system (theta, phi) with the metric tensor written in terms of theta and phi. Now i want to divide the 2-sphere into charts 4 charts then each will have its own...

Hi, 1. Homework Statement C : ℝ→ℝ3 given by C(t)= ( 1/2 [ (1+k)/(1-k) cos((1-k)t) - (1-k)/(1+k) cos((1+k)t) ] ; 1/2 [ (1+k)/(1-k) sin((1-k)t) - (1-k)/(1+k) sin((1+k)t) ] ) with 0<|k|<1 Show that C(t) is an epitrocoid and find R, r and d according to k Homework Equations Parametrization of...

Hope I am on the right forum (and that my question makes some sense-so here goes. Imagine we are a race of people living on a sphere (not hard because we are) However , rather than buying into the idea that lines are ideally straight we are and have always been well aware of how "parallel...

Homework Statement What is the area of a triangle on Earth that goes from the North Pole down to the equator, through the prime meridian, across the equator to 30 degrees east longitude, then back up to the equator? The radius of the Earth is about 6378 km. Homework Equations alpha + beta +...

Hello! Can you give me information about the subject Discrete Geometry? What is it about? What knowledge is required? (Thinking)

Hello, I am totally bad at geometry , by geometry I mean plane euclidean geometry with similarities and circles. I sometimes feel totally lost with problems. For example: The parallel sides of trapezoid ABCD are 3 cm and 9 cm(AB and DC).The non parallel sides are 4 cm and 6 cm(AD and BC).A...