Geometry Definition and 999 Threads

I'm taking general relativity and I understand how things work mathematically, but I'm trying to find ways of describing black holes to a general audience. Would it be fair to say that inside a black hole, space is curved in such a way that all possible paths lead to the singularity? Or, put...

New thread continuing a topic raised in https://www.physicsforums.com/newreply.php?do=newreply&p=3865854 Okay, so I saw on wikipedia that you can have a 'flat torus' --- at least a 2 dimensional torus inbedded in 4-space. So you can also have a 3-torus, that's flat? And would time just be...

Homework Statement Hey guys. As you can see, there are 5 questions to answer regarding this question. I'm working through it and need some help regarding a few of the questions. I have A.) The electric potential at the center of the circle is Zero. B.) The value of the electric...

Homework Statement A cylindrical tank of gas with a radius is viewed from the side (so that it looks like a circle, not a rectangle) and has a radius of 1m. Through a hole in the top, a vertical rod is lowered to touch the bottom of the tank. When the rod is removed, the gasoline level in the...

Homework Statement I have a piece of a plane in 3 dimensions (imagine holding an enevelope in the air), and two orthognal projections which form quadrilaterals, one on the xy plane (i.e. looking at the enevelope from above) and one on the xz plane (looking at it from the side). We know the...

Kisielowski Lewandowski Puchta have made a significant advance in calculating the transition amplitudes between quantum states of geometry. They have found a systematic algorithm that enumerates the (generalized) spinfoam-like histories by which one state evolves into another. And in this case...

I am reading Kane's book on Reflections and Reflection Groups and am having difficulties with some basic geometric notions - see attachment Kane paes 6-7. On page 6 in section 1-1 Reflections and Reflection Groups (see attachment) we read: " We can define reflections either with respect to...

I am completely lost with this question... for example for 2 electrons coupling that results in a singlet state with a spin momentum of 0 or a triplet state with spin momentum √2h-bar. How would you go to find the geometry of these states?

http://www.flickr.com/photos/66943862@N06/6868453382/in/photostream/lightbox/ http://www.flickr.com/photos/66943862@N06/6868453382/in/photostream/lightbox/ I was looking at a robotics kinematics analysis & there is one geometric equation assumed in the analysis which I can't seem to...

Which do you think are the main quantum geometry (QG) lines recently appearing to rival Loop? Do any look especially promising to you? Any favorites? Here are some to consider. The authors shown aren't a complete list! Just enough for an arxiv search: [Colored] tensor models (e.g. Gurau, Ryan...

Hello all I was hoping someone could help me with the following problem. I work on the railroads and my task is to improve the alignment of a curve. I have surveyed the existing geometry by going along the track and recording x, y, z co-ordinates at approx 1m intervals. I have...

Given the complete classification of finite simple groups, can one say that the number of all conceivable 2D/3D symmetrical geometric objects/arrangement is limited? Is spatial symmetry limited in our 3D world? IH

no gut? well, from GR or LQG as well, gravity is not force but geometry right? When einstein knew gravity is geometry and not force, why did he try to unify them? Will we have 3 fundamental forces. Is gut ruled out?

I need to find the total surface area of the hollowed out hemisphere (picture attached), with an inner diameter of 1.86 cm and what looks like an outer radius (also what I am assuming as height) of 1.25 cm. Surface area of a sphere is 4∏r2, so half the sphere is 2∏r2. Since the outer...

Homework Statement Points S and T lie on the line 2x+y=3. If the length ST is 13 units, and the coordinates of S are (2, -1), determine all possible coordinate pairs for T, correct to two decimal places. For simplicity, determine the coordinates for T, relative to S from the left.Homework...

A problem I should be able to solve :( (geometry) This is a random problem I discovered on the internet: If the area of a rectangle is diminished by 36%, what are the sides of the original rectangle if the sides of the diminished one are 36mm and 48mm? My answer: Let a and b be the...

I'm not sure why but I can't seem to figure this problem out at all... You have a slice of a banked circular track... Find the angle theta. See attachment, My first guess was to use the pythagorean theorem + the fact that the two lengths are both equal to angle/360* 2 * pi * r where r is...

Hi all, I've been wondering about this for some time. While I am only familiar with the basics of differential geometry, I have come across the Lie bracket commutator in a few places. Firstly, what is the intuitive explanation of the Lie bracket [X,Y] of two vectors, if there is one? In...

I do not understnad how x+y+z=0 can be a plane, I thought a plane has 2 dimensions, this is all :) thanks.

So I'm currently a sophomore math/CS major. I'm interesting in taking the algebraic geometry sequence next year; however I don't have the formal prereqs for the class, first year graduate algebra, which I would be taking simultaneously with the algebraic geometry class. I'm wondering if this...

Homework Statement Let A, B, C be three points on a plane and O be the origin point on this plane. Put a = OA and b = OB, and c = OC, (a,b and c are vectors). P is a point inside the triangle ABC. Suppose that the ratio of the areas of the triangles PAB, PBC and PCA is 2:3:5 (i) The...

Homework Statement I have 2 parametric vector equations (of a line) r(t) = (2,-4,4) + t(1,-3,4) s(t) = (1,-1,0) + t(2,-1,1) how do i find the coordinates for which they intersect each other? The answers is (1,-1,0) Homework Equations x=a+λv, for some λ in ℝ (parametric vector...

I am trying to figure out what size eaves we need for our house extension. I've tried a few calculations and now I'm posting here in the hope that a logical thinker will be able to tell me what I'm doing wrong. We live in Adelaide, Australia, and we want to put in glass double-doors on a...

Show that the ray is well defined / independent of ruler placement. Ruler placement postulate says Given two points P and Q of a line, the coordinate system can be chosen in such a way that the coordinate of P is zero and the coordinate of Q is positive. I know you can place ray AB where B can...

Hey guys, I'm looking for a good treatment (good = concise, and clear) of affine geometry. Connections, parallel transport, etc. I'm looking for this from a mathematical P.O.V. Most of the differential geometry books I have deal only with the exterior forms, and general manifolds without this...

Hello, I never took Geometry in high school, and I am currently in college studying both math and physics. Consequently, I decided to pick up a basic geometry textbook to try and learn it on my own; but I have found I have limited time due to my college studies. I am wondering, is it even...

Homework Statement Can a trapezoid ever be a kite? Can a kite be a trapezoid? 2. The attempt at a solution I believe that the answer to both is no. 1. If a trapezoid was a kite, wouldn't the pair of parallel sides, along with the congruent consecutive sides, imply that it was a...

Homework Statement The measure of the sides of an isosceles triangle are represented by x + 5, 3x +13, and 4x + 11. What are the measures of the sides? Two answers are possible. Homework Equations The Attempt at a Solution Well, I set up three different triangles, to account for the...

Homework Statement Th measure of the sides of an equilateral triangle are represented by x + 12, 3x - 8, and 2x + 2. What is the measure of each side of the triangle. Homework Equations The Attempt at a Solution Well, I know that each side of this triangle are equal, resulting...

First, let me apologize for my bad English, it's not my native language. Most areas of math for me aren't really an issue. I'm actually quite good at it. But there's one thing I absolutely despise and also something I'm very bad at: geometry. I was planning on studying theoretical physics...

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...

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...

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...