Geometry Definition and 999 Threads

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...

What books should I read as prerequisites for Spivak's Differential Geometry Series? Trying to pick up Diff Geom for graduate physics but right now it is pretty daunting. I've got single variable calculus and linear algebra under my belt. Just looking for bare minimum requirements here to...

Homework Statement Find the radius of a circle inscribed in a quadrant of a circle with radius 5 Homework Equations The Attempt at a Solution I worked this but I'm not sure if its correct. I looked at the first quadrant so a quarter of a circle with radius 5. I drew the radius...

Hello all I work in transport engineering. i have come across what seems to be a simple maths problem but i do not understand it. The problem relates to geometry i.e. calculating the radius of a curve using a chord and a versine. The problem is this:- " a general rule of thumb is as...

please suggest the books 'must do' in eucleodian geometry for elementary and pre college level. Is doing 'Advanced Eucleodian Geometry' by Roger A.johnson enough?

please suggest what books should I do to strong my concepts in eucleodian geometry (ELEMENTARY & PRE COLLEGE LEVEL)? ( in case for more than 1 book please refer the order in which they should be done) Also tell me , whether doing only ADVANCED EUCLEODIAN GEOMETRY by Roger A. JOHNSON IS ENOUGH...

Geometry - Topology; "What is the difference?" It is certainly important for a good understanding of a lot of modern problems. So I think it could be important to explain clearly the difference(s) between these two notions. Can you help me?

\stackrel{\rightarrow}{PQ} bisects \angle{ABC}. If m\angle{ABD} can be represented by 3a + 10 and m\angle{DBC} can be represented by 5a - 6, what is m\angle{ABC}? What I did was add the two representations together and multiplied by two, which would give me 16a + 8. Does that sound correct?

Hey guys, Well, it's the end of the academic year. I just had my last biweekly geometry class yesterday. I hope I did well on the chapter test I took yesterday. Anyways, as the title suggests I'll be going into Algebra II next year. Based on my experience in geometry class, I can...

[b]1. The area of a parallelogram is 60 square units. A segment is drawn from one vertex to the midpoint of an opposite side. The diagonal is drawn between the other two other vertices. Find the area of the four regions formed. Homework Equations [b]3. I found that two of the...

Hi! I stumbled upon something I need to implement my problem in a computer. Because I think its actually fun to puzzle on, I thought it might be nice to post it here. The problem is this: If you have a 4D hypercube, (a_1,b_1)\times(a_2,b_2)\times(a_3,b_3)\times(a_4,b_4), what is an easy...

Dear all, I am a medical doctor stuck with a mathematics problem. I have taken a project to map the 3D movement of a particular bone and describe its motion. My maths knowledge is a bit lacking. However using logic I felt that I would need to track 3 constant markers on the particular bone...

Hello! I'm looking for a good analytic geometry textbook. I'm studying circumferences and sphere and I'm using the book Analytic Geometry: A vector approach from Wexler but I find this book quite bad. I want some suggestions! Thank you.

I was trying to think of natural physical reasons to want to study noncommutative geometry, and it seems to me that it should be relevant even in a classical scenario. Let me know what you think of this as I am no expert. I'm not being terribly precise, either, so let me know if I should...

I think this a map of the Klein four-group geometry. Comments? http://dl.dropbox.com/u/13155084/prime-%20square-klein%20four%20group.png

I have to choose which math course I'm going to take next term. I want to take both but I'm already taking two physics courses and my college's distribution requirements require that I take an English next term... bleh... I could audit one of the physics and then take both math courses, but that...

According to the Inflation Theory our Observable Universe is but a small part of the total universe created in the Big Bang. Our observable universe appears to be flat (just like Earth at sea level may appear flat), while the total universe may be shaped like a balloon. If we assume our...