Geometry Definition and 999 Threads

I am currently looking at grad schools, and I am wondering if anyone knew who are the leading researchers in differential geometry. I know that question is a little vague considering how diverse differential geometry is, but I was hoping that something could direct me in the right direction...

Homework Statement Picture: http://matematikk.net/res/eksamen/1T/kort/1T_V11.pdf Task 5, the one the with a triangle inside a square. I'ts not in English so i'll transalate. I managed to do task a The picture above shows a square ABCD. The sides in the square have length 1. E is the center of...

Homework Statement One of the sides of a triangle is 7.0cm, another side is 11.0cm. A Decide the biggest area this triangle can have. B Make calculations and show how the triangle could look like if the area is 30 square cm. Homework Equations Area of a triangle: 0.5*g*h or 0.5*a*b*sinV The...

Hello all, I was accepted into a program that allows me to take a free college course and I was hoping to take a math/science course. I am most interested in Physics, but I don't know Calc so that isn't really an option, and I was thinking of taking Calculus and Analytic Geometry. However, I am...

Hello I do not fully grasp the concept of Riemann geometry.Please can you use mathematical descriptions but explain them because I am only a 10 year old but of course I know significantly the theories of dimensions. Thank you.

Hi, I was just wondering if someone could help clarify how pi - theta = phi? That is the link to the youtube video I was watching, the guys pretty good check him out if you want to learn how to derive the differential scattering cross section.

I'm quite aware of how to compute how FAR you are from the horizon, but my question is, how WIDE is the observable horizon at sea level (like, from left to right, how many kilometers is this): http://www.jeicentral.com/wp-content/uploads/2014/10/far_sunset_in_te_ocean_horizon-wide.jpg Thanks!

Hello everyone This is sort of a geometry problem. I'm sure it has an easy answer but it just won't come to me. Here's my problem A close packed colloidal aggregate of smaller spherical colloidal particles can be thought of as small spheres within a sphere. I have the relationship...

Given a cyclic quadrilateral $PQRS$ where $PQ=p,\,QR=q,\,RS=r$, $\angle PQR=120^{\circ}$ and $\angle PQS=30^{\circ}$. Prove that $|\sqrt{r+p}-\sqrt{r+q}|=\sqrt{r-p-q}$

The title above give my name. I am a pure maths PhD with an interest in physics and geometry. I am currently studying physics for fun and I am very interested in current progress. I am especially interested in quantisation of space time, holographic theories and dualities. Regards John

Homework Statement What is the largest possible radius of a sphere which is inscribed in a regular tetrahedron a=10 ( this is the side of the tetrahedron) r=? r=5*√6/6 Homework EquationsThe Attempt at a Solution So first I calculated the Height of pyramid a2=(2/3*va)2+h2 h=√(a2-(2/3*a*√3/2)2)...

Hello! We are working with some ferrite rods to build solenoid magnetorquers for a cubesat design. The geometry on these rods is unique. Are there benefits to this type of a geometry? They are 19.6 cm length x .67cm diameter.

Homework Statement [/B] A parallel quadratic slab of glass (n = 1.55 and thickness d = 2 cm, L = 21 cm) rests on a large slab of glass (n = 1.55). To prevent the optical contact weld forming between the two polished surfaces, a small teflon ball (D = 1 cm) is inserted between the slabs on one...

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown > Find the equation of a line passing through point A (1, 2) and whose perpendicular distance from origin is maximum.

Homework Statement In the attached drawing, find R in terms of L and c. Also, at the bottom of the picture I wrote something wrong. I said c, which equals 0.5, is the arc-length of each semi-circle, but I really meant to say each quarter circle. My bad. I'm not given a number for L so that can...

Hello everybody, I am trying to implement a geometry of a human prostate gland derived from MRI imaging in COMSOL and combine it with some cylindrical structures inside the prostate. My goal is to give different parameters to the cylindrical parts of the prostate. However i can combine an...

When I studied General Relativity using Misner, Thorne and Wheeler's "Gravitation", it was eye-opening to me to learn the geometric meanings of vectors, tensors, etc. The way such objects were taught in introductory physics classes were heavily dependent on coordinates: "A vector is a collection...

I've recently finished tackling differential equations. I want to start learning general relativity, but from what I've read, I need to have a firm footing in differential geometry first. So where do I start learning DG? I really don't want to do a half-hearted job in an attempt to quickly jump...

Suppose that $PQRS$ is a square with side $p$. Let $A$ and $B$ be points on side $QR$ and $RS$ respectively, such that $\angle APB=45^{\circ}$. Let $T$ and $U$ be the intersections of $AB$ with $PQ$ and $PS$ respectively. Prove that $PT+PU\ge 2\sqrt{2}p$.

I am a first year computer engineering student. Having programmed several years, I realize my math skills are not adequate for my liking (planning on improving them before tackling some more advanced data structures and algorithm books). My plan is to read how to prove it, spivak calculus, a...

I am taking thermodynamics this semester as well as a course in differential geometry of surfaces, and I am seeing a lot of overlap. For example, I can create a "state space" isomorphic to R3 of TxPxV I can then define a surface on this space of PV=NkT I can define quasi static state equations...

Homework Statement [/B] Hello! I have this question which I don't quite know how to solve... ABC is an equilateral triangle - the length of its sides equal to (a). DE is parallel to BC 1. What length should DE be to achieve the largest possible area of triangle BDE? 2. What length should DE...

I have the hardback 5 volume set of Spivak's A Comprehensive Introduction to Differential Geometry that is in pretty good shape. Is there any value to that set? I tried looking it up, but I don't really see many people selling whole sets, so I can't tell... Thanks.

In the process of descending from a higher dimension to a lower one, there must be more than one factor that could not be solved (or descend.) My little own experiment.. http://mr-none.meximas.com/public_html/pic/1.JPG Steps: 1, wrap a plastic bag around a basketball. 2, draw a "triangle" with...

Conventional GR is based on the Levi-Civita connection. From the fundamental theorem of Riemann geometry - that the metric tensor is covariantly constant, subject to the metric being symmetric, non-degenerate, and differential, and the connection associated is unique and torsion-free - the...

I'm really stressed out at where I should be in my college career. In high school, I had taken trigonometry and analytical geometry. But when I went to college and took calculus, I was completely dumbfounded on what was being taught. I felt like I should have known the material. Google tells me...

I need to perform geometry matching of curves (see http://www.tiikoni.com/tis/view/?id=c54d9b8 ). As it can be seen, the big problem is that curves might be rotated, though they have similar shape. Do I need to make curve fitting and look at the parameters of analytical models? But, I guess...

I have a doubt in 3d geometry. I calculus and I know how to do partial derivatives.(but I don't know what it means). If you have a parametric equation ##x=t, y=t^2,z=t^3## (the equation is randomn) What does ##\vec{r}=t\hat{i}+t^2\hat{j}+t^3\hat{k}## represent? now if it represents the position...

Homework Statement Problem 99 from "Kiselev's Geometry Book I - Planimetry": Two isosceles triangles with a common vertex and congruent lateral sides cannot fit one inside the other. Homework EquationsThe Attempt at a Solution The statement is obviously true. If we visualize each isosceles...

I'm preparing for my Foundations of Geometry Course by self-learning topics before the semester starts. I've been reading Geometry: A Comprehensive Course by Dan Pedoe, and it's covered a lot of good topics. Any online resources you recommend?

Hey, I've spent ages trying to solve what seems to be a pretty simple geometrical problem and I was wondering if anyone could help me solve it/give me some tips. I am trying to model how the suspension of a car behaves as a result of a displacement of the wheels. What the attachment shows is a...

Sorry for the confusing tittle but I could not explain it better. Here is what I am trying to ask: When you have 2 axis(x and y) such as the image below, the sum of the two angles, a and b will always be equal to 90 degrees. a + b = 90degrees However when you add a 3rd axis(x, y and z, making...

I'm a beginning graduate student in string theory and I'm in the process of teaching myself algebraic geometry. I'm using lecture notes that go without mention of physics. I'm curious if there is a introductory book, or paper, or set of lecture notes that describes the application of alg...

Homework Statement Problem 55 from Kiselevś Geometry - Book I. Planimetry: "Prove that each diagonal of a quadrilateral either lies entirely in its interior, or entirely in its exterior. Give an example of a pentagon for which this is false." Homework EquationsThe Attempt at a Solution The...

I am looking for a good intermediate introduction to Euclidean Geometry. I have knowledge of ordinary differential equations (first course), elementary linear algebra, and multivariable calculus. My geometry foundation is rather weak and I would like to improve it. I purchased Kisselev...

Homework Statement Why is it necessarily true that for a hyperbola, the focus length, ##f ## has got to be greater than the semi-major axis , ## a## - ## f >a ## ? Homework Equations - The Attempt at a Solution I needed to derive the cartesian equation of a hyperbola with centre at ##...

If we choose rational numbers to represent points on a line then there will be gaps on the line and consequently the plane will be full of holes. Then we cannot say that two non-parallel line must intersect on a point (because they may meet at the gaps). So obviously we need point arranged more...

I was thinking about the situation given my text about a plano convex lens which was produced with a manufacturing defect. It's plane surface is tilted outwards by a small angle 'z'. In the text its written that when a parallel light beam enters the lens parallel to x-axis , it will still be...

So, I was trying to do a derivation of my own for the FLRW metric, since I couldn't understand the one Wald had. The spatial slice M is a connected Riemannian manifold which is everywhere isotropic. That is, in every point p\in M and unit vectors in v_1,v_2\in T_p\left(M\right) there is an...

I was going through a p and c problem where I had to find the number of non congruent RECTANGLES. Answer includes number of squares as well. SHOULD SQUARE BE TAKEN AS A RECTANGLE?

Hello, This spring, I will have the opportunity to do a one-on-one independent study in math or physics. I've narrowed down my choices to differential geometry and general relativity. I'm thinking about the future here- will studying general relativity this spring better prepare me for...

I was recently exploring time dilation from Gravity and from velocity and I came up with an interesting derivation that I have not seen before. I was wondering if there is a paper published showing these relationships like this before and where I could find it? First you start with the...

Hey, I am a freshman in High School and I have a very superior IQ but I am in normal classes. This is due to ADHD and I used to be lazy in school. Anyways, algebra 1 is VERY boring. I want to teach myself geometry, algebra 2, Pre Cal, and Calculus because I love math. Also I feel like it will...

Homework Statement I'm not in grad school but I've been trying to teach myself some GR and I asked a professor what problems he thought would be good to study. He mentioned this one. I'd ask him for help, but he's out of town this week. I've also attached a picture to this problem. (It seems...

I was tutoring a student and I came across the following question. I feel like I'm missing something obvious, but it seems like there are too many variables for an answer to be determined. The attached picture contains all of the question details.

Homework Statement I'm having trouble figuring out how to use Christoffel symbols. Apart from the first three terms here, I can't understand what's going on between line 3 and 4. What formulas/definitions are being used? How do you find the product of two chirstoffel symbols? Where are all the...

I've read an article about computational chemistry in which the authors were performing a geometry optimization. For this purpose, they firstly optimized the geometry at HF/6-311++G(d,p) level with full relaxation on the potentiel energy surface (what does that mean exactly ? Can we extract this...

Hi, Kindly assist with the attached circle geometry questions. Thales theorem concept and Euclid circle theorems are the concepts that come readily to mind. Still "battling" with the questions though. I have attached the attempts made by me so far. Thanks.

Homework Statement Attached here is a diagram. My questions are, how to compute for the value of the chord? How to compute for the value of the tangential line? Please help.. Thank you in advance.

Hi all, I was wondering what the relationship between the Riemannian Geometry exponential map and the regular manifold exponential map and for the reason behind the name.