Geometry Definition and 999 Threads

Given ##ds^2 = y^{-2}(dx^2 + dy^2)##, I am trying to prove that a demicircle centred on the x-axis, written parametrically as ##x=r\cos\theta + x_0 ## and ##y= r \sin \theta ## are geodesics. Where ##r## is constant and ##\theta \in (0,\pi)## I have already found the general form of the...

Is there a way to create/force air flow without using electronic components?

Greetings everybody. This is my first post and I am looking for help with a little math/geometry/engineering problem. This has been a real brain buster for my colleague and I the past couple days so I am hoping somebody can help. I am not sure if this is the best section for it, but it...

<Moderator's note: Moved from another forum.> The book I'm reading says that ##\star \sigma = 1## and ##\star 1 = \sigma##, but I'm not sure about the last one. The space is ##V = \mathbb{M}^4## and we choose the canonical base ##e_0,e_1,e_2,e_3##. This means that ##g_{ij} =...

What is the shape and geometry of BrF3?

please interpret this observation. There is a specific radius through a given equation that always gives the correct mass to any star or planet, as well a density. What is the logical explanation for this? Mass = (4π/3) x schwarzschild radius of the star x 4π/3 x (726696460.5 cm.) cube. For...

Homework Statement I need to obtain the equation of 2 paraboloids separated by a distance L. Homework Equations I think that the equations should be: z_1=x^2+y^2 z_2=x^2+y^2-L The Attempt at a Solution The problem is that when I plot the region between two inequations, x^2+y^2>=z and...

I'm learning Differential Geometry (DG) on my own (I need it for robotics). I realized that there are many approaches to DG and one is Cartan's, which is presented in Vargas's book. I think that book is highly opinionated, but I don't know if that's a good or bad thing. Does anyone of you know...

<Moderator's note: Moved from another forum and thus no template.> I have a project from my Mechanics class which consist on building the system on the picture. It has a spring, cable and a protractor. I have to do an approximation of the mass and weight of the object that is put in the...

Hello I was reading some article on angular momentum. And at some point, the author started talking about the symmetric objects and axis of symmetry. Now I am wondering if the author means the geometrical symmetry or the symmetry in physics. For an example, if we take a uniform rod of length...

I've been trying to wrap my head around the geometry of the expansion of space, from Science Channel shows I vaguely understand the "every point in space is moving away from every other point in space" and iirc this was uniformly so. Is that correct? If not ignore the rest of this post I suppose...

I have computed a line from point A to point B by just subtracting the coordinates as below: line = np.array (x2-x1, y2-y1) I am not sure if I need to form the formula for this line first by computing the slope and intercept but I continued my code as below, slope being m and b being the...

This is a refinement of a previous thread (here). I hope I am following correct protocol. Homework Statement I am studying Spacetime and Geometry : An Introduction to General Relativity by Sean M Carroll and have a question about commutators of vector fields. A vector field on a manifold can...

Homework Statement I am studying Spacetime and Geometry : An Introduction to General Relativity by Sean M Carroll and have a question about commutators of vector fields. A vector field on a manifold can be thought of as differential operator which transforms smooth functions to smooth functions...

What do you think about the article Exceptional Quantum Geometry and Particle Physics Posted by John Baez https://golem.ph.utexas.edu/category/2018/08/exceptional_quantum_geometry_a.html and the following discussion? It also includes links to the original papers. Exceptional quantum geometry...

Hi I have always had an issue with understanding the definitions used in mathematics. I need examples before I can start using and reasoning with them. However, with tensor products, I have been completely stuck. Stillwell's Elements of Algebra was that made abstract algebra "click" for me...

Hello. I am wondering how I can find the area of a trapezoid from its two legs and bases. My problem: ABCD is a trapezium with AB parallel to CD such that AB = 5, BC = 3, CD = 10 and AD = 4. What is the area of ABCD? If we trace a straight line from A down parallel to the height of the...

Hi! I'm asked to find all the non-zero Christoffel symbols given the following line element: ds^2=2x^2dx^2+y^4dy^2+2xy^2dxdy The result I have obtained is that the only non-zero component of the Christoffel symbols is: \Gamma^x_{xx}=\frac{1}{x} Is this correct? MY PROCEDURE HAS BEEN: the...

Hello. I am studying Analysis on Manifolds by Munkres. My aim is to be able to study by myself Spivak's Differential Geometry books. The problems is that the proof in Analysis on Manifolds seem many times difficult to understand and I am having SERIOUS trouble picturing myself coming up with...

Attached is a sketch of geometry in question, sketch.pdf. I am trying to determine the circle's radius ##R## given half corner angle ##\beta##, contact angle ##\alpha##, and displaced vertex ##h##. What I find from law of sines is ##R = h \sin\beta / \cos\alpha##. However, when I plot this I do...

Dear Physics Forums members, I have a research problem that involves electrostatics. My education is as a chemist, and thus I struggle to accurately represent my problem, so I thought that you guys could help me (and would be interested in the exercise). Here is an image to summarize my...

I am doing a problem from Schutz, Introduction to general relativity.The question asks you to find a coordinate transformation to a local inertial frame from a weak field Newtonian metric tensor ##(ds^2=-(1+2\phi)dt^2+(1-2\phi)(dx^2+dy^2+dz^2))##. I looked at the solution from a manual and it...

Homework Statement Find x. L1 and L2 are parallel choices: a)2°40' b)2°30' c)2°45' d)2°15' e)2°20' Homework Equations Σleft∠ = Σright∠ The Attempt at a Solution 2x+1+4x-1+4x-1 = 2x-1+2x+4+3x+2 10x-1=7x+5 3x=6 x=2° Not sure how the answers include minutes ' Maybe I'm overlooking something?

Homework Statement Find x. L1 and L2 are parallel Choices: a)100 b)120 c)140 d)150 e)135 Homework Equations From the image, the angles of the polygon in blue should satisfy: 6θ + 90 + 4θ + 2θ + 90 + x = 540 12θ + x = 360 x = 360 - 12θ The Attempt at a Solution I couldn't figure out how to...

Hello! I just start looking at SDG and I'm already having difficulties with a few concepts as expressed by A Kock as: "We denote the line, with its commutative ring structure (relative to some fixed choice of 0 and 1) by the letter R" "The geometric line can, as soon as one chooses two...

I am reading Spacetime and Geometry by Sean Carroll. In section 1.10 on classical field theory, he uses this formula (1.132) The curly L is a Lagrange density. S is an action, Φ is a vector potential. Could the integral also be written as follows?

The equation is $$\|\left(\begin{array} &a\\b\\c\\d\end{array}\right)\|^2=1$$ I was wondering if the number of parameters is 6 and not 3, since we can consider rotations in the differents planes : we choose 2 directions among 4 hence $$C^4_2=6$$ possibilities ?

Hey guys, I would appreciate some help with the math behind creating a working coordinate system for a robotic arm. I am currently trying to determine what servo angles are necessary to align a robotic arm's claw to the given coordinates. Geometrically simplified, the robotic arm is a...

A geometry problem I'm working on has boiled down to finding a function ##f(t)## such that $$f'' + \frac{2}{t}f' + \frac{f'^2}{\left( 1 - \frac{f}{t} \right) t } + \frac{f'f}{\left(1- \frac{f}{t} \right) t^2} = 0$$ It has two fairly simple solutions, namely ##f(t) = a## and ##f(t) =...

<< Mentor Note -- 2 threads merged >> 1. Homework Statement I need help with question 43 it is attached as an attachment Homework Equations #a^2+b^2=c^2# Sin(a)/A=sin(b)/B The Attempt at a Solution Well if I draw a line from the left corner of the bown down to the water it forms a right...

Let △ABC be a triangle. Let AD and CE be its internal bisectors, with D lying on BC and E lying on AB. Given that ∠CED=18° and ∠ADE=24°, how can I find angles ∠A and ∠C without aid of softwares? Angle ∠B is easy to calculate, as ∠CED+∠ADE=∠CAD+∠ACE=∠A+∠C2=180°−∠B2 42°=180°−∠B2 ∠B=96° The other...

Hi everyone. I want to build beautiful objects in a computer - object means something which has shape and behavior. I feel comfortable in writing down behavior of an object but I am struggling with writing shape of an object. A Table: Wave-forms: Is it possible to build any shape and any...

Hi, this is my first post with a problem that I have during my Msc Project. I will briefly discuss my project and the reason why I would like to solve this problem, if you do not want to read this part you can skip it. I am doing experimental research on the scaled laboratory setup where I...

Why is it that variable geometry nozzles, like those found on jet engine(iris nozzles), are not used as rocket nozzle to provide better altitude compensation?

MATH 4300 - Modern Geometry (3) Prerequisite: MATH 3450 with minimum C grade. Topics selected from advanced Euclidean geometry, non-Euclidean geometry, projective geometry. May be repeated once for credit with approval of instructor as subject matter changes. The above paragraph is the course...

Would need help with the design and material required to punch slots in an AISI 316 stainless steel plate, .039" thick. Slots geometry is .039" width x .500" long. The parts are"scallops" (an oil refinery equipment within distillation towers). Have tried several designs but non of them work...

I know about the construction of the algebra in which operators as in Hilbert spaces are developed from Connes' non-commutative geometry, but I don't find any references [besides further publications by Connes himself] which say that this has turned out to be useful in physics for more than a...

Hello, does anyone know an (more or less) easy differential geometry book for courses in generall relativity and quantum field theory? I'm looking for a book without proofs that focus on how to do calculations and also gives some geometrical intuition. I already looked at The Geometry of...

In plane geometry it is impossible to construct a line equal to the (cube root of 2) times the length of a side of a cube, making it impossible to double a cube with a compass and straight edge. Maybe plane geometry needs one more dimension. What happens if we extend the geometry to 3D(solid...

I would like to ask what I hope are two simple questions about what I recognize to be a complicated subject. I did make an effort to search the Internet for the answers, but the two most promising looking sources I found did not help...

I'm requiring help on a circle geometry question I've done. The line L, has equation of y=0, and intersects the circle with (3,0) and radius of 29. Find the points of intersection. My working out: 292 = 841 It's centre is 3,0, Inserting that in circle equation gives (x-3)2+y2 = 841 Solving...

Hi I've done a masters taught module in GR and from what I've learned these are two of some of the most important significance of needing a Riemannian Geometry: 1) If we consider the Lagrangian of a freely-falling particle given by ##L= \int ds \sqrt{g_{uv}\dot{dx^u}\dot{dx^v}} ## and find the...

Hello fellows My background is architecture (bachelor in2016) but for unknown reasons I’ve been fascinated by geometry since last year. it was roughly at the stage where I was trying to grasp ‘the truth ‘ of architecture and somehow got into geometry... happy coincidence. Since I hadn’t...

Hello, I've been trying to improve my algebra since I've never been particularly good with math. I'm going through Serge Lang's Basic Mathematics textbook and while I have been learning a lot his proof-based exercises are a pain to get through and the back of the book only provides answers for...

Hello! Currently I own Differential Equations by H.B Phillips, a really old book, but difficult and does it´s purpose. I have only 1 problem, certain exercises require certain geometrical functional study I suppose, for example: "find the equation of the curves so that the part of every tangent...

My question is not a math question. I know about the calculus sequence (CAL 1, 2 and 3). I plan to go through all 3 in time. There is no rush for me. However, I know there is a course by the title of Calculus and Analytic Geometry. I want to know when this course is given. Is it given after...

I used to think it was called Zeno's tower, but then realized I probably called it that because it reminded me of his paradox. I have been unable to find this shape on the internet, although I saw a small steel tower outside Stonybrook using this geometry. I have attached an image of the basic...

I've been trying to wrap my head around equidistant points, like platonic solid vertices inside a sphere where the points touch the sphere surface. This led me to the strange and unusual world of mathematical degeneracy, henagons, dihedrons, and so on, along with the lingering question of...

For anyone who is familiar with the book "Geometry, Topology and Physics" by Nakahara, what do you think are the mathematical and physics prerequisites for this book ?

Mod note: Moved from a technical forum section, so missing the homework template. @fab13 -- please post homework problems in the appropriate section under Homework & Coursework. I have the following exercise to solve : I have to find all the points on the surface ##x^2+y^2+z^2=36## (so a sphere...