Geometry Definition and 999 Threads

Can anyone recommend a good on-line class for differential geometry? I'd like to start studying GR but want a good background in differential geometry before doing so. Many thanks.

Hello everyone. I was browsing through Amazon and found the aforementioned book by Theodore Frankel. As it is available at a relatively cheap price and covers a TON of material I was considering buying it for future use . Although the author says the prerequisites are only multivariable...

ok this is an observation question but many seem to miss the answer What theorms would rely on to get the correct answer

In Miles Reid's book on commutative algebra, he says that, given a ring of functions on a space X, the space X can be recovered from the maximal or prime ideals of that ring. How does this work?

Here is my attempt to draw a diagram for this problem: I'm confused about the "the perpendicular bisector of ##BC## cuts ##BA##, ##CA## produced at ##P, \ Q##" part of the problem. How does perpendicular bisector of ##BC## cut the side ##CA##?

In terms of diff geo it seems like an obvious fact, that a manifold can be equipped with quite a variety of different Riemann metrics. But when it comes to physics (relativity theory in particular) it seems there is a very specific metric singled out. Now i do not entirely understand the...

Hi, My name is Cam and I've just literally joined so wanted to say hi first 🙂 I'm self studying Maths and Physics and wanted to know a good textbook that deals with arithmetic/pre-algebra/basic geometry? I know Physics mainly used Applied Maths, but I'm wanting to educate myself as thoroughly...

I need help with these quiz

Hello, I am studying geometry with an app on my phone. There was a difficult problem, which had two different explanations for solving. I correctly understood one explanation. I reviewed later without memory of the problem at all. There was an obvious attempt from what was learned previously...

Dear Everybody, I am in the process of relearning high school geometry through Khan Academy. I am current an graduated undergraduate student in mathematics. I am doing this because geometry is one of my weakest subject in mathematics. Second reason is that I want to reason out a problem...

Dear Everybody, I am in the process of relearning high school geometry through Khan Academy. I am current an graduated undergraduate student in mathematics. I am doing this because geometry is one of my weakest subject in mathematics. Second reason is that I want to reason out a problem...

I couldn't make progress in this problem, I would appreciate some suggestion on how could I attack this problem. Thanks in advance!

Hello. Questions: do you know any applications of spherical geometry in physics? Are there any relations between spherical geometry and hyperbolic geometry? Why does Riemannian geometry use sphere theorems so much? Thank you.

120-48=72 72/4=18 The solution appears too simple to be the correct to me.

In the book: The Elements Euclid defined 5 postulates: 1) A straight line segment can be drawn joining any two points. 2) Any straight line segment can be extended indefinitely in a straight line 3) Given any straight line segment, a circle can be drawn having the segment as radius and one...

Hi guys, Hopefully, no geometry-enthusiasts are going to read these next few lines, but if that's the case, be lenient :) I have always hated high-school geometry, those basic boring theorems about triangles, polygons, circles, and so on, and I have always "skipped" such classes, studying...

I am new to Comsol. I want to draw my model which is a Tesla valve. The geometry is little complicated and I don't know how to draw a semi-circle tangent to a line. Is it possible? I draw it in Solidworks and imported it into Comsol but it gives error and I think it is better to draw inside...

Recently came across this concept. It looks like a combination of dg and statistics. It sounds interesting, but I do not feel competent enough to make an informed decision. For example see https://arxiv.org/abs/1808.08271

Instead of talking about the simple of case of reflection interference due to a single film, this book starts off with two films with an angled air wedge between them. They talk about the "thickness", ##t##, of the wedge, but this thickness varies along the length of the films (Figure 35.`12)...

Hello dear PhysicsForums attendees! I tried to solve for somebody the aforementioned problem. But I am not sure if my attempt is correct. So I am writing down what I suggested. Looking at eq 2.46 in Carrolls book; The metric is Lorentzian in General Relativity so that ##g^{\mu \nu} =...

i'm trying to find what sort of 2-d geometry this system is in, I've been given the line element 𝑑𝑠2=−sin𝜃cos𝜃sin𝜙cos𝜙[𝑑𝜃2+𝑑𝜙2]+(sin2𝜃sin2𝜙+cos2𝜃cos2𝜙)𝑑𝜃𝑑𝜙 where 0≤𝜙<2𝜋 and 0≤𝜃<𝜋/2 Im just not sure where to start. I've tried converting the coordinates to cartesian to see if it yields a...

Is there a general method to determine what geometry some line element is describing? I realize that you can tell whether a space is flat or not (by diagonalising the matrix, rescaling etc), but given some arbitrary line element, how does one determine the shape of the space? Thanks

Hi PF, What would you say is the level of importance of Geometry, as opposed to say, Algebra I or II, in a future Mathematician's mathematical foundation? Would not covering it thoroughly leave holes that would show up later in higher mathematics? Any thoughts?Thank you, Chandller

I started off by indicating ##p=-\frac{1}{m}## since it's perpendicular. The sum ##m+p## is now ##\frac{m^2-1}{m}##. Honestly, I can't go beyond that. The interceptions with the y-axis are of course unuseful, I tried algebraically intersecting the two lines but I came up with nothing... and I...

I'm currently studying Algebra and have collected Euclid's Elements, Lang's Geometry, Gelfand's Trigonometry, and Rhoad and et al's Geometry for Enjoyment and challenge. A quick perusal of the books seem to involve coordinates and algebra knowledge. From what I've heard Euclid is closer to Pure...

In ##\mathbb{R}^2##, there are two lines passing through the origin that are perpendicular to each other. The orientation of one of the lines with respect to ##x##-axis is ##\psi \in [0, \pi]##, where ##\psi## is uniformly distributed in ##[0, \pi]##. Also, there are two vectors in...

I want to find the probability that the two points ($x_1, y_1$) and ($x_2, y_2$) lie on the opposite sides of a line passing through the origin $o = (0, 0)$ and makes an angle $\psi$ that is uniformly distributed in $ [0, \pi]$ with the $x$ axis when the angle is measured in clockwise direction...

Is the intersection of a 4D line segment and a 3D polyhedron in 4D a point in 4D, if they at all intersect? Intuitively, it looks like so. But I am not sure about it and how to prove it.

Hello there.Could coordinates be functions?For example in a n-manifold with (x1,...xn) let be the coordinates could they be functions of a coordinate system not belonging to the n-manifold?Or we could first use a coordinate system then have our results, and then have a second coordinate system...

Indeed, if we take a vector field which dual to the covector field formed by the gradient from a quadratic interval of an 8-dimensional space with a Euclidean metric, then the Lie algebra of linear vector fields orthogonal (in neutral metric) to this vector field is isomorphic to the...

Hi, I take a big number of disks to composed a circle of a radius of 1 m, the blue curved line is in fact several very small disks: I take a big number of disks to simplify the calculations, and I take the size of the disks very small in comparison of the radius of the circle. The center A1 of...

In the first sentence of Chapter 2 in Ben Crowell's "General Relativity" he states: "The geometrical treatment of space, time, and gravity only requires as its basis the equivalence of inertial and gravitational mass". This is stated as if it's an obvious fact, but I don't understand why. Why...

Hi PF! I'm given a circle with parametric representation ##x=r\sin\theta,y=h+r\cos\theta##. There is also a line, which has the parametric equation ##x=x,y=\cot (\beta) x##. Note the line makes angle ##\beta## with the y-axis. When the circle intersects the line, it makes an angle, call this...

A recipient (cube) of 1m³ is filled of small spheres, there are for example 1000³ spheres inside the recipient. There are also 1000³ elastics that attract the spheres to the bottom. The elastic are always vertical. One elastic for each sphere. One end of the elastic is fixed on a sphere and the...

Could someone please write out or post a link to the Riemann Tensor written out solely in terms of the metric and its first and second derivatives--i.e. with the Christoffel symbol gammas and their first derivatives not explicitly appearing in the formula. Thanks.

I can guess this question, by seeing that the surface area of the curved part must be in the form pi r l. Don't know how to get to this formula though. Answer is A

The $\triangle ABC$ and $\triangle AEF$ are in the same plane. Between them, the following conditions hold: 1. The midpoint of $AB$ is $E$. 2. The points $A,\,G$ and $F$ are on the same line. 3. There is a point $C$ at which $BG$ and $EF$ intersect. 4. $CE=1$ and $AC=AE=FG$. Prove that if...

I was just thinking, if is said to me demonstrate any geometry statement, can i open the vector in its vector's coordinates? I will say more about: For example, if is said to me: Proof the square's diagonals are orthogonal, how plausible is a proof like?: d1 = Diagonal one = (a,b,c) d2 =...

Could you provide recommendations for a good modern introductory textbook on differential geometry, geared towards physicists. I know physicists and mathematicians do mathematics differently and I would like to see how it is done by a physicists standard. I have heard Chris Ishams “Modern Diff...

Can anyone help me get started with this problem? What should I use for Gni? I've tried to produce Tni by working out Rni (using methods developed in an earlier chapter) but the results don't lead me anywhere. I'm really stuck for a way forward on this problem so if anyone can help, it...

In convex quadrilateral $ADBE$, there is a point $C$ within $\triangle ABE$ such that $\angle EAD+\angle CAB=\angle EBD+\angle CBA=180^{\circ}$. Prove that $\angle ADE=\angle BDC$.

Summary:: Suggest a geometry Hello! I have difficulties with this question. It is translated from Swedish so if something's weird tell me. The speakers in headphones often work with the help of magnetism, when a varying voltage is applied across a coil attached to the speaker membrane. The...

In "The Geometry of Minkowski Space in Terms of Hyperbolic Angles" by Chung, L'yi, & Chung in the Journal of the Korean Physical Society, Vol. 55, No. 6, December 2009, pp. 2323-2327 , the authors define an angle ϑ between the respective inertial planes of two observers in Minkowski space with...

Hey! 😊 Between the following two topics: Elementary Geometry Fibonacci and its sequences which would you suggest for a presentation? Could you give me also some ideas what could we the structure of each topic? :unsure:

I am unsure how to go about this. I tried following the suggestion blindly and end up with with some cumbersome terms that are not the answer. From what I understand the derivative at each point would equal to T? Answer: I just can seem to get to this. I think I'm there but can't get it in...

My context here is Finsler geometry with Cartan connection. I use ##x^\mu## for the usual spacetime position coordinates, and ##u^\mu \equiv \dot x^\mu## for velocity coordinates (the overdot denotes differentiation by an arbitrary parameter, not necessarily proper time). To explain the problem...

Consider a point A outside of a line α. Α and α define a plane.Let us suppose that more than one lines parallels to α are passing through A. Then these lines are also parallels to each other; wrong because they all have common point A.

Summary:: Suggest a textbook Good Morning I have repeatedly tried to read Frankel's "Geometry of Physics" and I get swamped and overwhelmed. (I hasten to add that as a MECHANICAL engineer, my math background has been deficient.) I retire in about 10 years and I am looking to learn the...

CONTEXT: We are finding the the buoyancy force on a boat which is upright in a still water (Fluid at rest) and the only gravity is acting as the external force. So, first we go for imaging a proper geometry of our boat. See this figure : For this figure the book writes: Fig 8 represents...