Geometry Definition and 999 Threads

So I'm reading the Schaum's outlines while trying to prepare for a big test I have in September. And I'm trying to understand something here that maybe someone can offer some clarification and guidance. So, using Coulomb's Law, we can find the electric field as follows: \begin{equation} dE...

micromass submitted a new PF Insights post Groups and Geometry Continue reading the Original PF Insights Post.

It's been a long time since I posted a riddle, and probably nobody missed them. Anyway, here is a collection of 3 well known geometry problems with different difficulty levels. The only reason there is an "I" prefix is because of the third part of the problem, which is a bit harder. The first...

[Moderator's note: this thread is spun off from another thread since it was a subthread dealing with a separate topic.] There is definitely a maximally extended spacetime but there is no maximally extended spacelike surface of constant Schwarzschild coordinate time t. The spatial curvature...

What unsolved geometry problems are there?

Hello everyone, I've 2 books on manifolds theory in e-form: 1) Spivack, calculus on manifold 2) Munkres, analysis on manifold What would be good to begin with? :oldconfused: Thank you in advance

Let $U$ be a compact set in $\mathbb{R}^k$ and let $f:U\to\mathbb{R}^n$ be a $C^1$ bijection. Consider the manifold $M=f(U)$. Its volume distortion is defined as $G=det(DftDf).$ If $n=1$, one can deduce that $G=1+|\nabla f|^2$. What happens for $n>1$? Can one bound from below this $G$? If...

HI , i am having a problem in reinmann geometry as i am not able to cope up with the language used in "introduction to reinmann geometry-with applications in mechanics ang relativity".Can anyone suggest an easy to go with book, for a beginner for self study

I just want something easy to boost my gpa and these are my two options. The geometry course is euclidean not topological. Thanks

hi, Initially, I know how to take surface integral of möbius band via given parameterization, but I really wonder how these parameters are created. How can we derive these parameters ?? What is the logic of deriving such a good parameters?? Could you give some proofs??

It is said that curves of the second order which we usually refer to as ellipse, parabola and hyperbola, i. e. conics, are all represented on projective plane by closed curves (oval curve), which means there is no distinction between them. Why is it? Projective space can, in principle, be...

I made a picture because I'd struggle to get out a question without it. In the picture all things are constant except the strength of the magnetic field. It is at two different values. We see 2 cycloid paths of electrons that starts at rest. The circumference of the large path is exactly twice...

Homework Statement Say we have two manifolds N(dim d) and M(dim d-1). Let Φ: M →N be a diffeomorphism where Σ = Φ[M] is hypersurface in N. Let n be unit normal field (say timelike) on Σ and ⊥ projector (in N) defined by: ⊥^a_b = \delta^a_b + n^a n_b Where acting on (s, 0) tensor projection...

So I was reading now about the new geometries and I wanted to know if I can study the Reimann Geometry knowing that I finished high school or if I could just know about it but not about the formulas. I am so interested in the subject because it is used in astronomy.

I have found this paper on the internet and think it might be interesting for some on this forum because there are frequently questions similar to the ones the paper tries to answer. http://arxiv.org/abs/1605.00890 http://arxiv.org/pdf/1605.00890v1.pdf

Homework Statement Hello, my friend asked my If I could help him with this problem. However I just can't seem to find a way to solve this. Ellipse Focus(2,2) vertex(2,-6) Point(26/5,2) a+e=8 find the equation of the ellipse Homework Equations (x-m)^2/a^2+(y-n)^2/b^2=1 Center(m,n) a=moyor axis...

Homework Statement Given that the sum of interior angle measures of a triangle in hyperbolic geometry must be less than 180 degree's, what can we say about the sum of the interior angle measures of a hyperbolic n-gon? Homework EquationsThe Attempt at a Solution So in normal geometry an n-gon...

Hey PF! I'm going through a textbook right now and it just said "obviously, you can't have an equilateral pentagon with 4 right angles in spherical geometry (Lambert quadrilaterals). However, I am not able to make the connection. can somebody help me understand why this is?

I am planning on doing a huge self-studying over geometry and hopefully a little bit a trigonometry session over the summer at my public library. Over at a friends house, I see that he has a book about "algebra 2 for dummies" in his pile of science books and it got me wondering, are the "For...

Homework Statement On the picture, ##ABCD## is a parallelogram, ##(EF) // (AB) ##, and ##(GH) // (BC)##. The problem is : show that lines ##(EB)##, ##(HD)##, and ##(IC)## either all meet in ##M##, or are parallel. Homework EquationsThe Attempt at a Solution I've solved the problem...

Homework Statement If ##α, β, γ, δ## are four complex numbers such that ##\dfrac{γ}{δ}## is real and ##αδ - βγ ≠ 0##, then ##z = \dfrac{α + βt}{γ + δt} , t \in ℝ## represents a (A) circle (B) parabola (C) ellipse (D) straight line Homework EquationsThe Attempt at a Solution Eqn of circle is...

Can you suggest a book that discusses properties of triangles and circles? (Like properties and theorems on circumcircle, excircle, nine point circle, etc). Most of the geometry books are either to basic or too advanced. I have read a book on complex numbers by Liang Shin Hahn. But the...

Mod note: Member warned that homework questions must be posted in the Homework & Coursework sections http://imgur.com/zGB2dnY Was given this problem a few weeks ago and I'm not sure how I should be approaching it. Please let me know which theorems I should look into in order to solve the problem.

Homework Statement write the proof Homework Equations none The Attempt at a Solution I've tried 5 times, got nowhere

Let $ABCD$ be a convex quadrilateral such that $AB=BC,\,AC=BD,\,\angle CBD=20^{\circ},\,\angle ABD=80^{\circ}$. Find $\angle BCD.$

Homework Statement In the attached diagram,the edge of the square is a. find the area of the shaded region Homework Equations area of circle = πr^2 ,area of square,triangles (Please avoid using integration/radian angle/tangent...Since this problem is found in a maths exercise suitable for a...

Homework Statement In a methane molecule, determine the length of the distance between a hydrogen atom at A and the carbon atom at O (see diagram) in terms of the length of the edge (e) of the cube at four of whose corners the hydrogen atoms rest. Homework Equations pythagorean theorem...

In discussing proportions (a topic to which I have not been properly exposed) Legendre states that, adding the antecedent of a proportion to the consequent, and comparing the sum to the antecedent, one obtains a proportion equal to the original plus unity. Legendre's book is apparently...

Hi I'm an advanced undergraduate physics student and I'm currently searching books for my career project. The topic I selected is titled: Algebra and geometry in modern physics. So I'm currently looking for books that cover modern aspects of physics in a more mathematical approx. In specific I'm...

Homework Statement A piece of wire, 100 cm long, needs to be bent to form a rectangle. Determine the dimensions of a rectangle with the maximum area. Homework Equations P = 2(l+w) A = lw The Attempt at a Solution This is what I don't understand, the solutions that I saw from looking around...

Hello all, I am not too experienced with geometry. I am just curious whether it would be possible to define a shape based on variables. Say you have a simple relationship between volume and some variables. V=x+y. This tells you about the volume of a 3D object, however, it does not describe the...

Hello, A friend of mine gave me this puzzle and I'd like to share it with you, math enthusiasts: Two ladders intersect in a point O, the first ladder is 3m long and the second one 2m. O is 1m from the ground, that is AC = 2, BD = 3 and OE = 1 (see the image bellow) Question: what's the value...

In the question they say a "1/2 by 2 in rectangular cross section". Does this mean the dimension of 1/2 is actually into the page and not as shown in the diagram? Also, In the solution there is mention of "the base metal adjacent to the weld" and "shank of the attachment". What areas are these...

Hello all! I've just started to study general relativity and I'm a bit confused about dual basis vectors. If we have a vector space \textbf{V} and a basis \{\textbf{e}_i\}, I can define a dual basis \{\omega^i\} in \textbf{V}^* such that: \omega^i(\textbf{e}_j) = \delta^i_j But in some pdf and...

Imagine a planet similar to Earth, but exposed to a completely different star. The star has the same mass and emits the same amount of photons as the sun, but it is a huge, extremely slender torus made of 1 mm diameter neon tubing. The planet is on the axis of the torus and at the same distance...

micromass submitted a new PF Insights post How to Self Study Geometry. Part I: Pure Geometry Continue reading the Original PF Insights Post.

I'm having trouble understanding the terms "flat geometry of the universe" and "baseline curvature of the universe." How can a 3D universe be flat?

I would appreciate any help with this questions because I truly horrid at geometry questions. I've only done (i) to which I've found the answer to be (E). I can't do from from part (ii) on.

Homework Statement Given points of a triangle: A(4,1,-2),B(2,0,0),C(-2,3,-5). Line p contains point B, is orthogonal to \overline{AC}, and is coplanar with ABC. Intersection of p and \overline{AC} is the point B_1. Find vector \overrightarrow{B_1B}. Homework Equations -Vector projection - Dot...

Please I need help on how to creat double layer 36 slot IPM Motor using Ansoft/Rmprt software.

Hello First of all, I was told this is a physics problem. If it's incorrect, I apologize. I have an image I want to know the length of the black ship (the ship which is carrying a ship). Let's assume that I know the length of the text on the ship (I have a reference object). Is this...

Please bear with me because I'm only in Pre-calculus and am taking basic high school physics. This is completely outside of my realm but curiosity has taken the better of me. I just learned last week about the difference between Euclidean Geometry and Riemmanian Geometry (from another thread...

I am trying to build up a kind of mind map of the following: Module (eg. vector space) Ring (eg Field) Linear algebra (concerning vectors and vector spaces, from what I understood) Multilinear Algebra (analogously concerning tensors and multi-linear maps) Linear maps & Multilinear maps The...

Hi, i would be very interested to start learning hyperbolic geometry, what would be the necessary prerequisites to begin it's study? :smile:

I need help to visualize the geometry involved here, How can I visualize the last paragraph? Why is the surface of fixed r now an ellipsoid? Also for r = 0, it is already a disk? I've tried searching for the geometry of these but I can't find any image of the geometry that I can just stare...

Homework Statement A square with each side of 5 cm in length.Now if 4 parallel wires in each 4A current is flowing were placed on the vertex of the square.How can I find the center of the square of the magnetic strength? Homework Equations I am not sure what equation should be used.If I knew I...

I'd appreciate some explanation on how does one understand/reconcile the seemingly alternative concepts of gravity as (i) due to the warping of space by matter vs (ii) the exchange of gravitons. Is the latter a construction of how gravity can be considered within a quantum mechanics framework ...

Could you suggest me any textbook on Co-ordinate Geometry and Vector Analysis?

Reading a somewhat long and argumentative thread here inspired the following unrelated question in my mind: Where does a 2 dimensional flat Lorentzian geometry depart from Euclidean geometry as axiomatized by Euclid? I.e. Euclid's axioms (in modern language) can be taken to be: We can...

As I understand it, a Cartesian coordinate map (a coordinate map for which the line element takes the simple form ##ds^{2}=(dx^{1})^{2}+ (dx^{2})^{2}+\cdots +(dx^{n})^{2}##, and for which the coordinate basis ##\lbrace\frac{\partial}{\partial x^{\mu}}\rbrace## is orthonormal) can only be...