Geometry Definition and 999 Threads

Homework Statement Suppose that ##s \to A(s) \subset \mathbb{M}_{33}(\mathbb{R})## is smooth and that ##A(s)## is antisymmetric for all ##s##. If ##Q_0 \in SO(3)##, show that the unique solution (which you may assume exists) to $$\dot{Q}(s) = A(s)Q(s), \quad Q(0) = Q_0$$ satisfies ##Q(s) \in...

Homework Statement A simple method for determining the focal length of a negative lens is shown below. Prove this is true. Homework Equations The Attempt at a Solution The linear magnification formula relates magnification, the distance from the lens to the image (i), the distance from...

When building a tall support, often the self weight of the support must be considered. For an optimal support, the volume of material, and hence the cost, will be a minimum. If the maximum allowable stress in concrete is 15 MPa, determine the optimal geometry of a column 100 metres tall made of...

I'm interested in elliptic space from an intrinsic point of view(manifold pov) rather than the models based in Euclidean embeddings. Would it be correct to say that the isometry group of this geometry is isomorphic to SU(2), i.e.:versors or unit quaternions?

Can someone recommend some background texts which can build me up with the necessary pre-requisites to learn about Riemannian Geometry? I have been self studying single and multi variable calculus but lack the mathematical rigour. Some resources/textbooks that can cover the background material...

Homework Statement I just came across a couple of expressions in a textbook I don't particularly understand. Caption: "A point lensing mass L moving with velocity v perpendicular to the line of sight. O is the observer and S' is the projected position of the source in the plane of the lens...

You are given a cone with height/length "L" and radius R. This cones Length is parallel to the Z axis in an XYZ frame of reference while the radius is parallel to the XY-plane. This cone is then revolved(spun) around the y-axis, graph the area "touched" by the cone on the YZ-plane. I am...

Hello, I have been doing a review test on Geometry 1 on Sparknotes (http://www.sparknotes.com/math/geometry1/review/quiz.html), however I came across two questions which I got incorrect answers for and which I found the provided solutions questionable. The first is Question 1 (attached). I...

I would like to refresh my "normal" or Euclidean Geometry quickly and then proceed to Non-Euclidean Geometry. But I don't have a clue where to start. (It's because I want to learn more about Relativity, but my geometry hasn't got an update since long time ago) I don't know what a...

Hi. I am looking for the most basic intro to differential geometry with plenty of worked examples. I want it to cover the following - differential forms , pull-backs , manifolds , tensors , metrics , Lie derivatives and groups and killing vectors. Problems with solutions would also be good as I...

I am planning on taking a course in differential geometry. I have looked at the notes and they cover - differential forms , pull-backs , tangent vectors , manifolds , Stokes' theorem , tensors , metrics , Lie derivatives and groups and killing vectors. I have a book called Elementary...

Basically the symbols like force f and d/dt (mv) for these subjects. Physics Geometry Calculus Astronomy Cosmology Biology Algebra Trigonometry Chemistry Could you try to get as many symbols in or like a website. It is really hard to find a good list of symbols.

Somebody can give me some tips? I'm really bad at this.

Hello everyone! I recently bought a small raspberryPi board, with its small "camera board". (link for camera reference) I want to use a CS lens on this camera (CS lens from the security camera industry). I have been able to attach the lens, and it focuses very good, yet not "excellent"...

I'm looking for a book or two that details affine spaces and transformations, then differential geometry of surfaces in affine spaces, starting at a level suitable for a year 1-2 undergraduate. In particular, I'd like to understand a few properties (e.g. what's the gradient and curvature at a...

I bought a book (Differential Geometry by Kreyszig) based on really good reviews because I'm planning to learn general relativity later. I guess I didn't pay enough attention to the description because apparently it's completely focused on "three-dimensional Euclidean space." Will this book...

Is the bottom half of an egg a hemisphere?

So I am trying to test into the Calculus with Analytic Geometry class at my school. I've already taken the first AP Calculus class my senior year of high school (but wasn't particularly concerned with my grade, and never took the test, since it was an extra curricular class for me). Then I took...

Also, is there a special term for the geometry typically taught in high school? And how does topology fit in here? It seems that topology is a form of geometry as well.

I'm watching a lecture by Edward Witten here: In it, he mentions that String/M-theory seems to be hinting toward a new kind of geometry where you don't talk about space/time points, but the interactions between quantum world sheets (around 37:00 minute mark.) Does this new geometry have...

can someone tell me if i drew these right. and also I am stuck on part (f). how do i draw that? i attached the original questions and my drawings. for part (a) and (e) i used the parallelogram law

A first stage of the determination. We have a body of length L = AB, which moves along the x-axis with velocity v, say that coming to us. A -------- B v <--- | | h - vertical distance | ./ - a light converges to us with the speed eq. c | / O ---------> x At some time t = 0, we see the point A...

Homework Statement 1. A group of American physicists works on a project where planar lines are in the form X=t⋅P+s⋅Q where P , Q are two fixed different points and s,t are varying reals satisfying s+t=1 . They need to know formulae for the images of the line X=t⋅P+s⋅Q in the following...

2. A group of Japanese physicists works on a project where planar lines are in the form of solutions to equations a⋅x+b⋅y+c=0 where a , b , and c are fixed reals satisfying a2+b2≠0 . They need to know formulae for the images of the line a⋅x+b⋅y+c=0 in the following cases: 1. Under the...

Homework Statement ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Then prove that ∠D=90°-(∠A/2) Homework Equations The Attempt at a Solution I guess I want to prove an untrue thing because by drawing a diagram and...

http://arxiv.org/abs/1402.2158 Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology Yuri I. Manin, Matilde Marcolli (Submitted on 10 Feb 2014 (v1), last revised 9 Jul 2014 (this version, v3)) We introduce some algebraic geometric models in cosmology related to the...

Let $A$ be the intersection point of the diagonals $PR$ and $QS$ of a convex quadrilateral $PQRS$. The bisector of angle $PRS$ hits the line $QP$ at $B$. If $AP\cdot AR+AP\cdot RS=AQ\cdot AS$, prove that $\angle QBR=\angle RSQ$.

Definition/Summary In Euclidean coordinate geometry, a Line usually means the whole (infinitely long) Line. (In ordinary Euclidean geometry, a Line usually means a line segment between two points.) The equation of a Line in n dimensions is a combination of n-1 linear equations of the...

Hi, I visited my Mother and Stepfather recently, and admired the tall trees around their house. We estimated them to be around 180-200 feet tall. I told my Stepfather that the *Actual* height could of course be calculated. I said there are three angles and three lengths for any...

If ABCDEFG is a regular heptagon prove that $\frac{1}{AB}=\frac{1}{AC}+\frac{1}{AD}$.

even γ: I-> R ^ 2 curve parameterized as to arc length (single speed) with curvature k (s)> 0 and torsion τ(s)> 0. I want to write the γ(s) as a combination of n(s), t(s), b(s). these are the types of Frenet. the only thing i know is that the types of Frenet are t(s)=γ'(s) ...

Dear all, I am looking for an interactive software that can let me play with 3d geometry. I apologize, as I am not sure of the right technical term of the sorts of shapes I am interested to work with. I am not a mathematician or physicist, but rather use these as philosophical metaphors and...

Consider the surface S defined as the graph of a function z = 2x ^ 2 - y ^ 2 i) find a basis of the tangent plane Tp surface S at the point p = (-1,2, -2) ii) find a non-zero vector w in Tp with the property that the vertical curvature at point p in the direction of vector w is zero for...

whether γ=γ(s):I->R^3 curve parameterized as to arc length (single speed). Assume that γ is the surface sphere centered on the origin (0,0). Prove that the vector t(s) is perpendicular to the radius of the sphere at point γ(s), for each s. i know that t(s)=γ΄(s) but i don't know how to...

Hi! I've been to the math book listings and there is no such book recommendation on elementary geometry, only the classical geometry of the greeks,I need something that will prepare me for trigonometry can I have suggestions on which book I should use? (Please don't mention Kiselev's Geometry...

A rectangle with sides $x$ and $y$ is circumscribed by another rectangle of area $A^2$. Find all possible values of $A$ in terms of $x$ and $y$.

I'm interested in spherical geometry in 4 dimensions. Surely someone has done this, but what is it called? I can't find it.

I know there's no definitive answer to this, and there's a few different models that give different explanations on why they're using a flat model, or a curved model, but my question is why wouldn't the geometric shape of the universe be spherical or a hyperbolic sphere since everything else is...

Dear physicist, I am designing a device that will use firetruck/hydrant water pressure (~150 psi) and fire hose (5" diameter) to lift up a device in the air and into a burning room. Please advice me and help understand how water flow, pressure and areas influence thrust. My goal is to input...

Let A(1, 2), B (3,4), C( x, y) be points such that (x- 1) (x-3) +(y-2) (y-4)=0. Area of triangle ABC=1. maximum number of positions of C in the xy plane is (a) 2 (b) 4 (c) 8 (d) None of these I have tried using the staircase formula which gives me something like x-y=2. Therefore I see only...

Hey Guys, I'm stuck with this problem, we want to compare the curve of a beam to it's horziontal deflection, it's for an experiment we're performing on a very elastic beam. In the attachment you see a flexibel beam getting deflected by a force, this causes displacement x. We don't know (or...

My daughter needs some math assistance that I am not able to help her on. I would like someone who is experienced in middle school math (12-14 year olds) and who can explain how to go about each of these problems. The actual test is in 12 hours and will have different problems. But these six...

My name is Caleb, I am 12 years old and going into 8th Grade. I will be taking a geometry course next year and my dad suggested coming here for a Summer assignment. What would be some good assignments (links, advice, observable experiments, etc.) that would prepare me for my geometry course?

Please read the attached file to answer my question. Thanks a lot.

Hi, So basically I am wondering how can you increase damping within a part, just by altering its geometry. I've researched this topic, but haven't yet found anything significant. Here are my main findings: - Rayleigh Damping uses the equation: [C] = α[M] + β[K], which to me shows that mass...

Find the length x if the shaded area is 1200 cm^2 I tried to solve this is what I get since $A_{triangle}=(\frac{1}{2})({x-1})(x)$ and $A_{rectangle}=x$ $A_{rectangle}+A_{triangle}=2400$ Is the set-up of my equation correct?

Any good textbooks on differential geometry for self study? I'm not the best at reading comprehension. I've already studied Calculus, differential equations, and linear algebra.

in a plane point is said to be rational if both x and y co-ordinates are rational. Show that if in a $\triangle$ ABC all the vericles A , B, c are rational then $\triangle$ cannot be equilateral

... gravitons and Higgs bosons to convey mass or make space curve? And to make us fall towards a massive object space is then larger the closer we get?

I have a Physics background and have done the relevant maths ie. calculus , linear algebra , vector calculus and differential equations. Do i need any "extra maths" before starting a course in differential geometry ? Any recommendations for a book on the subject that would suit a Physicist ? Thanks