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Questions tagged [geometry]

To be used for questions on geometry closely pertaining to physics. Includes differential geometry and euclidean geometry.

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252 views

What are the points in spherical coordinates?

Let's use the spherical coordinates so that $\vec P=(r, \theta, \phi)$. In this context i've read that it's possible to write $$\vec P'=\vec P + d\theta\ \vec e_\theta+d\phi\ \vec e_\phi+dr\ \vec e_r$$...
32 views

What is the definition of a Projection? [on hold]

This may be a stupid question. But here it is... Can the scenarios below be reffered to as projections? 1) A projector projects an image onto a white screen. 2) A LCD display forms an image on a ...
20 views

With north and south poles fixed, do all geodesics have constant $\theta$ and $\phi$?

I was going thorough reading Kolb and Turner's The Early Universe where in Section 2.2 it starts by asking the following question. For a comoving observer with coordinates $(r_0,\theta_0,\phi_0)$, ...
58 views

Does temperature coefficient of resistance depend on geometry?

By temperature coefficient of resistance of a material about a reference point $T_0$, I mean $${1\over R(T_0)} \left.{dR\over dT}\right|_{T_0}.$$ All the sources (that I’ve seen) that quote this ...
52 views

What's the meaning of the coordinates if we use a polar coordinate system?

In general, the coordinates of a vector are defined as the projections of it onto the coordinate axis. Moreover, in a polar coordinate system, the basis vectors $\hat e_\phi$, $\hat e_r$ depend on the ...
28 views

Computation with bispinors for a compatible pair of pure spinors in N=1 supersymmetric vacua compactified down to 4-dimension

I ask this question basically because I need help, just an hint, for a computation with bispinors. The background is string theory / supergravity, where many data of a supersymmetric vacuum can be ...
100 views

3 Dimensional Law of Cosines? Magnetic Vector Potential Problem

I am working on a problem similar to one in my textbook - however, I am having an issue understanding the example. Can someone explain the formulas from this picture? I am confused about using the law ...
41 views

Intuitive understanding of angular momentum in cartesian coordinates

If a point-mass body is moving in a plane $z=0$, its angular momentum can be taken to be a scalar, and from the vector product formulas (assuming $m=1$ as I'm only interested in geometry), its value ...
8k views

Is the “spacetime” the same thing as the mathematical 4th dimension?

Is the "spacetime" the same thing as the mathematical 4th dimension? We often say that time is the fourth dimension, but I am wondering if it's means that time is like the fourth geometrical axis, or ...
52 views

Are there two ways of representing a vector i.e., parrallelogram and resolution?

the question was: The component of a vector is (a) Always less than its magnitude (b) Always greater than its magnitude (c) Always equal to its magnitude (d) None of these ...
90 views

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Definitions of area and volume in $d$-dim spacetime

I am reading Erik Verlinde's paper "Emergent Gravity and the Dark Universe". Equations 2.12 and 2.13 give the area $A(r)$ and volume $V(r)$ respectively. Do $d$ dimensions comprise of both space and ...
29 views

Inside a shell full of strings, what are the components of the network, and what the possible defects?

Imagine that we have a (very) large shell full of holes, and flexible strings go (randomly) from one hole to another. Inside the shell, there will be a network of strings. Can one split this network ...
43 views

What fraction of events goes through a small area $dA$ a distance $r$ from a spherically symmetric point source as $r\to 0$?

I'm not sure how to use limiting principle to estimate the N fraction when r -> 0 and small area dA stays fixed $\lim N_{r\to\infty} = \lim\delta A/(4\pi r^2)_{r\to\infty}$ = 1/2 N ? How?
141 views

Number of GPS satellites required to give 100% coverage

I am a Belgian school student in sixth grade of secondary school (the Belgian equivalent of High school). Together with two class mates we were assigned to write some kind of essay about the Global ...