The Stack Overflow podcast is back! Listen to an interview with our new CEO.

Questions tagged [geometry]

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

Filter by
Sorted by
Tagged with
2
votes
1answer
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 $$\vec P'=\vec P + d\theta\ \vec e_\theta+d\phi\ \vec e_\phi+dr\ \vec e_r$$...
-1
votes
0answers
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 ...
0
votes
0answers
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 $(r_0,\theta_0,\phi_0)$, ...
1
vote
3answers
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 ...
3
votes
1answer
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 ...
0
votes
0answers
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 ...
1
vote
4answers
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 ...
1
vote
1answer
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 ...
30
votes
10answers
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 ...
0
votes
2answers
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 ...
3
votes
1answer
90 views

Why does a wormhole have this metric?

I asked this (or something similar) within another question and was asked to post it separately, so here goes: The metric for flat Minkowski space is: $$ds^2 = -dt^2 +dr^2 +r^2(d\theta^2+d\phi^2\sin^...
2
votes
1answer
64 views

What's the problem with Euclidean geometry for astronomical phenomena?

This passage from John Pierce, An Introduction to Information Theory: "also note that while Euclidean geometry is a mathematical theory which serves surveyors and navigators admirably in their ...
0
votes
1answer
95 views

Weird assumption in a paper to prove equation [closed]

Let $M_k$ and $M_{k+1}$ be two successive positions. Supposing the road is perfectly planar and horizontal, as the motion is locally circular, we have: Where $\Delta$ is the length of the circular ...
0
votes
0answers
32 views

Is every observer equidistant in all directions from the point of origin of the universe? [duplicate]

I am interested in the origin and present structures of the dimensions of space and time. I do not think space/time can be correctly described by an ordered set of scalars: (x,y,z,t). So. If every ...
1
vote
0answers
29 views

Square gears pitch curve relationships [closed]

I am trying to design square gearset using MATLAB program. I have designed several ones (elliptical, eccentric, spiral, circular ....etc). But when I came to the square gears, I needed the ...
3
votes
1answer
42 views

Are special conformal transformations continuous?

My understanding of special conformal transformations (SCTs) is fairly limited, but I believe that they are composed of an inversion, a translation and another inversion. Since inversions are discrete ...
1
vote
1answer
58 views

Why do the rail tracks seem to converge and vanish? [duplicate]

Why do railway tracks seem to converge at a far away point? Can this phenomenon occur with a very far away tall wall (considering I stand on a flat plane, not the curved surface of earth). Isn't ...
0
votes
1answer
89 views

How did German radio beams reach distant English cities during WWII? [closed]

During WWII, the Germans were using radio beacons (the "Knickebein" system) to guide their bombers into English territory. They set up two beacons, one in Kleve, a city in West Germany, and one at ...
3
votes
1answer
32 views

How can we find the charge distribution of $n$ external electrons on the surface of a conducting cube? [closed]

Suppose we take 'n' electrons and put them on the surface of a conducting cube. How can we calculate the charge distrubution and position of these electrons once the static situation has been arrived ...
0
votes
0answers
28 views

General force between two point particles, one of which has “spin”

Consider two points in the empty (isotropic and homogeneous) space: since the only vector that "makes sense" (the only vector that we can define) is the vector given by the difference of the two ...
0
votes
2answers
48 views

How to determine the minimum force in these questions?

Take a look at this example The author mentioned that the shortest path when the angle is 90 which is clearly obvious. Now take a look at the following problem from the same book The author has ...
1
vote
2answers
192 views

Confusion about a claim in the “Brief History of Time” by Hawking

In the first chapter, while talking about how Aristotle was able to conclude that the Earth is spherical, Hawking says that had the Earth been a flat disk the shadow of the on the Earth on the moon ...
1
vote
2answers
103 views

If vector $a$ rotate about vector $b$, does vector $b$ also rotate about vector $a$?

For $2$ vectors $\, \vec a,\vec b$, both originate at $[0,0,0]$: If vector $\vec a$ rotates about vector $\vec b$ when observed from a coordinate system fixed to vector $\vec b$, does vector $\vec b$ ...
0
votes
2answers
67 views

If body's movement is described with x(t) = cos(t), y(t) = sin(t), z(t) = At, why isn't the circumference of this curve (circle) equal to 1? [closed]

Each equation gives information about the body's location on each axis in Cartesian coordinate system (A is some constant and $t$ is time). We know that $\sin^2(x)+\cos^2(x)=1$ (Pythagora's theorem ...
1
vote
1answer
49 views

Theoretical question regarding two elliptic trajectories

I am new to Newtonian Mechanics, and I was wondering regarding the following: Are $$\vec{r}(t): a \sin(ωt)\hat x +b\cos(ωt)\hat y$$ and $$\vec{r}(t): a \sin(ωt^2)\hat x +b\cos(ωt^2)\hat y$$ ...
1
vote
0answers
21 views

Consistency with calculating the Solar Azimuth Angle

I am struggling to find consistency regarding the calculation of the Solar Azimuth Angle. The equations across multiple publications have similar terms, but differ significantly. These differences ...
0
votes
2answers
93 views

Why Air bubble are always sphere in shape? [duplicate]

Everyone of us had noticed air bubbles once in his life. They are Sphere in shape. But I want to know why the are sphere in shape, instead of any other shape.
1
vote
1answer
84 views

How is the constant “284” derived within the Solar Declination Angle equation?

How is the constant "284" derived within the Solar Declination Angle equation? The earth's axis results in a day-by-day variation of the angle between the earth-sun line and the earth's ...
0
votes
3answers
116 views

Reason behind vector addition law

What is the reason behind triangle law of vector addition, in other words, how is this really justified?
1
vote
0answers
93 views

Time after which the 3 particles will meet? [closed]

Problem is from Classical Mechanics: I am a beginner in Physics trying to understand the solution to the given below problem. Problem Statement: 3 particles are placed at the vertices of an ...
0
votes
1answer
14 views

volumetric density from linear densities in the three directions x,y,z

I have a cube and I know the linear density of particles along each axis (I mean- the number of particles per unit length along each axis). How can I get the volumetric density?
-3
votes
1answer
57 views

Finding angles in three dimensions [closed]

Suppose there is a line making an angle $\theta$ with $z$ axis in three dimensions. Then what will be the angles of that line with $x$ and $y$ axes?
4
votes
1answer
74 views

Maximum Vertical Velocity of Pendulum

Say there is a 10N pendulum held parallel to the ground. In a frictionless environment, it will continue swinging along a semicircular path. The pendulum tip should have the highest horizontal ...
0
votes
1answer
47 views

Geometry with differential angles

In the solution to a problem, the author considers the normal force provided by an arc length of string with a differential subtended angle size, $\textrm{d}\theta$. The author reasons that this ...
2
votes
1answer
77 views

Why did staining marks on these paving slabs form geometric shapes?

[edited to add more examples] Along several streets in London I can see paving slabs that have become stained in the middle of the slab with white-ish marks forming different shaped patterns. The ...
1
vote
1answer
86 views

Lorentz Factor from Minkowski's Original Paper 'Space and Time'

Consider the following figure: Minkowski, in his paper 'Space and Time', derives the Lorentz factor $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ from considerations of this figure. He ...
1
vote
1answer
52 views

Is there a definition for a *geometric entropy*?

In statistical mechanics, entropy of a system is usually defined as a measure of the system's micro-state randomness, or as an averaged "surprise" of its micro-state: \begin{equation}\tag{1} S_{\text{...
15
votes
11answers
1k views

Is there a proof that the set of real numbers can exactly represent distances? [duplicate]

Mathematicians define real numbers in an abstract way - as an 'ordered field' with 'the least upper bound property'. In physics, we use real numbers to represent distances. For us to be able to do ...
0
votes
0answers
12 views

What’s the topology of critical region?

Duhem said the aim of physics is natural classification. I think topology and geometry are a wonderful way to link analogous parts among different phenomena. Thus we can classify and predict facts. ...
4
votes
0answers
97 views

Method to build a polyhedral die with given probabilities [closed]

Let's define a die as a polyhedron that, if rolled over a perfect horizontal plane, ends up being in a physically stable unambiguous state labelled $n$. The die has $N$ states. Each state $n$ has a ...
1
vote
1answer
80 views

A problem in newtonian physics [closed]

Hello! I have solved problem 89 using analytic way, i.e, the length of the string will always be constant, so repeated substitutions and differentiating will make way(i got answer as "c"). But is ...
2
votes
1answer
62 views

Can a black hole have a finite perimeter but an infinite radius/diameter?

Recently, I attended a talk at UNC Chapel Hill by Kip Thorne and I recall that he mentioned that black holes can have a finite perimeter but an infinite radius/diameter (since spacetime is curved with ...
2
votes
1answer
40 views

Change in area on a 3-sphere bounded by a trajectory due to a differential change in trajectory

I have a 3 dimensional spherical topology, and I draw a curve onto the sphere labelled by $\vec{n}(\vec{r},t)$. The area bounded by the curve is termed the "Wess Zumino Action" (Hence my motivation to ...
2
votes
2answers
58 views

Why is the angular part of the Schwarzschild metric is not affected by function of $r$ and $t$ as opposed to the first two?

Consider the Schwarzschild metric $$ds^2 = A(r)dt^2 −B(r)dr^2 −C(r)r^2(d\theta^2 +\sin\theta^2d \phi^2),$$ where $A,B,C$ are some functions of $r$. There is no loss of generality if one takes $C = 1$....
1
vote
1answer
50 views

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 ...
0
votes
0answers
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 ...
0
votes
1answer
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?
4
votes
2answers
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 ...
1
vote
2answers
37 views

How is depth perception linked with the separation between our eyes? [duplicate]

I came across a comment online which mentioned that one of the main benefits of having 2 eyes is that we can perceive depth. I tried closing one eye and seeing for myself if somehow everything would ...
10
votes
3answers
1k views

In a ball with random thread/strings, how does the density of threads/strings change with radius?

A large plastic ball full of holes is given. (So the holes are in a plastic shell.) Straight threads connect these holes randomly, by passing through the interior of the ball/shell. For a big ball or ...