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
0
votes
2answers
955 views

How do I find the longitude of the subsolar point? [duplicate]

On December 21, 2018 at 2:23pm PST I want to be standing as directly under the sun as humanly possible. Obviously the latitude of that point will be the Tropic of Capricorn. Assuming I have the right ...
-2
votes
2answers
36 views

Optics(interference) [closed]

I'm a student at physics department, and I have a question about optics. In interference phenomenon we have two experiments: one with name Michelson and the other is the double slit experiment. In ...
1
vote
1answer
48 views

Why can an object not be pulled beyond the polygon which is forming from the attachment points?

I am looking for the physical equations that explains why a 2D object on a 2D surface, e.g. a rectangle cannot be pulled further than the greatest/smallest x/y coordinates of the points it is attached ...
1
vote
1answer
56 views

Is a displacement a vector, a line segment, or something else?

It probably seems ridiculously naive of me to ask such a basic question, but I have a need to use accurate language. Typically, I think of a displacement as a directed line segment whose end-points ...
5
votes
1answer
219 views

How does projective geometry related with Fourier transform via Lorentz transformation?

On one hand, the Lorentz transformation plays an important role in classical electromagnetism. On the other hand, each Lorentz tranformation is also a Möbius transformation of $\Bbb C$ (Needham, ...
1
vote
1answer
70 views

Doubt in the equation of trajectory of partical moving under central Force

In the book by Goldstein (Third Edition, Page 95) on classical mechanics, Goldstein derives equation of the trajectory of particle moving under center force. The equation he derives is given by: $$r= ...
3
votes
2answers
116 views

Magnetic equivalent of a pointy edge at a voltage

A pointy edge set at a given electric voltage will usually induce localized but high potential gradients, hence high electric fields. Is there something equivalent for magnetic fields? A simple ...
1
vote
3answers
105 views

How strict are the boundaries that divide dimensions? Is a single-layer sheet of graphene 2D or 3D? [closed]

I would like to know if there is any theory that describes a set of rules that define the boundaries of dimensions. For example, does a single layer sheet made of graphene considered a two or a three ...
3
votes
2answers
147 views

Surreal numbers and “zig-zag” shapes [closed]

This question has been reworded. Is there an experiment which can distinguish between mathematical models of physical space based on real numbers and models based on other types of numbers e.g. ...
0
votes
0answers
38 views

Why geometrically does the orientation of a scalar particle plane wave relate to its velocity

In this question I am trying to think about quantum field theory geometrically. I abbreviate "in the zero speed direction" to "vertically" and "in the equal-time plane" to "horizontally". I base my ...
0
votes
1answer
37 views

Solving for $x$ and $y$ image coordinate given a 3D point

I have a 3D point, $(X, Y ,Z)$ and I want to know where it's imaged, $(u, v)$. I'm assuming a pinhole camera model with no lens distortion. I have the distance from the pinhole to the object ($z$), as ...
1
vote
4answers
450 views

What is a physically intuitive description of the “dot product” and “cross product”? [duplicate]

I just learned about the definition of the vector dot product and cross product. Almost every source says that the dot product is the: Product of the $\cos(\theta)$ component of a vector along ...
-2
votes
2answers
55 views

Vectors and quantity [closed]

The magnitude of a vector quantity is a scalar quantity (a number) and is always positive.. I believe That direction must be always Positive but Why magnitude of Vectors must be always Positive (...
-3
votes
1answer
45 views

Galactic Distances

I'm trying to show: 1 arcsec on the sky is approximately 5d parsecs at a galaxy, d parsecs away Could someone show me a proof of this statement, because it is bamboozling me!
0
votes
1answer
402 views

Dot product and cross product Intuition [duplicate]

I know that the dot product and cross products of two vectors represent their components acting in each other's direction but it always puzzles me to think why and how, particularly what bangs my head ...
3
votes
2answers
2k views

What does the term “inversion symmetric” mean?

I've read the responses to the question `"Lack of inversion symmetry" in crystal?' but I'm still unsure about the meaning of inversion symmetry. Which of the following two dimensional ...
1
vote
0answers
74 views

What does $\pi^2$ represent in real life? [closed]

I am in physics 2 and learning about induction and inductance, as well as LC and RLC circuits, I am encountering the value $\pi^2$ a lot. I wanted to know what $\pi^2$ represents, either geometrically ...
2
votes
2answers
596 views

What would the horizon look like on an infinite plane? [closed]

What would the horizon look like on an infinite plane? I can imagine the growth of a horizon to be similar to a decreasing exponential function. Where the growth of horizon decreases more as the ...
1
vote
0answers
27 views

Attitude quaternion from 2 vector measurements

I am using a method proposed by R. G. Reynolds to estimate attitude based on two vector measurements, taken from: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19990052720.pdf Suppose we ...
-1
votes
1answer
330 views

Why is the area of an elemental ring with radius $r$ and width $dr$ is $2πr dr$?

As shown below the topic is to calculate Electric Potential due to a disk whose surface charge density is $ \sigma $. To do this we considered an elemental ring with inner radius = $r$, outer radius =...
0
votes
1answer
42 views

Rewritting $\frac{\partial g^{ik}}{\partial x^k}$ in terms of $g$ instead of $g^{-1}$?

I have the following $$\frac{\partial g^{ik}}{\partial x^k}$$ which appears in a computation that I am doing. As you can see it is a derivative of the inverse of the metric tensor $g$. How can I ...
2
votes
2answers
2k views

Derivation of $d\theta = ds/r$

I was reading about Uniform Circular motion and I came across this formula: $d\theta = ds/r $. ($r$ being the radius, $d\theta$ being the angle swept by the radius vector and $ds$ being the arc length)...
1
vote
1answer
297 views

What is a general coordinate transformation?

I know about special relativity and Lorentz transformations. However, there is also the general coordinate transformation (GCT) which is allegedly used in general theory of relativity. What is GCT and ...
7
votes
2answers
282 views

Intuition for Interchange Symmetry of the Riemann Tensor

Is there an intuitive/geometric picture for the interchange symmetry of the Riemann tensor? I have seen plenty of algebraic derivations, but would like to understand if the symmetry expresses ...
2
votes
0answers
120 views

What would gravity be like on the surface of a right rectangular prism?

Let's assume there is a right rectangular prism floating about in space, what would the gravity be like across its 6 flat surfaces? Let's assume that this right rectangular prism has a constant ...
145
votes
9answers
23k views

Why are the wet patches on these floor tiles circular?

My friend's 3-year-old daughter asked "Why are there circles there?" It had either rained the night before or frost had thawed. What explains the circles? Follow-up question: Ideally, are these ...
0
votes
4answers
325 views

Is a shadow 2D?

I had always thought anything below third dimensions couldn't exist in our 3rd-dimensional world. Correct me if I'm wrong but anything 0d 1d or 2d is massless and also can't have energy so it just can'...
40
votes
7answers
8k views

Why does the full Moon appear?

I know that the full Moon appears when Sun, Moon and Earth are in a straight line, but if we consider that they are in straight line, why is the Moon illuminated? I mean to say that Earth should ...
-2
votes
2answers
1k views

Flying with or against rotation of a planet

So, I've read a bunch of articles about how, somewhat contrary to intuition, it's usually faster to fly with the rotation of the earth versus against it. All the answers have to do with wind and ...
1
vote
1answer
95 views

What's the distribution of scattering angles for hard spheres with random impact parameter?

I am modelling the scattering of hydrogen atoms against each other. In this model, one hard sphere scatters elastically off another hard sphere, they are identical with radius $r$. They meet with ...
0
votes
2answers
36 views

Prove expression for center of mass of a curve [closed]

While reading a book, I have come across the following expression for the abscissa of the center of mass of a curve $y=y(x)$, $a\leq x\leq b$: $$\frac{\int_a^bx\sqrt{1+y'^2}\ dx}{\int_a^b\sqrt{1+y'^...
1
vote
2answers
19k views

Moment of Inertia of an Equilateral Triangular Plate [closed]

I was reading about moment of inertia on Wikipedia and thought it was weird that it had common values for shapes like tetrehedron and cuboids but not triangular prisms or triangular plates, so I tried ...
2
votes
3answers
531 views

The commutation of partial derivatives in curved spacetime

While following a lecture series on General Relativity, an argument was presented that in order the spacetime to be flat, a vector parallel transported along two different paths should yield the same ...
-4
votes
2answers
143 views

The shortest distance along the surface of the sphere [closed]

Imagine we have a sphere. And inside the sphere there are two points. Now we have an arc that is connecting these two points and it is said that arc that goes through the center of the sphere is the ...
0
votes
0answers
96 views

Geometry of gauge theory [duplicate]

In this Ted talk The Geometry of Particle Physics: Garrett Lisi at TEDxMaui 2013 is he referring to the gauge group space while using the toys ? (Seems so to me). Can someone provide some references ...
1
vote
3answers
227 views

Why does the Earth not cast a shadow straight like a cylinder in the opposite direction of the Sun?

Why does the Earth's not cast a shadow straight like a cylinder in the opposite direction of the sun? Instead, it forms "cones," the umbra and penumbra.
2
votes
2answers
76 views

Algorithmic approach to finding two vectors that span a plane

I am working on an experiment where I need to align a magnetic field to be parallel to a nanoscale wire embedden in a microscale planar structure. My tools for doing so are two-fold: the planar ...
-1
votes
1answer
68 views

Angle in a triangle [closed]

The question I'm dealing with here deals with mechanics but my specific question concerns the geometry of the shapes involved (I didn't post this to the math stack exchange because it's more likely ...
1
vote
1answer
111 views

Minimum force needed to start a wheel on a slope?

I have been messing up with this for at least two hours , but can seem to find anything rather than a small angle! The question is to find the magnitude and the direction of the smallest force (say ...
0
votes
1answer
119 views

Proving the centre of mass formula with integral [closed]

I came across a question: Find $f(r)$ and prove the centre of mass formula: $$\vec{r_{cm}} = \frac{1}{V} \int f(r) \vec{dS} $$ Where $V$ is the total volume and our surface integral is ...
3
votes
0answers
123 views

Collision detection of two circles rotating around fixed points in 2D [closed]

Recently I have learned how to predict the time of collision between two circles moving linearly. Positions of $P$ and $Q$ after time $t$ are: $P(t) = P_0 + vPt$ $Q(t) = Q_0 + vQt$ The goal was to ...
0
votes
1answer
64 views

Converting 180° of motion to 270° of motion via gear ratio [closed]

I am very new to math / physics not sure if this is the best network to ask or if math is better but I am working on a project where I only need 270° of motion to turn a potentiometer from a servo ...
5
votes
2answers
656 views

Rotation in Higher Dimensions

In a world of three spatial dimensions plus time, every atom rotates around a line, the axis of rotation. In a world of $N$ spatial dimensions where $N$ is greater than 3, must every atom rotate, ...
0
votes
0answers
137 views

Is there a book about projective geometry in physics?

From Complex projective space: In quantum physics, the wave function associated to a pure state of a quantum mechanical system is a probability amplitude, meaning that it has unit norm, and has an ...
2
votes
0answers
72 views

Conformal angle transformation [closed]

As I understand a conformal transformation transforms the metric $g_{mn}\rightarrow f^2(x)g_{mn}$ for some function $f$ that is non-zero everywhere. Why does this preserve angles? I know that $\...
1
vote
1answer
137 views

Do we $\textit{need}$ to use a torsion-less connection(Riemann-Levi Civita) in General Relativity?

While learning General Relativity, we always use the Levi-Civita connection, which has the special property of being torsion-less. My question is: Do we need to use a torsion-less connection to study ...
1
vote
1answer
202 views

What does the Kretschmann scalar really tell us about the geometry of spacetime? [duplicate]

The Kretschmann scalar is one of the measures of spacetime curvature. For flat (Minkowski) spacetime it is zero. The dimensions of the Kretschmann scalar are $[L]^{-4}$. What does that physically ...
2
votes
3answers
821 views

Painting with a Pendulum: Would it be possible to graph the pattern?

I intend to try and replicate an experiment that I found online: The idea seems to be: Attach a string to a fixed, overhead object Attach a can of paint to the string Put a hole in the bottom of the ...
1
vote
1answer
46 views

In order for spherical mirror to focus, why do we need $\mu > h_1$?

We know that in order for a spherical mirror to focus, the equation $$y^2 = 4fx - x^2$$ do behave like the parabola equation $$y^2 = 4fx,$$ so we need $$f>> x.$$ However, it is told me that the ...
1
vote
1answer
387 views

Equating a radian to a steradian

I've been staring at a formula for a while now which equates an angle with a solid angle. I can see how the equation is dimensionally consistent, which settles well with me, but I get tripped up at ...

1 2 3 4 5 13