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

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4
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2answers
188 views

How were the ratios of distances between planets and the Sun first calculated?

I was reading some literature and I found that long before the actual distances between other planets and Earth or distance between Sun and Earth were known, physicists had calculated the ratios ...
1
vote
2answers
76 views

How many are the points which are $n$th nearest to a certain point in a hexagonal lattice

Suppose there are infinite points arranged as hexagonal lattice. The question is the one as the title. First we choose a point called $A$. Then when we count the $n$th nearest points to $A$, what ...
0
votes
2answers
30 views

How to calculate centre of mass

How do I find the centre of mass with given coordinates? For example if we have four objects with mass $m$ at coordinates of a square $(0,0,0),(0,0,a),(0,a,0),(0,a,a)$ or another example with eight ...
14
votes
7answers
3k views

Experimental evidence of a fourth spatial dimension?

As human beings, we observe the world in which we live in three dimensions. However, it is certainly theoretically possible that more dimensions exist. Is there any direct or indirect evidence ...
0
votes
2answers
5k views

How does one calculate the volume of a nucleus and the volume of an atom (in this case hydrogen)?

The hydrogen atom contains 1 proton and 1 electron. The radius of the proton is approximately 1.0 fm (femtometers), and the radius of the hydrogen atom is approximately 53 pm (picometers).
0
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0answers
18 views

Constructing uniform mesh in reciprocal space?

This is a bit of a mental exercise for me to get comfortable with the math of reciprocal spaces since I am going to start doing some research that requires knowledge of reciprocal spaces. Let's say I ...
0
votes
1answer
37 views

How to derive path difference ($\Delta l=d\sin \theta$) for double-slit interference?

The Wikipedia page for the double-slit wave interference experiment states that the path difference between waves diffracting from the two slits is equal to: $$ \Delta l=d\sin \theta $$ where $d$ is ...
2
votes
2answers
401 views

Finding the illuminance from a triangular light source

Since most light sources in games are point-like, it's pretty difficult to approximate area light sources with point sources. As triangles are a universal form to represent 3D models (thus area light ...
0
votes
2answers
619 views

Tensor of inertia

The tensor of inertia of a solid sphere is $I_{ii}=\frac{2}{5}MR^2$ about an axis passing through its CM. Why would the tensor of inertia of each hemisphere about that axis be ...
1
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3answers
154 views

Are circles stronger than triangles?

I've often herd in engineering that "there is no shape stronger than a triangle". I also recall that arches are very strong shapes as well, which can be crudely described as a ...
1
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0answers
152 views

Can the universe be round but still infinite?

Can the universe still be infinite in space if its curvature is > 1? Is a manifold of positive curvature necessarily compact? Does the Tarski paradox have any bearing on the finite or infinite ...
3
votes
1answer
268 views

Why are three parameters required to express rotation in 3 dimension?

We know that in spherical coordinates angle $\theta$ and $\phi$ (two angles)are enough to express three dimensional rotation of matrix. But to express rotation mathematically as a transformation ...
6
votes
2answers
400 views

Is Dyson Sphere a stable construction?

Suppose that a star is encompassed by a Dyson Sphere. Do we need a position control system for the Dyson Sphere to keep its origin always aligned with the center of the star? Will it stay aligned ...
0
votes
0answers
22 views

Radian Zeno-version paradox: Can a particle moving in the circular path reach the angular position of non-terminating decimal form radian value?

Consider a particle P moving in a circle of radius r as shown in the figure. Premise 1: Position of the particle can be described by the angle $\theta$. Premise 2: Particle reaches the position ...
-2
votes
0answers
25 views

How does the Integraph work?

I've been researching the integraph and I am absolutely fascinated by it! But wherever I look I can't find any mathematics explaining how it actually works! Can anyone point me in the right ...
1
vote
1answer
117 views

Structure factor of crystals (X-ray crystallography)

How can one prove that the degree of each node in a distance graph must be at least four in order to obtain a unique solution to an exact distance geometry problem with sparse distance data? The ...
18
votes
4answers
2k views

Distinguishing between solid spheres and hollow spheres (equal mass)

If there are two spheres (hollow and solid) with equal mass and radius and we want to find the hollow sphere without using any equipment. What's the best way(s) to recognize the hollow sphere and ...
0
votes
1answer
42 views

Constrained Motion of Connected Particles, Small Calculation Question

I am looking at this sample problem from Meriam Kraige - Engineering Mechanics Dynamics: When I do the differentiation, I end up with $\large -2\dot y+\frac{x}{\sqrt{x^2+h^2}}$ Where is the $\dot ...
0
votes
1answer
142 views

Center of mass of equilateral triangle

I'm trying find the center of mass ($R$) of a uniform density equilateral triangle without using symmetries to find the x coordinate of the vector $R$, but I can't get the expected $R_x = ...
1
vote
1answer
47 views

Calculating the area of region of the sky

I am given the right ascensions ($\alpha_1$ and $\alpha_2$) and declinations ($\delta_1$ and $\delta_2$) of a specific region of the sky. How can we find the area of this region? I know that there ...
-1
votes
1answer
468 views

Internal forces in a truss and its geometry [closed]

I'm to work out the internal forces in a truss, but I can't get my head around the geometry of the truss itself. I'm starting to think there may have been information on the diagram which I missed. ...
10
votes
3answers
1k views

How many times can light revolve around a black hole?

Take a light ray approaching a black hole from infinity which goes out again to infinity. What is the maximum finite rotation it can describe? (I know it can loop around indefinitely in the ...
2
votes
2answers
4k views

Why do far away objects appear to move slowly in comparison to nearby objects?

When we are in a moving train, nearby stationary objects appear to go backwards. In Physics, relative velocity can be employed to explain the phenomenon: velocity of object w.r.t train = velocity ...
1
vote
0answers
50 views

Justifying the use of real numbers for measuring length

I am not sure if this is the most appropriate place to post this but here goes nothing: Assume we were trying to come up with system of numbers $S$ to model our intuition of length. We want $S$ to ...
4
votes
10answers
2k views

Is it possible for a physical object to have a irrational length?

Suppose I have a caliper that is infinitely precise. Also suppose that this caliper returns not a number, but rather whether the precise length is rational or irrational. If I were to use this ...
0
votes
1answer
42 views

Quantum physics and constructable numbers [duplicate]

I do not know much about quantum physics. However, I do know it believes the world is discrete ( has quanta). This seems to contradicts the fact that we can create an object of length root 2 since you ...
0
votes
0answers
23 views

Is the total length of the inner sheet of a two ply roll of toilet paper shorter than the outer sheet?

If you look at any individual square of two plies, each ply looks the same. But musn't the inner ply be shorter? Wouldn't the inner ply develop kinks if it was the same length as the outer ply? Or ...
0
votes
1answer
29 views

Electric Flux - Vector Components

How is $vcos(\theta)$ the perpendicular vector? I think I'm missing something fundamental in my trig and vector knowledge...
1
vote
1answer
89 views

Geometric Interpretation of Rotated basis of Hamiltonian and collective Dicke states

Suppose I start with a basis of states for a two spin-1/2 particle system, namely, $\{\left|\uparrow\uparrow\right\rangle, \left|\downarrow\downarrow\right\rangle, ...
0
votes
0answers
30 views

Why is space 3 dimensional and could it be different? [duplicate]

Is there any particular physical law or property which caused space to be 3 dimensional, and is there theoretical possibility of having more or less dimensions in physical space?
2
votes
2answers
483 views

Spacetime geometry around two black holes

For space-time geometry we all know images like he one below. But if I were to take a neutron star and put it right next to but not touching a black hole what effect would that have on the geometry of ...
2
votes
2answers
138 views

What is the connection between geometry of physical space and Hilbert space?

In Quantum Mechanis (QM), the dynamical variables are the (quantized) coordinates $x_j$ and their canonical conjugate $p_j = -i\partial_j$ with the commutation relation $[x_j,p_k]=i\delta_{jk}$ ...
0
votes
0answers
42 views

What's wrong with this calculation of the center of mass of a triangle?

Find the center of mass $(x_G,y_G)$ of a homogeneous triangle of mass $m$. Divide it into infinitesimal rectangles of width $dy$, length $x$, mass $dm$ and area $dA$. We have $d A = x dy $ ...
0
votes
1answer
60 views

Weight of an object at different angles [closed]

I'm trying to either find a calculator online or help with an equation to work out how much weight I'm lifting when I pick up my dirt bike off the floor [edit: when it's lying on it's side on the ...
6
votes
5answers
1k views

Gravitation is not force?

Einstein said that gravity can be looked at as curvature in space- time and not as a force that is acting between bodies. (Actually what Einstein said was that gravity was curvature in space-time and ...
5
votes
2answers
89 views

Poisson equation in 2D and 3D: geometrical reason for the difference

The Poisson equation in 3D shows a fundamental solution in 3D which decays with $\sim 1/r$, whilst in 2D it shows a much different decay $\sim -\ln r$. While in 3D not only the solution, but also its ...
4
votes
3answers
756 views

Where do I start with Non-Euclidean Geometry?

I've been trying to grok General Relativity for a while now, and I've been having some trouble. Many physics textbooks gloss over the subject with an "it's too advanced for this medium", and many ...
2
votes
0answers
40 views

Is there a theory that physically explains the origin equivalence principle / explains gravity via acceleration?

I've been thinking about how gravity could arise from a 4th dimensional spinning cylinder with space-time that has pliability like rubber (which I think is a generally accepted analogy). The ...
3
votes
0answers
227 views

Geodesic distance in de Sitter space

Consider $N$ dimensional de Sitter space embedded in $N+1$ dimensional Minkowski space: $$\eta_{\mu\nu}X^\mu X^\nu=1, \hspace{1cm}\eta_{\mu\nu}=\text{diag}(-1,1,\dots,1)$$ where I set $H=1$ for ...
1
vote
1answer
100 views

Snell's law demonstration

I'm a bit confused about a Snell's law demonstration. I'm reading Communication Systems from W. Tomasi. In the chapter 11, the author applies the Snell's law to θent, and -here comes my problem- he ...
0
votes
1answer
87 views

How do you calculate the focal point location of a circular mirror? [closed]

I'm trying to find the focal point and center of curvature of a concave mirror. Just using the radius for the center doesn't seem to work. I know C = 2f, but I'm not sure how to find f or C, given the ...
6
votes
1answer
109 views

Null Coordinates

I have a very basic question: what are the advantages of writing a metric in the null coordinates? Which extra insight do they provide? I've looked in Caroll's "Spacetime and Geometry" and Wald's ...
2
votes
1answer
91 views

Geometry, Group Theory, and Statistical Mechanics

During the course of my first statistical mechanics course we generally concerned ourselves with a bulk amount of our system and considered it in terms of a set of lattice sites that had a state. How ...
5
votes
3answers
394 views

Textbook on the Geometry of Special Relativity

I am looking for a textbook that treats the subject of Special Relativity from a geometric point of view, i.e. a textbook that introduces the theory right from the start in terms of 4-vectors and ...
105
votes
2answers
6k views

Why do sunbeams diverge even though the sun is much more than a few kilometers away?

Consider this picture of sun beams streaming onto the valley through the clouds. Given that the valley is only (at a guess) 3km wide, with simple trigonometry and the angles of the beams, this ...
6
votes
4answers
3k views

How far into space does one have to travel to see the entire sphere of earth?

Virgin Galactic will take passengers aboard SpaceShipTwo as high as 65 miles above the surface of the earth. But from this altitude, passengers will only be able to see a certain segment of the ...
1
vote
2answers
95 views

4- dimensional space geometry, what is the point? [closed]

I just read about the 4 dimensional space. I found a nice article describing how to visualize a 4-D object into our 3-D world. This is really fascinating. However, what's the point of researching in ...
0
votes
1answer
56 views

How do I calculate the right ascension of the points along the ecliptic at given elevations?

How do I calculate the right ascension of the point along the ecliptic nearest the sun at sunset and sunrise that is at a given altitude/elevation? For example, I'd like to compute the right ...
0
votes
1answer
113 views

How to calculate the horizon line of a satellite?

I need an equation to calculate a list of Earth-centered, Earth-fixed (ECEF) XYZ coordinates on the earth that represent the visibility limit of satellite given its ECEF XYZ coordinates. For any ...
1
vote
4answers
269 views

Why drops form spheres?

Consider a drop of water floating in an inertial frame in STP air (e.g., the ISS). Intuitively, the equilibrium shape of the drop is a sphere. How would one prove that? Is it equivalent to showing ...