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

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3
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2answers
167 views

Proof that a spherical lens is stigmatic

In geometric optics, we generally allow that, for example in the case of a convex lens, rays coming from a particular point get refracted towards another particular point on the opposite side of the ...
4
votes
1answer
454 views

How is the equation of motion on an ellipse derived?

I would like to show that a particle orbiting another will follow the trajectory \begin{equation} r = \frac{a(1-e^2)}{1 + e \cos(\theta)}. \end{equation} I would like to do this with minimal ...
0
votes
0answers
68 views

Water Stream from a Horizontal Surface

If water was projected from a flat surface where gravity was equal all over the surface. What would happen when the water fell in on itself? The water is in a continuous stream and is perfectly ...
3
votes
1answer
547 views

Nanotube chiral angle as a function of $n$ and $m$

I'm looking into nanotubes and I thought I'd assure myself that the basic geometry equations are indeed correct. No problems for the radius, I quickly found the known formula: $$R = ...
4
votes
1answer
125 views

How to assign coordinates to the elements of a flat metric space

Consider the metric space $(M, d \,)$ where set $M$ contains sufficiently many (at least five) distinct elements, and consider the assignment $c_f$ of coordinates to (the elements of) set $M$, $c_f ...
4
votes
1answer
136 views

Flat space metrics

This question concerns the metric of a flat space: $$ds^2=dr^2+cr^2\,\,d\theta^2$$ where $c$ is a constant. Why is it necessary to set $c=1$ to avoid singularities and to restrict $r\ge 0$? Thanks.
2
votes
1answer
131 views

Can we project a 4D world using 3D video technology?

Traditional movies, TV, etc, faithfully show our 3-dimensional world using 2 dimensions. So can we have a movie that shows a 4-dimensional world using 3D technology?
4
votes
10answers
1k 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 ...
2
votes
5answers
814 views

Do perfect spheres exist in nature?

Often in physics, Objects are approximated as spherical. However do any perfectly spherical objects actually exist in nature?
7
votes
2answers
472 views

Geometrical interpretation of the Dirac equation

Is there an intuitive geometrical picture behind the Dirac equation, and the gamma matrices that it uses? I know the geometric algebra is a Clifford algebra. Can the properties of geometric algebra, ...
5
votes
2answers
338 views

Space-time geometry and metric

I am confused in one question in general relativity, why we can always express a space-time geometry only by metric. It means a metric, which is just about distance in tangent space, can tell us all ...
0
votes
2answers
7k views

What is the characteristic length of a cylinder

I have a cold cylinder that is submerged in hot water and I need to find the convective heat transfer coefficient. I can do the whole process but I am stuck finding the characteristic length. I found ...
2
votes
0answers
60 views

Dirichlet's work on gravity in non-Euclidean space?

In the book The Norton History of Astronomy and Cosmology by the late John North I have found the following statement (page 514): "The German mathematician Lejeune Dirichlet studied the law of ...
2
votes
1answer
897 views

Tiling hexagons on a sphere surface

In attemopt to understand basic principles of non-Euclidean geometry and its relation to physical space, I am reading General Relativity by Ben Crowell. On page 149 there is a discussion of hexagons ...
1
vote
0answers
164 views

Inscribed and Escribe Squares and Circle [closed]

Assume a circle(a) of diameter d. Inscribe a square A centred in the circle with its diagonal equal to the diameter of the circle. Now escribe a square B with the sides equal to the diameter of the ...
3
votes
5answers
172 views

Why is the world sheet of an open string a cylinder?

I went to a lecture a few weeks ago and was told the following: The world sheet of a closed string is a normal, standing cylinder. The world sheet of an open string is a cylinder on its side. This ...
4
votes
1answer
223 views

How would one calculate the amount of water contained in a cloud?

So I was looking out the sky one day and I wondered how I would go about calculating how much water was contained in a cloud. I figured the following simple outline 1) We need to roughly know how big ...
2
votes
0answers
143 views

Getting the AdS metric from maximally symmetric spaces

I am familiar with the way we derive the form of the FRW metric by just using the fact that we have a maximally symmetric space i.e the universe is homogeneous and isotropic in spatial coordinates. ...
-1
votes
1answer
402 views

Internal forces in a truss and its geometry

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. ...
3
votes
1answer
161 views

How far does typical view of clouds/atmosphere extend?

The specific "sub questions" I'm asking are: When you are looking at clouds just on the horizon, how far away would they be? How wide (in km) is that total field of vision at roughly cloud height. ...
1
vote
1answer
239 views

The equation of a ferrofluid under a magnetic field?

What is the parametric equation guiding the geometry of a ferrofluid under a magnetic field? See also this Wikipedia page. From previous research, Maxwell's Equations and Navier-Stokes Equations were ...
4
votes
1answer
280 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 ...
3
votes
2answers
308 views

Shape of electric charges on sphere in equilibrium state

When electric charges of equal magnitude and sign are released on a regular sphere (and assume that they stick to the surface of the sphere, but they are free to move along its surface), what is the ...
2
votes
2answers
6k views

Determining the center of mass of a cone

I'm having some trouble with a simple classical mechanics problem, where I need to calculate the center of mass of a cone whose base radius is $a$ and height $h$..! I know the required equation. But, ...
2
votes
1answer
231 views

Why is physical space equivalent to $\mathbb{R}^3$?

Why is physical space equivalent to $\mathbb{R}^3$, as opposed to e.g. $\mathbb{Q}^3$? I am trying to understand what would be the logical reasons behind our assumption that our physical space is ...
1
vote
0answers
115 views

How far is the horizon, if a 2m tall man watches to the sea?

How far is the horizon, if a $r=2 m$ tall man watches to the sea? I have calculated that it would be even just about 6 km. if R = radius of earth( $6370 \cdot10^3$ m ). By pythagorean theorem we ...
2
votes
2answers
134 views

Stroboscope-and-telegraph problem

Narrative: Consider, in a suitably flat region, two straight lines which don't necessarily intersect. Let vector $\mathbf{x}$ point along one line, and vector $\mathbf{y}$ point along the other. Let ...
0
votes
2answers
6k views

How do you calculate angle of projection?

At what angle the projectile should throw with initial velocity v in order to reach distance d? discard the air resistance, only gravitation acts. So far I got the equations for horizontal and ...
5
votes
2answers
208 views

Is a semi-Euclidean space possible?

Does exists a geometry (3d for example) which is Euclidean in 2 dimensions (x and y coordinates) and non-Euclidean when the third dimension (z) is taken into account? In other words a space where it ...
5
votes
5answers
802 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 ...
0
votes
1answer
130 views

Find the real height of an object by eyes

I wonder if I can get the height of an object (tree or a building) with the knowledge of: The distance between me and the object? The apparent height of that object?
0
votes
1answer
844 views

How do I show that all Brillouin zones have the same volume?

I have read in a few books that all Brillouin zones have the same volume, and I can vaguely see how it works, but have not been able to think up a formal proof. Help?
3
votes
4answers
355 views

Formulation of general relativity

EDIT: I think I can pinpoint my confusion a bit better. Here comes my updated question (I'm not sure what the standard way of doing things is - please let me know if I should delete the old version). ...
0
votes
4answers
207 views

Isotropy and Noise

If you have a field which value is just Gaussian noise plus a constant do you call it isotropic? there is no preferred direction however it is not "the same" in all directions if "the same" means ...
4
votes
1answer
188 views

Euclidean Geometry in Classical Thought - Realization or Representation?

First post! :] This has been bothering me for a while now: [Taken from John J. Roche's "The Mathematics of Measurement: A Critical History"] When physico-mathematicians in the seventeenth ...
1
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0answers
84 views

Geometry as Physics [closed]

What would be good introductory and follow-up references to understand the close ties between physics and geometry. I'm a retired engineer with the math background to handle Shankar's Principles of ...
4
votes
2answers
594 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 ...
1
vote
0answers
102 views

Does the measure of proximity of two theories in “theory space” run?

From reading this article, I have learned that two effective QFTs can be very close together in the "theory space" appropriate to describe for example physics at the LHC scale, whereas the ...
2
votes
1answer
185 views

No attraction radially in an cylinder of spherical magnets

I have a set of small magnetic spheres the size of ball bearings. When many of them are built into a cylinder such that they are hexagonally packed, there is no magnetic attraction radially (between ...
0
votes
0answers
219 views

Extrinsic curvature versus Intrinsic curvature (Euclidean versus Riemannian)

Do we believe the universe has any extrinsic curvature at all? As far as I'm aware extrinsic curvature is only used in geometry/math to model the intrinsic curvature, correct? From the answers to ...
0
votes
4answers
2k views

What's the displacement between two opposite corners of a cube?

A cockroach is crawling along the walls inside a cubical room that has an edge length of 3 m. If the cockroach starts from the back lower left hand corner of the cube and finishes at the front ...
1
vote
2answers
739 views

Does a cycle (in Simple Harmonic Motion) have to equal 2π?

So, I search for the definition of cycle and I get this in Wikipedia: A turn is a unit of angle measurement equal to 360° or 2π radians (or ...). A turn is also referred to as a revolution or ...
0
votes
1answer
205 views

Simplifying some math for an ant-on-rubber-band problem

OK, I've been doing this problem for fun (it's a great problem, BTW!): http://www.physics.harvard.edu/academics/undergrad/probweek/prob76.pdf Here is the solution: ...
1
vote
2answers
3k views

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

When we are sitting in a moving train than nearby stationary objects appear to go backwards...in terms of physics we can use the formula velocity of object with respect ...
6
votes
2answers
488 views

Why are conformal transformations so prevalent in physics?

What is it about conformal transformations that make them so widely applicable in physics? These preserve angles, in other words directions (locally), and I can understand that might be useful. Also, ...
3
votes
1answer
206 views

What's a pseudo-rotation?

I'm sorry for this lexical, probably extremely elementary, question. But what is a pseudo-rotation? I just read this term for the first time, in the beginning of the 4th chapter book of CFT by Di ...
2
votes
1answer
137 views

Are there any clear and expressive plainword sense of metric tensor components?

Can the following groups of components of metric tensor can assigned a clear sense? https://docs.google.com/drawings/pub?id=1kVqkN1gT-a2fDy2S851l9iQKaMfaatCDo517OSZBHEo&w=467&h=228 I have ...
-5
votes
3answers
1k views

Should linear algebra and vector calculus from traditional courses be replaced with `geometric algebra`? [closed]

geometric algebra gives geometric meaning to linear algebra and much more. it can provide a coordinate free geometric interpretation of spaces. those who learn of ...
1
vote
2answers
279 views

Is it necessary to embed a 4D surface in 5D space?

Lets consider the line element: $$ds^2=dr^2+r^2[d\theta^2+\sin^2\theta d\phi^2]$$ There are three variables r,theta and phi. If we use a surface constraint like r=constant the number of independent ...
0
votes
0answers
127 views

How long until “final totality”? [closed]

It is given that the angular size of the Sun as viewed from Earth is $0.533^\circ$, the distance of the Moon from Earth at perigee is $3.633\times 10^5$ km, and the mean radius of the Moon is $1737.1$ ...