Tagged Questions

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

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0
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1answer
913 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
359 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
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4answers
212 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
190 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
614 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
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0answers
103 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
191 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
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0answers
222 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
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4answers
3k 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
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2answers
778 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
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1answer
214 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: ...
2
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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
505 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
207 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
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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
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2answers
283 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
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0answers
130 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 $1737.1$ ...
11
votes
4answers
36k views

Does the rotation of the earth dramatically affect airplane flight time?

Say I'm flying from Sydney, to Los Angeles (S2LA), back to Sydney (LA2S). During S2LA, travelling with the rotation of the earth, would the flight time be longer than LA2S on account of Los Angeles ...
2
votes
2answers
256 views

The shape of the earth$\ldots$

....is an oblate spheroid because centrifugal force stretches the tropical regions to a point farther from the center than they would be if the planet did not rotate. So we all learned in childhood, ...
2
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0answers
92 views

Self-organizing maps

I'm currently interested in this subject but all I can see is about neural networks and I'm more interested on the Theoretical point of view: "how can a system (Lagrangian/Hamiltonian) alter it's ...
1
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1answer
219 views

Angular Diameter - Perceived size of Objects [closed]

I'm currently in the process of writing a 2.5D application that should display the perceived size of an object. For example, When I have a ball that has a diameter of 1 meter, how big would it appear ...
3
votes
1answer
113 views

How does holographic voxel density scale with holographic film metrics?

I'm trying to understand how one can generate bounds on the effective number of voxels (volumetric pixels) in a hologram, or information density, provided various metrics for the two-dimensional ...
15
votes
2answers
403 views

Generalized Complex Geometry and Theoretical Physics

I have been wondering about some of the different uses of Generalized Complex Geometry (GCG) in Physics. Without going into mathematical detail (see Gualtieri's thesis for reference), a Generalized ...
-1
votes
1answer
318 views

How to get new coordinates after a certain distance was travelled (while accounting for altitude)?

Suppose you start at a location identified by a set of coordinates (latitude, longitude) on Earth, then move a given distance in a given direction. What is the equation that gives you the coordinates ...
6
votes
1answer
416 views

Why are fractal geometries useful for compact antenna design?

While most of what I've read about fractals has been dubious in nature, over the years, I keep hearing that these sorts of self-similar (or approximately self-similar) geometries are useful in the ...
6
votes
2answers
646 views

Prerequisites to start the study of noncommutative geometry in physics

What are prerequisites (in mathematics and physics), that one should know about for getting into use of ideas from noncommutative geometry in physics?
5
votes
1answer
153 views

An astronaut and a vengeful pole

Imagine an astronaut floating in free-space with no significant nearby gravitational influences. The astronaut takes an arbitrarily thin pole of uniform density with length $l$ and mass $m$, orients ...
7
votes
1answer
391 views

The role of metric in the Wave Equation

The wave equation is often written in the form $$(\partial^2_t-\Delta)u=0,$$ involving the Laplace-Beltrami operator $\Delta$. However, the Laplace-Beltrami operator $\Delta$ is defined only in the ...
2
votes
1answer
198 views

Is it possible to mechanically isomerize an sp3 hybridized carbon center?

Imagine I have an sp3 hybridized carbon attached to four separate polyethylene chains. By pulling on the polyethylene chains in some manner, is it possible for me to mechanically isomerize the chiral ...
6
votes
1answer
545 views

Is C60 really the “most spherical” fullerene?

In the late 80's and early 90's, Smalley and others made claims that the C60 fullerene bearing icosahedral symmetry was the most spherical molecule known, and perhaps the most spherical that could ...
3
votes
2answers
783 views

Why was the truncated icosahedron (i.e. soccer ball) geometry chosen for the implosive lenses in the “Fat Man” atomic bomb?

Quoting from Wolfram Mathworld: " It is the shape used in the construction of soccer balls, and it was also the configuration of the lenses used for focusing the explosive shock waves of the ...
1
vote
2answers
855 views

How to deduce this free body diagram?

Can someone provide a trigonometry/geometry insight to deduce the angle of the plane is the same as the angle of the component of the weight?
1
vote
1answer
294 views

Calculating angles for tetrahedral molecular geometry

Let's say I have a molecular like CH3F (i.e. fluoromethane), and I'm able to measure the angle (theta) between the C-H bonds. Provided (theta) what is the angle between the C-F bond and the C-H ...
1
vote
2answers
4k views

The resultant of two forces acting at any angle?

I am studying about forces as vectors. And they give me this equation: $c^2 = a^2 + b^2 - 2ab \cos C$ Can anybody explain me the second part of the equation? I perfectly understand $c^2 = a^2 + b^2$ ...
4
votes
2answers
262 views

Can the electroweak/strong forces, and/or quantum mechanics be thought of as geometric?

Can the electroweak and strong forces be written as geometric theories? - Why and why not? Can quantum mechanics in general? For example, the Kaluza-Klein theory explains the electromagnetic field ...
2
votes
1answer
2k views

How to calculate the projected area at different angles/vectors?

Please help me with the following. I want to know if there is an equation/set of equations to find out the projected area of a (3-D) cube when it is oriented at different angles of attack to the fluid ...
4
votes
1answer
282 views

Relativistic space-time geometry

What subject (suggest book titles, etc.) should I study to get a clear grasping of hypersurfaces, 2-surfaces, and integration on them, mostly in special relativity (I'm not messing with general ...
10
votes
2answers
646 views

The Reeh-Schlieder theorem and quantum geometry

There have been some very nice discussions recently centered around the question of whether gravity and the geometry and topology of the classical world we see about us, could be phenomena which ...
5
votes
1answer
105 views

Is there an upper bound on the gauge group rank in F-theory compactifications on CY 4-folds?

It is known that in F-theory compactifications on CY 4-folds one can get gauge groups with very large ranks. The largest single factor* gauge group for compact CY 4-folds I found in the literature is ...
8
votes
3answers
329 views

Question about associative 3-cycles on G2 manifolds

Let $X$ be a manifold with $G_2$ holonomy and $\Phi$ be the fundamental associative 3-form on $X$. Let $*\Phi$ be the dual co-associative 4-form on $X$. Now consider a particular associative 3-cycle ...
11
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 ...
17
votes
3answers
4k views

Why can't a piece of paper (of non-zero thickness) be folded more than $N$ times?

Updated: In order to fold anything in half, it must be $\pi$ times longer than its thickness, and that depending on how something is folded, the amount its length decreases with each fold differs. ...