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

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11
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4answers
33k 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
254 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
votes
0answers
91 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
vote
1answer
214 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
112 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
385 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
313 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
406 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
591 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
388 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
537 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
765 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
795 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
292 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
259 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
277 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
626 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
328 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
2k 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. ...