# Tagged Questions

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

6answers
66k views

1answer
42 views

### New direction vector after collision of spheres [closed]

I have a volume in 3-space in which random spheres are spawned in motion. They have the following attributes to them: position known (in three axes) a direction vector (in three axes) a scalar speed ...
1answer
56 views

### 3D donuts and the centre of a black hole [closed]

I have been trying to imagine ways to visualise the gravitational field of the earth... It's near zero at the outer edges of the atmosphere, strong at sea level, strongest at the quarter point, then ...
9answers
4k views

### Why do objects appear smaller when viewed from a distance? [duplicate]

Yes, I know all about perspective (I'm an artist). I even have some basic knowledge of descriptive geometry. I know how it works. My question is more about why it works. I have a sneaking suspicion ...
2answers
595 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 ...
2answers
880 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 ...
0answers
406 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 ...
4answers
747 views

### How did “no prior geometry” father 50 years of confusion?

I've come across this quote attributed to Misner, Thorne & Wheeler from their book, Gravitation: Mathematics was not sufficiently refined in 1917 to cleave apart the demands for "no prior ...
4answers
437 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). ...
2answers
240 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 $[x_j,p_k]=i\delta_{jk}$ ...
3answers
538 views

### What is the exact meaning of homogeneity in cosmology?

I understand that, in general, homogeneity is the physical attribute of being uniform in composition (" of the same form at every point"), but I'm slightly confused when it is used in cosmology as ...
1answer
5k views

### How to calculate roll, yaw and pitch angles from 3D co-ordinates (Euler Angles)

I have digitized a video of a flying fly in a 3-dimensional space. At all instants I know the x, y, and z co-oridinates of the following points on the fly's body --- The points are my choice, and ...
0answers
43 views

### Can a value of “length, in meters” be attributed to a pair of ends which are rigid (but not at rest) to each other? [duplicate]

The definition of the SI base unit "metre" [1] doesn't seem to rule out explicitly that a certain value of "length, in meters" could be attributed to a pair of ends which are rigid to each other, but ...
0answers
66 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 ...
1answer
519 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 ...
1answer
155 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.
1answer
1k views

2answers
59 views

Let $\mathcal{S}$ represent the set of all points in physical space. Using measuring rods and assuming our use of them does not depend on time, we can establish a one-to-one correspondence between $\... 1answer 68 views ### Understanding Euler's rotation theorem According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible. If two rotations are forced at the same time, a new axis of rotation will ... 1answer 101 views ### What does the$a\$ stand for in this picture? (And some clarification)

$$I_{triangle} = \frac{b^3h-b^2ha+bha^2+bh^3}{36}$$ $$I_{total} = \sum^n_{k=1}(I_{triangle}+Md^2)_k$$ Source is here. I'm trying to understand the mass moment of inertia in order to create a 2d ...
0answers
33 views

### Get actual object size in mm using camera [closed]

How to get actual object size in mm when we know Object distance, focal length, image width in pixels and camera angle,