The geometry tag has no wiki summary.
8
votes
6answers
1k 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 ...
2
votes
1answer
185 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 ...
7
votes
4answers
9k 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 ...
12
votes
2answers
173 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 ...
3
votes
11answers
764 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 ...
6
votes
1answer
285 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 ...
4
votes
1answer
102 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.
3
votes
1answer
158 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 = ...
3
votes
1answer
166 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 ...
-1
votes
1answer
1k views
how to calculate the angle in the x-y, y-z, x-z plane given only 3D vector direction and magnitude? [closed]
Please help me solve this. I have been thinking of all sorts of ways to solve this but can't figure out how :(. Ok here's the problem:
I am given a three dimensional velocity vector (i know the ...
