All Questions
7 questions
3
votes
0
answers
179
views
Dynamics of electrons on a sphere
Suppose one place $n$ electrons closely surrounding the north pole of a sphere, forming
a perfect planar regular $n$-gon:
Q1.
What will happen if the electrons ...
- 151k
15
votes
4
answers
888
views
Orthogonal mud cracks and Maxwell's reciprocal figures
Is there a succinct mathematical/physical explanation of why mud cracks
tend to meet orthogonally?
Wikipedia image in this ...
- 151k
9
votes
1
answer
3k
views
Oloid and sphericon: rolling develops entire surface
Wikipedia says that,
"The oloid is one of the only known objects, along with some members of the sphericon family, that while rolling, develops its entire surface."
Below are illustrations of ...
- 151k
14
votes
1
answer
1k
views
Egg-ovoid rolling down an inclined plane
I am seeking a mathematical analysis of an egg-ovoid rolling down an inclined plane,
for pedagogical reasons.
It is well-known folk lore that the shape of an egg prevents it from rolling away from
...
- 151k
8
votes
1
answer
787
views
The rain hull and the rain ridge
Rain falls steadily on an island, a 2-manifold $M$, which you may
assume, as you prefer,
is: (a) smooth, or (b) a PL-manifold, or perhaps even
(c) a
triangulated irregular network (TIN).
After a time,...
- 151k
11
votes
2
answers
1k
views
Floating polyhedra with fair equilibria
Is there a homogeneous convex polyhedron
which floats so that some subset (perhaps all) of its faces
is distinguished as "up" (above the water line)
in stable equilibrium, each face with equal ...
- 151k
7
votes
1
answer
815
views
Rolling a convex body: Geodesics vs. rolling curves
What are the curves of contact on a convex body $B$ rolling down an inclined plane?
Assume $B$ is smooth, and there is sufficient friction to prevent slippage.
Certainly, one can develop a geodesic ...
- 151k