All Questions
Tagged with classical-mechanics mg.metric-geometry
10 questions
25
votes
1
answer
7k
views
Hanging a ball with string
What is the shortest length of string that suffices to hang
a unit-radius ball $B$?
This question is related to an earlier MO question, but I think different.
Assume that the ball is frictionless.
...
- 151k
63
votes
8
answers
14k
views
Fair but irregular polyhedral dice
I am interested in determining a collection of geometric conditions that will guarantee that a convex polyhedron
of $n$ faces is a fair die in the sense that, upon random rolling, it has an equal $1/n$...
- 151k
33
votes
4
answers
3k
views
Does there exist a shot in ideal pocket billiards?
Assume you have one shot with the cue ball in pocket billiards (a.k.a. pool), with
the game idealized in that no spin is placed on the cue ball in
the initial shot, all collisions between billiard ...
- 151k
21
votes
1
answer
1k
views
Which convex bodies roll along closed geodesics?
An ellipsoid could be rolled (without slippage) on a horizontal plane so that its point
of contact traces out a closed geodesic on its surface:
...
- 151k
14
votes
2
answers
1k
views
Polygonal billards programs
I'm looking for software that will give billiard trajectories in arbitrary plane polygons. After much work I was able to produce this figure.
(source)
It was a good exercise, but at this point I ...
- 22.8k
10
votes
1
answer
495
views
Ping-pong progress through a quincunx
A quincunx or
Galton board consists of
staggered pegs from which ping-pong balls bounce and eventually display
a binomial / normal distribution in catch-bins. I am wondering if the
downward progress ...
- 151k
9
votes
0
answers
369
views
Periodic orbits of a spinning ball in a square
Periodic orbits of a billiard ball bouncing in a square have been well-studied.
I am seeking similar analysis of what is sometimes called a rough ball, one
whose high friction causes it to pick up ...
- 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
7
votes
0
answers
336
views
Hanging a cube with string
This is a variation on a (much) earlier MO question, Hanging a ball with string.
Here instead the task is to arrange a net of string to hang
a unit cube. Assume:
The string is inelastic.
There is no ...
- 151k
5
votes
0
answers
166
views
Pocket billiards with balls in general position
There were at least two earlier MO questions about ideal pocket billiards.
(Ideal: frictionless, perfectly elastic collisions.)
Perfectly centered break of a perfectly aligned pool ball rack.
Does ...
- 151k