# Tagged Questions

**11**

votes

**5**answers

502 views

### To what extent does trajectory determine gravity sources?

Suppose one has in-hand an accurate time-space trajectory in $\mathbb{R}^3$ of a (small) body,
say an asteroid or satellite—effectively a point.
To what extent does this trajectory determine the ...

**7**

votes

**1**answer

299 views

### Generalizing a square wheel to a body rolling on a surface

A square wheel rolling on a catenary road maintains the wheel center at a fixed
height, a well-known construction previously discussed on MO
(e.g.,
"Generalizing square wheels rolling on inverted ...

**10**

votes

**0**answers

373 views

### Functions approximated by rolling epicycle curves

Imagine a decreasing sequence of (positive) radii $r_1 > r_2 > r_3 > \cdots$
and a series of nested circles $C_1 \supset C_2 \supset C_3 \supset \cdots$
with these radii,
initially each ...

**10**

votes

**2**answers

571 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 ...

**3**

votes

**1**answer

559 views

### Which motion is exclusive in 3D or higher dimensions?

Hi guys,
I have a simple question
Linear movement can be found in 1D, 2D and 3D world objects
Rotation can be found in 2D and 3D world objects.
Now, are there any kind of motion can only be found ...

**43**

votes

**8**answers

5k 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 ...

**28**

votes

**4**answers

2k views

### $\exists$ 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 ...

**14**

votes

**1**answer

1k 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 ...

**21**

votes

**3**answers

2k views

### Parabolic envelope of fireworks

The envelope of parabolic trajectories from a common launch point
is itself a parabola.
In the U.S. this weekend many will have a chance to
observe this fact direcly, as the 4th of July is ...

**6**

votes

**2**answers

1k views

### Generalizing square wheels rolling on inverted catenaries

It is not uncommon to see in a science museum a bicycle with
square wheels that rides smoothly over a washboard-like
surface made from inverted catenary curves (e.g., at the Münich museum).
The ...

**11**

votes

**4**answers

889 views

### When sticks fall, will they weave?

Imagine $n$ $z$-vertical sticks uniformly spaced around a unit-radius circle in the $xy$-plane.
At $t{=}0$, each is randomly $\epsilon$-perturbed from the vertical, and they fall under
the influence ...