All Questions
Tagged with classical-mechanics discrete-geometry
6 questions
30
votes
5
answers
9k
views
Six yolks in a bowl: Why not optimal circle packing? [closed]
Making soufflé tonight, I wondered if the six yolks took on the
optimal circle packing configuration.
They do not. It is only with seven congruent circles that the optimal
packing places one in the ...
- 151k
4
votes
0
answers
158
views
On moments of inertia of planar and 3D convex bodies
The following observation can be readily proved using the perpendicular axes theorem and intermediate value theorem: "Given any planar figure C, through any point on it, there is at least one ...
- 5,979
33
votes
3
answers
5k
views
Do bubbles between plates approximate Voronoi diagrams?
For example, soap bubbles:
Image from UPenn:
"A 2-dimensional foam of wet soap bubbles squashed between glass plates, after 10 hours ...
- 151k
22
votes
4
answers
2k
views
Non-chaotic bouncing-ball curves
I was surprised to learn from two
Mathematica Demos by
Enrique Zeleny that an elastic ball bouncing in a V or in a sinusoidal channel
exhibits chaotic behavior:
(The Poincaré map ...
- 151k
23
votes
1
answer
524
views
Tying knots via gravity-assisted spaceship trajectories
Q.
Can every knot be realized as the trajectory of a spaceship
weaving among a finite number of fixed planets, subject to gravity alone?
To make this more ...
- 151k
3
votes
0
answers
122
views
A taut string of equilateral triangles
Let $T$ be a unit edge-length equilateral triangle composed of three cylinders each
of (small) radius $r>0$. (By "small" I mean approximately $< 0.1$.)
Think of $T$ as a physical, rigid triangle,...
- 151k