All Questions
Tagged with topology mathematics
12
questions
3
votes
3
answers
630
views
rope - knotted or does not knot [closed]
The figure shows the shadow of a piece of rope on the ground, and you can't see which part is on which part; Suppose the rope is placed completely randomly. Now tighten the two ends of the rope to the ...
- 101
-2
votes
2
answers
322
views
Are three colors sufficient to color a map with convex regions?
The four color theorem states that no more than four colors are required to color the regions
of any map so that no two adjacent regions have the same color.
If all regions are convex (i.e. the region ...
- 12.3k
2
votes
2
answers
2k
views
Connecting 6 dots with 6 curves
Can you connect 6 dots with 6 curves, such that every pair of curves touch each other exactly once? Curves can touch anywhere at their interior or at the dots, and the whole thing must lie in the ...
- 36.3k
2
votes
0
answers
78
views
Fair and square island hopping [duplicate]
If amateur fiction is not your thing skip to the bottom.
As IP (Implausible Physics) expert for DREAM, the Department for Reckless Engineering and Advanced Megalomania you have been tasked by sheikh ...
- 6,285
8
votes
3
answers
1k
views
Drawing a complete graph of 5 nodes on a torus
A complete graph of $n$ nodes is a graph where every node is connected to every other node. It is known that one cannot draw a complete graph of 5 nodes on a piece of paper (plane) without any ...
- 36.3k
8
votes
0
answers
201
views
Is it possible to create a knot that is locked only when the rope is stretched?
Is it possible to create a knot that is stable/locked when the rope is stretched?
When the tension is relived the knot should open.
- 273
5
votes
1
answer
158
views
The grandest zoo in Appelhaken
In the magnificent country of Appelhaken there is a zoo. Not just any zoo, but a grand zoo, a magnificent zoo, called Appelhaken Grand Magnificent Magnificent Grand Grand Zoo.
In this zoo there are ...
- 5,364
8
votes
1
answer
198
views
The grandest bridge in Appelhaken [duplicate]
In the capital of the grand country of Appelhaken there is a plane garden containing four magnificent monuments. So magnificent are they that the country has a Law requiring that there must be a ...
- 5,364
7
votes
2
answers
376
views
Teacup geometry
Inspired by the three utilities puzzle from prog_SAHIL I'm now posting a similar puzzle that makes use of the topology of a cup with a handle:
The question is:
How many distinct points can you ...
- 5,948
10
votes
2
answers
3k
views
The three utilities puzzle
Here is a variant of the three utilities puzzle.
Famously, It is impossible to solve it on a plane paper (Euler's theorem can prove that). But can you solve it on a coffee mug?
...
- 5,363
14
votes
1
answer
1k
views
Ernie and the Underground Network
I haven't seen Ernie for a few weeks - he's been on holiday in the People's Republic of Kzijekistan (PRK). But yesterday I got an e-mail and thought I would share it with you. It reads as follows:
...
- 14k
0
votes
2
answers
727
views
Number of ways to fold a 2x4 map
M.Gardner in his book "Mathematical puzzles and diversions" states that the following 2x4 map
$$
\begin{array}{|c|c|}
\hline
1 & \phantom{1} & \phantom{1} & \phantom{1} \\
\hline
\...
- 16.3k