All Questions
7
questions
7
votes
1
answer
527
views
Two arcs equal three arcs
(Gonna answer my own question, as is encouraged.)
To set the stage: an arc (or a Jordan arc) is a non-self-intersecting curve with two distinct endpoints. (For those who are familiar with topology, it'...
- 541
2
votes
1
answer
122
views
Make a topological torus-with-a-hole out of congruent squares that may share an edge or a vertex with other squares
Suppose we arrange, in 3-dimensional space, 8 identical solid cubes in space so they form a square-shaped ring (using a 3x3 arrangement of squares except for the one in the middle).
Its surface will ...
user76726
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
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
4
votes
2
answers
916
views
Join six five-link chains to form a circular chain
Join six five-link chains to form a circular chain.
To join two chains, you must cut, and then re-weld, a link.
The final number of links in the circular chain will be 30.
What is the minimum ...
- 1,788
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