Mobius Strip
For 50 years mathematicians wondered, what is the shortest strip of paper needed to make a
mobius strip?
Richard Schwartz, a mathematician, solved that.
The shortest possible mobius strip has an aspect ratio of a width of 1 and a height of root 3 or
about 1.73
Topology:
What is topology?
It’s a branch of mathematics concerned with the properties of a geometric object that is
preserved under continuous deformations.
It’s the study of shapes and spaces but without worrying about distance and angles, so geometry
but cooler!
We can stretch, twist, crumble and bend objects without changing it’s main structure, more to
understand the features that we’re interested in without breaking it.
It has applications in areas like biology, computer science, physics, robotics and also games and
puzzles.
A key concept in topology is the idea of spaces which are homeomorphic to each other.
In topology, the word space is general it could mean anything from a human or a line.
Homeomorphic, means same form, so two things could be homeomorphic if they are the same
form apart from bending or squishing.
So, in the world of topology a donut and a mug are the same thing. Can you tell me why?
Well basically that’s because they both have one hole, and if we take the logic of bend and
stretch without breaking then technically they’re the same thing and therefore homeomorphic.
Manifold: is anything that can exist in any dimension
The grandfather paradox:
The grandfather paradox is usually used to disprove the existence. The idea is that if you were to
travel back in time to kill your grandfather before he had your mother, then it would be
impossible for your mother to have been born and therefore you wouldn’t have been born to
travel back in time and kill your grandfather in the first place. AND SO IT’S A PARADOX!
If you think about it, because of this potential logical inconsistency, time travel cannot exist.
BUT a way to solve this, is by using a mobius strip.
The paradox suggests that a cause is eliminated by its own effect, thus preventing its own cause
and essentially becoming reverse causation.
Philosophers and physicists began seriously thinking about the grandfather paradox when Albert
Einstein's theories of special and general relativity suggested that time travel may be a theoretical
possibility.
The Klein bottle:
The mathematics of otherwise simple-looking objects can be surprisingly perplexing