Intuitively, just imagine picking a starting point on each of the circle and the knot. Now walk at different speeds such that you get back to the starting point at the same time.
In fact, that's what the knot is: a continuous, bijective mapping from the circle to the image of the mapping, i.e., the knot. (As the linked answer says.)
Edit: I see now that the article already has this intuitive explanation but with ants.
> Every knot is “homeomorphic” to the circle
Here's an explanation:
https://math.stackexchange.com/questions/3791238/introductio...
Intuitively, just imagine picking a starting point on each of the circle and the knot. Now walk at different speeds such that you get back to the starting point at the same time.
In fact, that's what the knot is: a continuous, bijective mapping from the circle to the image of the mapping, i.e., the knot. (As the linked answer says.)
Edit: I see now that the article already has this intuitive explanation but with ants.
A browser puzzle, based on "Knot Theory". Not sure I learned anything from playing this, but that was fun:
https://brainteaser.top/knot/index.html
This is relevant to my interests
At my age, I really have to restrain myself of these interests to spare my time for some other stuffs. :(
Teen mathematicians run circles inside you (if not around you).