If this Collatz Conjecture video is one you find interesting, here's some related stuff! Alex Bellos and colouring Collatz on Numberphile - this shows in a bit more detail a specific visualization...
If this Collatz Conjecture video is one you find interesting, here's some related stuff!
Alex Bellos and colouring Collatz on Numberphile - this shows in a bit more detail a specific visualization of the Collatz conjecture. It's generally presented to market his maths colouring book; it's less in depth, but it is very approachable and understandable. Indeed, one of the most delightful things about this conjecture is how approachable it is for the majority of people.
Perhaps my favourite link (with caveat: it's not worth clicking on): a proof of Collatz that was deemed insufficient. It's been a while since I waded through this, but it is quite opaque and I don't actually recommend jumping into attempting to read a dense, 32-page, insufficient proof for a conjecture, but it is perhaps interesting to show the depth of maths required to even attempt the solution of such a simple to state problem. Edit: Maybe the second page is worth reading, so I'll copy it here:
Author’s note:
The reasoning on p. 11, that “The set of all vertices (2n, l) in all levels will
contain all even numbers 2n ≥ 6 exactly once.” has turned out to be incomplete.
Thus, the statement “that the Collatz conjecture is true” has to be withdrawn,
at least temporarily.
June 17, 2011
If this Collatz Conjecture video is one you find interesting, here's some related stuff!
Alex Bellos and colouring Collatz on Numberphile - this shows in a bit more detail a specific visualization of the Collatz conjecture. It's generally presented to market his maths colouring book; it's less in depth, but it is very approachable and understandable. Indeed, one of the most delightful things about this conjecture is how approachable it is for the majority of people.
David Eisenbud talks about Collatz on Numberphile (and some extra footage)- this is another basic overview, not as in depth as Veritaseum's, but again highly approachable.
Perhaps my favourite link (with caveat: it's not worth clicking on): a proof of Collatz that was deemed insufficient. It's been a while since I waded through this, but it is quite opaque and I don't actually recommend jumping into attempting to read a dense, 32-page, insufficient proof for a conjecture, but it is perhaps interesting to show the depth of maths required to even attempt the solution of such a simple to state problem. Edit: Maybe the second page is worth reading, so I'll copy it here:
I found this visualization quite impressive, though the lede is buried near the end.