The 3x+1 Problem [video]
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The 3x+1 Problem [video]
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Re: The 3x+1 Problem [video]
#2This seems like a GREAT problem to suck kids into math and computer science. It’s simple enough to explain to an average 12yo, but has enough depth to still be vexing them after they complete their maths PhD. And it’s natural motivation for them wanting to learn basic programming so they can test billions of examples.
Re: The 3x+1 Problem [video]
#3This seems like a GREAT problem to suck kids into math and computer science. It’s simple enough to explain to an average 12yo, but has enough depth to still be vexing them after they complete their maths PhD. And it’s natural motivation for them wanting to learn basic programming so they can test billions of examples.
I was at the beginning of my highschool years and being a poker nerd I heard about Andrew Beal, an amateur mathematician and poker player. He offered a prize for a proof of Beal's conjecture, I was learning Pascal and decided to write a program to find a counterexample. Searching different optimization techniques I found a blog where a guy was trying to win the prize for his little girl. After some years, in college (CS) I learned that the guy was Peter Norvig. Great rabbithole.
Re: The 3x+1 Problem [video]
#4I recommend Veritasium, his videos are quite good. This one probably has good and useful visualizations but I was doing the cleaning while listening to it so I missed that. Still possible to follow without watching though.
Re: The 3x+1 Problem [video]
#5After watching this video, how many of us wrote a program to see if we could just randomly find a case which didn't converge? I wrote one, but of course, the program didn't prove the 3x+1 problem wrong.
Re: The 3x+1 Problem [video]
#6I first came across this problem in Gödel, Escher, Bach in the 80s sometime when I first read it. Hofstadter does warn the reader to bring lots of paper when trying 27. Did I listen? Of course not.
Re: The 3x+1 Problem [video]
#7After watching this video, how many of us wrote a program to see if we could just randomly find a case which didn't converge? I wrote one, but of course, the program didn't prove the 3x+1 problem wrong.
Hahahaha I came here to see if anyone else did this!
I didn’t think that a bit of coding was going to outpace hundreds of years of genius mathematicians - but a few minutes coding was a cheap price to pay to satisfy that ceaseless curiosity
Re: The 3x+1 Problem [video]
#8After watching this video, how many of us wrote a program to see if we could just randomly find a case which didn't converge? I wrote one, but of course, the program didn't prove the 3x+1 problem wrong.
I wrote one many years ago as part of going through (I think) the project Euler series. No hope of actually solving it ofc. It's a fascinating problem because it just seems so simple. I wouldn't be surprised if it turns out in the end that it's connected to some other seemingly unrelated (lack of) order in mathematics like prime numbers or whatnot.
Re: The 3x+1 Problem [video]
#9After watching this video, how many of us wrote a program to see if we could just randomly find a case which didn't converge? I wrote one, but of course, the program didn't prove the 3x+1 problem wrong.
Likewise, but more as a way to experiment with a big integer crate for rust.
Re: The 3x+1 Problem [video]
#10After watching this video, how many of us wrote a program to see if we could just randomly find a case which didn't converge? I wrote one, but of course, the program didn't prove the 3x+1 problem wrong.
I wrote one years ago, and whenever I got bored I'd revisit it and tweak certain things. Weird thing is, I felt like I found a reproduceable pattern in how numbers converged. Unfortunately I haven't been able to effectively communicate the pattern and I don't have the mathematical know-how to google for it.