I’m hardly a math genius, but isn’t this basically because he’s using polar coordinates, where nearly any trend is going to look like curves and spirals?
Hence, the video...
Why do prime numbers make these spirals? (2019)
21–30 of 141 posts
Re: Why do prime numbers make these spirals? (2019)
#22What's the commentary on prime numbers currently? Is it expected that there is some unfound pattern to them? Or will they always remain elusive?
Elusiveness is subjective, but there's certainly plenty of patterns to be found (though, to be fair, what constitutes a pattern might also be subjective). You should check out Terence Tao's blog [0], he's not only one of the most prominent mathematicians in the field but he's also excellent at explaining things. These slides [1] for example don't require any background in math.
[0] https://terrytao.wordpress.com
[1] https://www.math.ucla.edu/~tao/preprints/Slides/primes.pdf
Re: Why do prime numbers make these spirals? (2019)
#23I thought this video was fantastic. Just a great intro and example of how "playing" with numbers and visualizations can help you understand deeper, more profound concepts.
For commenters saying "well, doesn't anything in polar coordinates end up like spirals?", do yourself a favor and watch the video. He says as much pretty early on that yes, any plotting of the integers like that will look like spirals, but goes into excellent detail in my opinion explaining why the specific patterns you see with prime numbers are as they are.
Re: Why do prime numbers make these spirals? (2019)
#24Re: Why do prime numbers make these spirals? (2019)
#25I suspect most functions would make a spiral on a polar graph if you zoomed out far enough.
Well, except as the video points out - primes don't make spiral when you zoom out far enough, they make a "rays" pattern... which then if you zoom out even further becomes a much gentler spiral.
Re: Why do prime numbers make these spirals? (2019)
#26Bit of a let down when they reveal that plotting integers in general results in the same spiral pattern as primes. So naturally primes as a subset of integers also produce spirals. Seems the title is a bit misleading!
The whole point of the video is that asking these kinds of questions even if at first they seem kind of silly or arbitrary often lead to really interesting observations. In this case: Dirichlet's theorem on arithmetic progressions [0]
[0] https://en.wikipedia.org/wiki/Dirichlet%27s_theorem_on_arith...
Re: Why do prime numbers make these spirals? (2019)
#27Re: Why do prime numbers make these spirals? (2019)
#28Re: Why do prime numbers make these spirals? (2019)
#29> These patterns are certainly beautiful, but they don't have a hidden, divine message about primes. As far as we know, for now.
Yeah, it's clearly someone's fingerprint:
Re: Why do prime numbers make these spirals? (2019)
#30Earlier quoted context omitted.
Does it matter for math articles? It’s not like the math has changed in 4 years.
I double checked, 1+1 is still 2 in ios 16.3.1
Sometimes it's hardware