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Bit 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 a
by zmmmmm 4y ago
Bit 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!
- desertraven 4y agoA bit misleading I agree. I suppose since prime numbers DO make these spirals, it's not inaccurate.
- smitty1e 4y agoWe expect patterns from quotidian integers. The seeming chaos of primes, in contrast, brings the intrigue.
- Bytewave81 4y agoIt's referencing the Math Stack Exchange question which asked the same question: https://math.stackexchange.com/questions/885879/meaning-of-rays-in-polar-plot-of-prime-numbers/885894 https://math.stackexchange.com/questions/885879/meaning-of-r...
- crdrost 4y agoI don't know, for me the fact that this gives you a visualization of a totient is really interesting. Another really interesting idea is to deliberately change the thing which you are rationally approximating; you don't have to rationally approximate π if you don't want to, that's just if you make steps of 1 radian. Make steps of q radians and you get the denominators for rational approximations of q/π. This is used in the golden spiral algorithm[1] to evenly-ish distribute points on a sphere, we choose the most irrational number q/π = φ, the golden ratio. Since all of its rational approximations suck, the spirals are as inoffensive as they can be. 1. https://stackoverflow.com/questions/9600801/evenly-distributing-n-points-on-a-sphere https://stackoverflow.com/questions/9600801/evenly-distribut...
- subroutine 4y agoSomething less interesting is testing what the polar plot looks like if you plot the angle in degrees instead of radians. Or, like in this plot, where I defined 10 degrees as exactly one complete turn around the circle: https://i.ibb.co/59k5dRT/polarplot.png https://i.ibb.co/59k5dRT/polarplot.png Slightly more interesting is what the primes look like when one complete turn is defined as 1, 2, 3... 30 units: https://i.ibb.co/F0GvrSY/polarplot2.png https://i.ibb.co/F0GvrSY/polarplot2.png
- onethought 4y agoThe 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_arithmetic_progressions https://en.wikipedia.org/wiki/Dirichlet%27s_theorem_on_arith...
- laserbeam 4y agoI found it insightful, not a let down. It says a lot about human nature and our biases towards spotting patterns that may be incomplete or inaccurate.
- euroderf 4y agoIn the absence of reliable telepathy, there is indeed survival value in spotting patterns in incomplete information.