The symphonies between numbers and notes in one problem. If you don't like maths, click on this and I guarantee that you'll be more interested in it than you were before.
This video came up a bit late, even though it was published years ago, and I feel like if I was to have seen it a couple months ago, I wouldn’t have clicked on it because sequences didn’t really interest me, but now, me having been on a noble quest for a deeper understanding and knowledge of what the Fibonacci sequence is (I watched a video on that too, I’ll post the analysis soon) I wondered, what other interesting types of sequences are there? Then I came across this one: The Recamán sequence.
In this video, a person on the Numberphile sequence describes the Recamán sequence as “really interesting and fun.” It was invented by a teacher in Columbia called Bernardo Recamán who came up with it. The rule is "atrás siempre". Always back, but if you can't go back because the number has already been used then you got to go forward. So if you had it on a number line, you could have zero and you wouldn’t be able to add or subtract anything because… zero is zero, so then you move onto one, and you can’t move one back because then you’ll land on zero. Then two, can you go back two? No because you’ll end up on zero and that been used. It’s kind of hard to explain it if you haven’t got a number line to actually show it but if you had to see it on a number line it would look like this.
So kind of like someone really messed up a line graph.
But if you wait, you can see that if you continue with the sequence, you get something that looks kind of like this. *if it was plotted on a number line*
And this kind of drawing has been used all the time, and not just in maths, but even in art, which I thought was really interesting! In the video, he says this about the pattern: “It's standardly beautiful, but with a little bit of the unknown.” But if you look at the tiny little circle at the start, close to the left of the page, you can see that it is pretty much identical to the little circle that he drew on the number line, except his are a little more like a half oval. So, if you look at it that way, the number line would be the line drawn across the photo above in blue, or somewhat similar to that.
But where Alex had first heard of this sequence is from Neil Sloan, the owner of the online encyclopedia of sequences, and Alex had asked Neil which sequences he liked most and the first Neil answered was the Recamán sequence, because “it has this interesting clash between order and chaos.”
So I decided to visit this encyclopedia and look at the Recamán sequence, but what really surprised me was this button underneath it saying “listen.” And what happens if you press that button is, it’ plays the sequence as if it was taking the different segments of it on a number line as octaves, like 48 as one octave then 48 as the next, and plays it as if it’s a piece of music! It’s linked below if you copy and paste it into google.
So if you’re looking for a sequence that combines art, music, and mathematics, I highly Recamán-d this one! See you next time,
-thestudentsblogger
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