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Today I want to do a video response I respond to one of our own nucleophile videos because some time ago Brady made a video with our nucleophile composer Alan Stuart's it was a video it was 40 minutes long this video which was a test to our loyalty I think but in that video have you made it through Alan described composing one of his pieces about the Fibonacci sequence it involved the Fibonacci sequence, and he came up with a question as a challenge I guess to the number files I'm not quite good enough in laughs to be able to explain why that is maybe a number file will be able to explain like this I'm going to answer his question today so what Alan was doing was he was trying to involve the Fibonacci sequence in a piece of music so first let's have a recap of the Fibonacci sequence very important sequence in mathematics it's quite easy it starts with 1 then it's 1 again, and then you add the previous 2 value, so you add these two, and you get the next number, so that's just 1 plus 1 equals 2 then you add these two values that's 1 plus 2 equals 3 then you add the previous 2 that's 2 plus 3 equals 5, and you keep going in this way 6760 5 and so on okay, so there's the Fibonacci sequence and what Allan was doing was to turn this into a piece of music he was dividing by 7 he's going to divide all these Fibonacci numbers by 7 now you can't divide exactly by 7 most of the time, and so he looked at the remainder what you get left over when you divide by 7 that's one that's two that's three that's 5 now 8 when you divide 8 by 7 that's one with one left over that's what he wrote down then 13 divided by 7 is 1 with 6 left over 21 divided by 7 is 3 exactly it has zero left over, so you write zero, and we're going to continue in that way we're going to do all the remainders, so he wrote out all the remainders I need to make it a piece of music he turned to these remainders into musical notes, so it corresponds to notes, but he didn't notice a pattern when he did it curiously he found the pattern repeated it actually repeated every 16 numbers so here we go 1 1 2 3 5 1 6 0 6 6 5 4 – 6 1 0 1 1 2 3 and then the pattern repeated, and he asked what is this about is this a thing, and it is a thing it's actually called a Poisson Oh Pierre piano period is named after Leonardo Piano and if you think you haven't heard of him before are you wrong because that's just another name of Fibonacci, so this is a piano period now Allen chose seven to do this because that helps him make his musical notes if you'd pick any number though he would have got up here as well, but the length of the period would have been different, so he divided by 2/3 divided by 90 or 700 he would have got a cyclic pattern if we divide by 5 as an example this should be quite easy divided by 5 this is when I'll make a mistake 1 1 2 left over 3 divided by 3 5 plus 3 left over 5 divided by 5 is 0 0 left over 8 divided by 5 is a 1 a 3 left over would be a 3 4 left over that's one left over a 0 left...
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