Infinite Fractions - Numberphile
Matt Parker on Stern-Brocot numbers, fractions and rational numbers. More links & stuff in full description below ↓↓↓ Matt's book on Amazon US: http://bit.ly/Matt_4D_US Amazon UK: http://bit...
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I'm going to show you a number sequence which is better than the Fibonacci sequence. I know, I always say something is 'better than the Fibonacci sequence' because I don't really like it, but, in this case, this is something that is similar, but uses a different rule. So, the Fibonacci, just to remind everyone, you add 1 + 1, and that gives you 2... ...you add 1 + 2, that gives you 3... and each time, what you're doing is taking the previous two, and that gives you the next one, 5... then you take the those two and that gives you the next one, 8 then that gives you the next one, 13, so I'm adding them in pairs. I'm going to do exactly the same thing, but instead of just adding them, I'm also going to copy the last one...
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I'm going to show you a number sequence which is better than the Fibonacci sequence. I know, I always say something is 'better than the Fibonacci sequence' because I don't really like it, but, in this case, this is something that is similar, but uses a different rule. So, the Fibonacci, just to remind everyone, you add 1 + 1, and that gives you 2... ...you add 1 + 2, that gives you 3... and each time, what you're doing is taking the previous two, and that gives you the next one, 5... then you take the those two and that gives you the next one, 8 then that gives you the next one, 13, so I'm adding them in pairs. I'm going to do exactly the same thing, but instead of just adding them, I'm also going to copy the last one...
