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Whats more fun with this is to then ask what people think "raising e to the power of ..." actually means. Everyone thinks they know what powers mean, until you ask what it means to take something to an irrational power. What does 2 to the root 2 mean for example? Your calculator will happily give a numerical answer, but what does it mean? It's a fun story to tell.
There's a whole beautiful set of ideas linked together - powers, integration, logs, and you need them all to make sense of what's going on.
Little Jack Horner sat in the corner trying to work out pi. He said, "It's minus the log of minus one all raised to the power of i".
The Secret Rules of Modern Living: Algorithms
http://www.bbc.co.uk/iplayer/episode/p030s6b3/the-secret-rules-of-modern-living-algorithms
on iPlayer for 19 days, until the inevitable repeats bring it back.
(I wonder what algorithm controls Auntie Beebs decisions?)
No doubt, I agree that we have a ways to go. We can't even figure out how to factorise large numbers efficiently, which is the method by which our bank accounts stay secure
also you're welcome, i love maths (actual maths, what we have been talking about, not pre-A level rubbish) and there are topics which i could talk for a very long time about.
one of them is the most beautiful formula in existence in my opinion, the Euler product formula
also you're welcome, i like maths (actual mathematics, not the rubbish you're taught in high school) a lot so it's something i can talk a lot about.
the most beautiful formula in existence in my opinion is
which looks confusing right? well there are two huge symbols, one on each side, which mean two different things. the one on the left means 'SUM from 1 to infinity with n' and the one on the right means 'take a PRODUCT over all prime numbers p' of the things next to the symbols. so what this formula looks like without the notation is
1/(1^s) + 1/(2^s) + 1/(3^s) + 1/(4^s) + ... = 1/(1-2^(-s)) * 1/(1-3^(-s)) * 1/(1-5^(-s)) * ...
where * is multiply, and ^ means 'to the power of'.
why is the euler product formula the most beautiful formula in existence? it takes a sum over all numbers on the left hand side, (as in, n runs over 1, 2, 3, 4, 5, ...) and a product over all PRIME NUMBERS on the right hand side (p runs over 2, 3, 5, 7, 11, 13, ...)... how incredible is that? prime numbers are seen as being mysterious most of the time and we don't fully understand why they are distributed the way that they are (the Riemann hypothesis is a problem relating to these things, and you get $1 million if you solve it) but here we have a formula which EQUATES some kind of relationship between a sum over all natural numbers and a product over all prime numbers. how cool is that?
awesome. maths yeeeee
also you're welcome, i like maths (actual mathematics, not the rubbish you're taught in high school) a lot so it's something i can talk a lot about.
the most beautiful formula in existence in my opinion is
which looks confusing right? well there are two huge symbols, one on each side, which mean two different things. the one on the left means 'SUM from 1 to infinity with n' and the one on the right means 'take a PRODUCT over all prime numbers p' of the things next to the symbols. so what this formula looks like without the notation is
1/(1^s) + 1/(2^s) + 1/(3^s) + 1/(4^s) + ... = 1/(1-2^(-s)) * 1/(1-3^(-s)) * 1/(1-5^(-s)) * ...
where * is multiply, and ^ means 'to the power of'.
why is the euler product formula the most beautiful formula in existence? it takes a sum over all numbers on the left hand side, (as in, n runs over 1, 2, 3, 4, 5, ...) and a product over all PRIME NUMBERS on the right hand side (p runs over 2, 3, 5, 7, 11, 13, ...)... how incredible is that? prime numbers are seen as being mysterious most of the time and we don't fully understand why they are distributed the way that they are (the Riemann hypothesis is a problem relating to these things, and you get $1 million if you solve it) but here we have a formula which EQUATES some kind of relationship between a sum over all natural numbers and a product over all prime numbers. how cool is that?
awesome. maths yeeeee