The spark
August 18, 2008 at 11:54 pm | In Maths, number crunching | Leave a CommentIf you want any insight into how Mathematicians work, I will lead you on the merry train of thought I had tonight:
1. The square root of 2 is irrational (you can’t write it as a fraction like 1/2), I haven’t proved that in a while..
2. But why stop there? If √2 is irrational shouldn’t the cube root be irrational? Turns out it is.
3. In fact, shouldn’t any root of 2 be irrational? Yup.
4. But why stop at 2? What about proving parts 1-3, replacing “2″ with “3″? Yay, that works too.
5. Maybe it works with 4. Oh no, the square root of four is 2! It all falls down! Why not see if 1-3 apply for all the primes? By gosh it does, the nth root of any prime number (n>1) is indeed irrational.
6. I think that maybe I should point out that 1 is not a prime number (it’s actually a unit, fact fans), because people are often misinformed.
7. What about non-integer* rational numbers? Can I raise them to the nth power to get an integer? Golly gosh, I cannot, and this proves everything I was trying to prove already.
8. Maybe there’s another, broader way I can show that √2 is irrational? Nah, sod it, it’s time for bed.
* an integer is an element of the set Z, which is the ring of numbers generated by adding or subtracting 1, or whole numbers for those of you who speak english.
Now if only this stuff was actually any use for my thesis, I might actually get something useful done. But it is beautiful anyway.
Green
June 16, 2008 at 5:24 pm | In Flat life, Maths, number crunching | Leave a CommentOne aspect of flat living that is unavoidable is the designation of washing-up duties. We are currently in the process of trying to figure out the best way of allocating said duties for next year’s flat. There will be five of us, and the object is to design a flexible yet rigorous system to stop dishes piling up every night.
It occured to me that this is a highly mathematical problem, requiring some kind of neat optimization given the initial conditions of how many people are in the flat, expected amount of dishes and also number of other things that will need regular cleaning, such as the kitchen, the bathroom and the hallway, not to mention taking the bin out and recycling. Thus, my side project over the next few days will be to devise an algorithm for optimal sharing of cleaning duties given these conditions. I’m sure you’re all excited as to what I’ll come up with, so stay posted. If you have any ideas, please share them. “Buy a dishwasher” is discounted.
EDIT: In over 75 posts, this is the first I have posted in “Maths”. That I have resisted this long is perhaps just short of miraculous.
Number crunching #1: the supermarket
March 21, 2008 at 4:06 pm | In number crunching | 1 CommentI saw some odd things happening in the supermarket recently. Of course that assumes that amusing number oddities can “happen”.
The first concerned tuna. Cans of tuna were 56p each, but you could buy a four-pack for £2,25. To save you having to do the maths, 4 cans bought “loose” cost £2,24 , thereby making this less expensive than the four pack by a penny. Economies of scale dictate that buying in bulk means that everything is cheaper on average, so this took me somewhat by surprise.
But then I thought that perhaps Sainsbury’s was being a bit clever, for when you buy the four pack, you get an unnecessary extra bit of packaging (a plastic wrapper), so that extra 1p goes towards that. Pay less, get less packaging! And as we all know less packaging=good, so perhaps Sainsbury’s is trying to help the environment by stealth. However I doubt this, since most people wouldn’t bother working out the difference that buying them loose would make, much less worry about the extra penny. But if that is what they want to do, then kudos.
The other thing was Sainsbury’s “reduced sugar reduced salt” baked beans, which, it turns out, seem to be less healthy for you than the “standard” version. They contain a whole 2 (yes TWO) extra calories, not to mention 0,2g of saturated fat. On the upside they have 3,6g less sugar and 0,5g less salt. Mind you, two calories is but 0,1% of your RDA and the saturated fat counts for about 2% whereas the salt reduction is a whopping 5%.
In any case, the mistake that I made was to assume that somehow the “reduced” beans were “healthier” and although they never said they were, this is presumably what they want people to believe. Well I say that, but they are both the same price, so it’s not like they make extra money from it.
Finally, I came to the realisation that “half price” is a vastly better offer than “two for the price of one”. Ostensibly they are very similar, but the good thing about half price is that the initial financial outlay is lower i.e. to take advantage of the offer you only have to pay for half a thing rather than a whole thing. The other aspect is that you can just buy one thing, whereas if a free thing is forced upon you, you may not end up using it, particularly if it is perishable, so that will just have been a waste of packaging, as well as your money if you only bought the thing for the offer. BOGOF stationery, however, is great.
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