Mathematics

  I think i like maths. Strange thing to say but then i wonder sometimes if the only reason i think about it is as a means of defense against boredom and insanity. Anyway i've created this page as a kind of long-term project which i can keep adding to as i have more thoughts or make more discoveries be them already discovered by others (likely) or yet undiscovered (less likely - perhaps impossible).

Useless Facts

 This one occured to me the other day. A particularly long stint of thinking about numbers. My birthday is the 11th of March 1974. This year (2003) i became 29 on off course 11/3/2003. What's so special about that? 29, 11, 3, and 2003 are all prime numbers (i'm fairly sure 2003 is - i need to download a primality program. What's so special about that, you ask? Not a great deal i suppose but how many years in my life will all these numbers be prime ? 1997 seems prime. I would have been 23 so there's another (if 1997 is prime), but i bet there aren't/won't be many more.

 This one's a nice one. When you square a number greater than 1 the result is always a bigger number. 1 squared is 1. 2 squared is 4. 3 squared is 9 right? The gaps (differences) are 0 (between 1 and 1), 2 (between 2 and 4) and 6 (between 3 and 9). That's 0, 2 and 6. Is there a number whose square is exactly 1 bigger than itself? Should be a number between 1 and 2 if you look at what we've seen so far. What's the number? It's called the golden mean, or the golden ratio. It's exact value (you can work it out by fiddling with a quadratic equation) is (root2 + 1)/2. To 9 decimal places it's 1.618033989. So it's square is 2.618033989. I'm not sure if the reason i find this cool is due to a passion for maths or rather because i was bored one day and figured it out. Can't remember :)

Things i'd like to find out

 I'm no Professor of maths (maybe one day) but i'm sure many a respected mathematician would agree that one of the greatest things about maths (or math - which is right?) is that there's an (IMHO *almost certainly*) infinite scope for discovery. Anyone, like me for example can attempt to plunder the realms of the mathematically unknown.

  Here's a few things i've been wondering about over the years;

1. The quest for an odd perfect number.

 This still (i'm pretty sure) unsolved problem got me doing a lot of work. I've found out about it by reading a book called "Fermat's Last Theorem" by Simon Signh (i know that's not how you spell his surname - oh well) which i borrowed from a mate called Domonic (Dominic?) Hopkins whose has a first in maths and physics. It's not really a problem. More like a unanswered question; Is there a *odd* perfect number? What's a perfect number you say? Search for them on google (it's not very complicated, i'm just feeling lazy :|).

 Anyway i got to work with only an A-level maths for a background (a grade A though, i'll have you know :). How far did i get? Not very but i did get somewhere. I managed to prove that there cannot be a number which has *all unique* prime factors which is a odd perfect number. Woohoo!
 I later went to the UEA (University of East Anglia) had a look at a few books and was fairly disturbed by what i saw. I realised i was well out of my depth. I simply don't have the background to understand what work has already been done - what common understanding has already been established - by the mathematical community so far. I'd like to understand what has already been worked out though..... ......i need a maths degree!

2. Pentominoe packing.

 For my birthday this year i bought myself a box of plastic pentominoes from a games shop in the city. I was surprised because i thought they weren't all that well-known. In fact, as i've learnt they are quite popular - there's loads you can do with them - puzzles, games etc... . I've been fiddling around with them a bit. When i first got them i did a bit of maths in my head - that is i thought since there are 5 cubed units to each pentominoe, and there are 12 of them, the whole set must have 12*5 = 60 cubed units. I was pleased to find out that 60 has 3, 4 and 5 as it's factors ie 3*4*5 = 60 which means in the real (physical) world that you could definitely chop them all up into units and make an oblong of dimensions 3*4*5. The obvious curiosity is whether or not the twelve pentominoes can be arranged into this oblong as they are.
 I was at first pleased to find that one of the 'challenges' in the booklet that came in the box is to build such an oblong. I was later dismayed to find that the diagrams that are there, i think to aid one build it, don't actually make any sense. I asked my clever friend Ellis to have a go and he came upon the same problem. So as far as I'm concerned the oblong can't be put together in this manner but it may none-the-less be possible to do it another way.
 Not that i'm the one to judge or gauge how difficult a problem is(i use the word problem here in the mathematical snese of the word), but i think it must be generally considered to be a pretty tough one. This is another thing i'd like 'to find out' :)

 This was added Saturday 18th April 2003.

3. Infinity

 Whether or not there's any such thing as infinity. I'm no authority on such matters of course. I know that without infinity as a concept we'd still be living in the dark ages, but i wonder about it a lot.

 This was added Thursday 24th April 2003.


 This site is written and maintained by William Labbett. All the files (pictures and programs) on this site took me ages to do and belong to me. You may download anything, store it on your hardrive and do what you will with it but you may not use anything for commercial purposes. Doing so would not only upset me but be a flagrant transgression of common human decency. Thx. Copyright ©2003 by William Labbett. All rights reserved. Please, please declare your status as an official fan of my labours by sending me a email. Praise, comments, suggestions, requests etc.... all welcomed. Click here to e-mail me. Thx again :)

 
This page was created on Saturday 15th March 2003.