## Monday, 28 February 2011

### Pi

Pi (π), Mathematicians are engulfed by it and for good reason. It really is the definition of 'Eloquent Math'; an irrational number that is one of the most important constants used in Mathematics that can be so simply found and represented. Circumference of a circle/diameter of circle.

Pi is a number, which for a lack of better words is a number that is infinite and does not repeat its decimal representation at any stage; this alone makes it rather unique (barring Euler's constant and √2) and perhaps that is a reason behind it having such a huge popularity amongst Mathematicians and nerds alike.

At the current moment in time pi has been calculated to over one trillion decimal places, that my friends is how fixated Mathematicians are on pi! However this is really not necessary other than pure curiousity and looking for patterns in pi and to try and understand it some more. Pi calculated to 11 decimal places can accurately estimate the circumference of any circle that fits inside of the Earth to one millimetre; and if pi is represented to 39 decimal places you can estimate the circumference of any circle inside the observable universe to the radius of one hydrogen atom. To a trillion decimal places there would be nie on zero error whatsoever (about 3*10^-10 the radius of a hydrogen atom).

If you are beginning to be as fascinated with pi as I, and many others are, take a look around the internet and at the link to Yann Martel's "Life of Pi" that is a very compelling read.

Or if you'd prefer, the hardcover:

## Sunday, 27 February 2011

### Prime Numbers

Prime numbers, have exactly two factors. They are beautiful things; rare and incredibly unpredictable numbers, the only real thing we can see with any degree of pattern is diagonal lines in the Ulam spiral (to read more about this fascinating subject please go here, http://www.numberspiral.com/). Prime numbers are the building blocks of Mathematics, like anything you need to have some base as a starting point and in maths, primes are that. You can create any integer, any integer at all with only prime numbers. The fact alone that it is the building blocks of a subject that I love so much makes it interesting to me.

The most common method of finding 'new' prime numbers is via a method coined by Marin Mersenne (thus my name), there appears to be a reasonably high amount of prime numbers that can be found with 2^n-1. 3, 7, 31, 127 are the first four mersenne primes; there's a large jump up to the next one, 8191. In fact there is only 47 mersenne primes that have ever been found, which is staggeringly low, or so it appears. The method of finding primes in this way is the only real way to randomly stumble across a prime, and thus why it is still used, despite its small return rate. 9 of the top 10 largest prime numbers are mersenne primes, which shows how hard it is to actually discover one of the damn things!

The current largest prime is 243,112,609 − 1, and to put that into context it has: 12,978,189 digits, to write the number out with 75 digits per line and 50 lines per page you would need 3461 pages... That is a mammoth of a number. They're cool but what's the point? I hear you ask. Well, they are incredibly important in computer security; if you times two prime numbers together you get a number with only 4 factors, itself, 1 and two primes. This means it's very hard to break down and thus secure. These numbers are so important, and well interesting that there is a large amount of money dedicated to them. The first prime found with over 10,000,000 was awarded $100,000! The first person to find a prime with over 100,000,000 digits will receive a prize of$150,000. That's erious money. Want to join in but aren't a God of maths? GIMPS is amn online project dedicated to finding programs, it's a small program that runs in the background while you mind your own business and it hunts for mersenne prime numbers. Want to get involved? Go here; http://www.mersenne.org/.

### Computing

It kind of goes without saying that computing and mathematics go hand in hand. In fact, computing is really just a rather abstract branch of mathematics. 3D vectors, the original coding, a lot of computer programs; all rely on maths. IP addresses use prime numbers (which will be the subject of my next post). Not to mention the amount of programming that has to go into all programs on computers which again originated from mathematics.

I'm trying to give you a small idea about the implications maths has on every single aspect of your life. In my later posts I will delve into more complex mathematics.

### The beginning...

I will not begin my blog by boring the undoubted hundreds and thousands of you reading this (-ahem), but just start with a small little speech.

If you take a brief moment to sit back and think about the world, the universe, in which we live you will be simply amazed at the sheer size and beauty of which it possesses. And yet, not a single part of the wondrous magnitude of it all could be explained, conceived or created without basic and of course advanced Mathematics.

To try and explain everything, you will need Maths! And that is what fascinates me, how, in its complexness it is so simple, and yet so huge and daunting. I hope that if you read this you too are beginning to be inspired, or already are inspired, into a radiant love of the world of Mathematics.