### The Möbius Function

The Möbius function is denoted by , where is the Greek letter mu. Depending on the factorisation of , the function takes the values . The last says that if is even, then and if [more…]

### Making A Ruby Laser – Part Five

Melting a hole through steel: The above image needs a little explanation! The Doc messed up his camera settings and under exposed the image. So I loaded it into Gimp and played with the curves [more…]

### Making A Ruby Laser – Part Four

The Doc’s ruby laser focused onto a lighter flint. The flint has been glued to the end of a match stick. The ‘explosion’ measures approximately 4 inches diameter. Interesting things to note are the ‘candy [more…]

### Making A Ruby Laser – Part Three

More information on laser speckle can be found here:  Speckle pattern A Mirror Alignment Tool The most important part of constructing a ruby laser (or any laser with external mirrors) are getting the mirrors alligned [more…]

### The Fields Medal

“Rise above oneself and grasp the world” These are awarded every four years for advancement in the field of mathematics.  There is an age limit of 40 on the recipients.  It is a recognition of [more…]

### Euler’s Totient Function

Euler’s totient function counts the number of positive integers up to that are relatively prime to , where is considered to be relatively prime to all .  These numbers are called the totatives of . [more…]

### Making A Ruby Laser – Part Two

(a ruby rod lit by two bright blue LEDs. Due to the IR filter in my camera the pink colour is actually red. What you are seeing is the absorption of the blue light and the [more…]