Hobbies
The Orbit-Stabiliser Theorem
Some notation and definitions. is a finite group. is the order (size) of a group. is a finite set. is the order (size) of a set. Group action : For an action of the group [more…]
Mathematics
Hobbies
Proof by Necklaces
A proof of Fermat’s Little Theorem using necklaces. , where is prime and is any integer with gcd. Multiply both sides of the congruence by : Which gives : Subtract from both sides : [more…]
Engineering
Space Travel
It is the 7th May 1945 and on this spring morning in the Bavarian mountains, a few days after the death of Hitler, the soldiers of the 44th infantry division that are manning a checkpoint [more…]
Engineering
Space Travel
There are lots of technical problems in designing a liquid fuelled rocket; such as how do you light it, relight it, how do you stop combustion instability shaking the rocket to pieces, how do you [more…]
Hobbies
The Confusing Bit
When you do mathematics you spend much of your time being confused. We can go further with our counting and count the number of necklaces and bracelets with a particular colouring. When we counted the [more…]
Engineering
Space Travel
There are lots of weird and wonderful schemes for powering spacecraft, but in practice only three classes of engine have been built today that could realistically power a spacecraft in the next few decades. (aside: [more…]
Mathematics
What a load of Bolides!
The amount of times I see people posting here – “World ending asteroid hit us please now the world is too crazy!” Well I am here to bring a mild warning, many people understand what [more…]
Hobbies
The Dihedral Group of a Bracelet
A Dihedral group, , is the group of rotations and reflections (the symmetries) of a regular -gon. The order (size) of the group is . We considered the rotations in the Cyclic group of [more…]
Engineering
Space Travel
For those of us interested in space travel however we live in interesting times; as there is probably more development going on in the world today than at any time since NASA was spending an [more…]