### 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…]

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…]

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…]

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…]

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…]

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…]

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…]

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…]

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…]

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…]

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