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…]
Science
20th Century
Space Travel
It was the early evening of January 27th 1967. Gus Grissom, Ed White and Roger Chaffee had been in the Apollo capsule for six and a half hours conducting a full scale dress rehearsal of [more…]
Engineering
An Atomic (Alarm) Clock – Part 1
I like to find electronic oddities on eBay and then try to make something interesting out of them. Before the internet I used a company called Greenweld Electronics for surplus and unusual electronic components. In [more…]
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…]
Arts
3D Printing – a layman’s guide
The latest thing to grab the keen tinkerer’s attention is 3D printing. This has taken off in a huge way in the USA, and is gaining fans in the UK too. The concept is surprisingly [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
Return to Brigg
A few weeks back I did a piece on the spectacular Alishan mountain line in Taiwan. One day, I might do something on the Gono line around the wild, craggy northwest coast of Honshu. Or [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…]
Philosophy
Way too many people
The prologue: At the dawn of agriculture, about 8000 B.C., the population of the world was approximately 5 million. Over the 8,000-year period up to 1 A.D. it grew to 200 million (some estimate 300 [more…]