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Count down to Christmas with maths!

Where do the magnetic fields of planets and stars come from?

- In this podcast Paul Shepherd tells us about the maths of football stadiums and why his work required him to listen to Belgian techno.
Amidst all the controversy of the FIFA World Cup 2022 there is also some football to be played. And where there's football, there's maths...

Tosin uses maths to guarantee the continued production of chocolate.

It is the reflector (in another word: mirroring) that makes it impossible to encrypt any letter into itself. I am not sure whether the inventor of Enigma had intentionally made this effect. If he had, the reflector is really a clever way to guarantee this point. But if he hadn't, the only purpose of he introducing the reflector seems to be

making the processes of ciphering and deciphering symmetric on the same keyboard on the same machine, which is an aesthetic of this ciphering machine.

Note also, please: the mechanism of reflector contributes nothing to making the number of combinations larger and thereby making the ciphering more complicated.