Monthly Archives: October 2013

Cipher 50: Non-trivial evasion

Posted on October 30, 2013 by apgoucher

You may have wondered why the last few ciphers have been erratic. The answer is so that the 50th cipher will land exactly on Professor Imre Leader‘s 50th birthday, which was celebrated 14 hours ago. One of the main components … Continue reading →

Posted in Activities, Ciphers, Uncategorized | Leave a comment

Curves of constant width

Posted on October 27, 2013 by apgoucher

The 50-pence and 20-pence coins are regular curvilinear heptagons, where each edge is a circular arc centred on the opposite vertex. One may ask why the coins have such an unusual shape. One possible answer is that it is impossible … Continue reading →

Posted in Uncategorized | Leave a comment

Enumerating the rationals

Posted on October 24, 2013 by apgoucher

It is a well-known fact, attributed to Cantor, that the set of rationals is countably infinite or, equivalently, we can find a bijection between the rationals and integers. These are easy to construct, but typically quite ugly. If you want … Continue reading →

Posted in Uncategorized | Leave a comment

Cipher 49: Feline cartograph

Posted on October 21, 2013 by apgoucher

This one is entirely graphical: Thanks go to James Aaronson for the design.

Posted in Ciphers | Leave a comment

Punting in clearings of arbitrarily small Lebesgue measure

Posted on October 20, 2013 by apgoucher

Breaking news: A £500 prize for the most elegant solution in the British Mathematical Olympiad has been founded in the memory of Christopher Bradley, whose contributions to the United Kingdom Mathematics Trust were both plentiful and invaluable. Amongst his portfolio is the bestselling … Continue reading →

Posted in Uncategorized | Leave a comment

Mathematical innuendo

Posted on October 18, 2013 by apgoucher

Here are some primarily mathematical double-entendres conceived by members of the Trinity Mathematicians’ Alcoholic Society. Some of them are biological or particle-physical, but never mind. Also, some names are censored for legal reasons. Disclaimer: I accept no responsibility for any offence caused … Continue reading →

Posted in Uncategorized | Leave a comment

Mathieu groupoid

Posted on October 14, 2013 by apgoucher

You have probably encountered the 15-puzzle, where all but one of the squares of a 4 × 4 grid are occupied by counters. The only acceptable moves are to move a counter into an adjacent unoccupied square. Sam Loyd challenged … Continue reading →

Posted in Uncategorized | Leave a comment

MOG results released

Posted on October 11, 2013 by apgoucher

MOG results released The results for the aforementioned Mathematical Olympiad for Girls have now been released on Joseph Myers’ website. There are impressively many excellent scores, as compared with previous years, including some names previously unknown to us. Hence, the … Continue reading →

Posted in Uncategorized | Leave a comment

What should this group be called?

Posted on October 10, 2013 by apgoucher

Consider the Riemann sphere, obtained by adjoining a ‘point at infinity’ to the complex plane. The conformal maps from the Riemann sphere to itself form a group, the Möbius group, which is abstractly isomorphic to (and also the proper orthochronous … Continue reading →

Posted in Uncategorized | Leave a comment

Cipher 48: Endoplasmic reticulum

Posted on October 7, 2013 by apgoucher

After an important and immersive conversation lasting no fewer than four hours, I had very little time to compile this particular cipher. Its appearance reminded me of the endoplasmic reticulum surrounding the nuclei of biological cells, hence the name. I would … Continue reading →

Posted in Ciphers | Leave a comment