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Monthly Archives: October 2013
Cipher 50: Nontrivial evasion
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
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Curves of constant width
The 50pence and 20pence 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
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Enumerating the rationals
It is a wellknown 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
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Cipher 49: Feline cartograph
This one is entirely graphical: Thanks go to James Aaronson for the design.
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Punting in clearings of arbitrarily small Lebesgue measure
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
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Mathematical innuendo
Here are some primarily mathematical doubleentendres conceived by members of the Trinity Mathematicians’ Alcoholic Society. Some of them are biological or particlephysical, but never mind. Also, some names are censored for legal reasons. Disclaimer: I accept no responsibility for any offence caused … Continue reading
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Mathieu groupoid
You have probably encountered the 15puzzle, 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
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MOG results released
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
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What should this group be called?
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
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Cipher 48: Endoplasmic reticulum
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
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