Monthly Archives: October 2012

Happy Hallowe’en

Feeling that Complex Projective 4-Space isn’t sufficiently seasonal, I was compelled to alter the colour scheme of the banner to reflect the fact that today, the 31st October, is All Hallows’ Eve, popularly abbreviated to Hallowe’en. Anyway, I actually prefer … Continue reading

Posted in Uncategorized | 3 Comments

Fusible numbers

Quite a lot of interest originated from the following puzzle of unknown origin: Given two pieces of rope which burn in precisely 1 minute, time an interval of 45 seconds (3/4 minutes). The rope is not necessarily uniform, so you’re … Continue reading

Posted in Uncategorized | 6 Comments

MODA: Diophantine equations

Here’s the penultimate chapter of Mathematical Olympiad Dark Arts. This includes several methods of solving Diophantine equations, including Vieta jumping and the Sam Cappleman-Lynes Technique. Also included is an explanation of how to locate rational points on algebraic curves, up to and including elliptic … Continue reading

Posted in MODA | Leave a comment

GMT

We’re quickly approaching Ebenezer Scrooge’s favourite time of the year, Greenwich Mean Time. This brief post serves as a reminder to anyone who has forgotten about the temporal adjustment due to spending too little time in real Euclidean 3-space. Of course, if … Continue reading

Posted in Uncategorized | Leave a comment

Borromean strings

We’ll begin with an intriguing set of three interlinked rings, the Borromean rings. They can’t be realised as solid circular tori, but ellipses work just fine. Here is a visualisation: If you remove any one of the three rings, the … Continue reading

Posted in Uncategorized | 14 Comments

Markov basket-weaving

Shortly after publishing my third cipher, the second one (labyrinth) was solved by someone called Patrick. Gabriel had worked out the basis for solving the cipher ages ago, but didn’t actually do the necessary combination of brute-force frequency analysis to decipher it. I’m … Continue reading

Posted in Uncategorized | Leave a comment

Cipher 3: Chess cipher

Don’t forget that the MathsJam is today, held throughout the country and indeed the world. It is suprising that no-one has yet solved the maze cipher, and only one person has managed to assemble and decipher the Jigcypher. Perhaps I … Continue reading

Posted in Ciphers | 8 Comments