Monthly Archives: October 2012

Happy Hallowe’en

Posted on October 31, 2012 by apgoucher

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 →

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Fusible numbers

Posted on October 29, 2012 by apgoucher

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 →

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MODA: Diophantine equations

Posted on October 28, 2012 by apgoucher

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 →

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GMT

Posted on October 27, 2012 by apgoucher

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 →

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Borromean strings

Posted on October 26, 2012 by apgoucher

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 →

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Markov basket-weaving

Posted on October 24, 2012 by apgoucher

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 →

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Cipher 3: Chess cipher

Posted on October 23, 2012 by apgoucher

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 →

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MODA: Inversion

Posted on October 21, 2012 by apgoucher

On Tuesday (23rd October) at 7:00 pm, there is a monthly MathsJam gathering. It occurs simultaneously in various areas of the country, including the Castle Inn, Cambridge. I’ve heard rumours that there is a surprise party at the event for Tom Rychlik to … Continue reading →

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Combinatorial cake

Posted on October 19, 2012 by apgoucher

Forgive me if there is a slight lapse in the frequency of CP4space postings. You can attribute it to me lying in the quintuple-intersection of the following Venn diagram: This particular arrangement of ellipses partitioning the plane into 32 connected … Continue reading →

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Surfaces

Posted on October 17, 2012 by apgoucher

Many natural objects can be modelled by startlingly simple equations. For instance, there is a sextic surface (degree-6 polynomial equation in three variables) which resembles a heart. As such, it has been nicknamed the ‘heart surface’: Now that we’re approaching … Continue reading →

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