Monthly Archives: December 2012

Infinite monkey theorem

It is widely acknowledged that an infinite number of monkeys sitting at computers typing randomly will almost surely produce a properly-LaTeXed copy of the complete works of Shakespeare. This statement, known as the ‘infinite monkey theorem’, has received a wide amount of … Continue reading

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Treefoil

Knot theory is a branch of topology which considers the different embeddings of a cycle into three-dimensional Euclidean space, R^3. The simplest type of knot is the unknot, which is just an ordinary circle (which can be ‘thickened’ to form … Continue reading

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Cipher 7: Generalised RSA

The RSA cryptosystem is named after Rivest, Shamir and Adleman, who rediscoved it at MIT. It was created earlier by Clifford Cocks at GCHQ, but that information was classified. It is an example of a trapdoor cipher (others include elliptic … Continue reading

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BMO1 marked

My colleagues marked the first round of the British Mathematical Olympiad in Sidney Sussex College, Cambridge. You can view the leaderboard on Joseph’s website; well done to everyone who featured. There are quite a few new names on that list, … Continue reading

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Things go wrong eventually

The sinc function is important in signal processing for removing noise and reconstructing the original signal. It’s defined rather simply as sin(x)/x, so it’s surprising that it actually has its own special name (you have to be careful at x … Continue reading

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Triangling the square

Quite a few things are described as ‘X-ing the Y’, where X and Y are the interiors of piecewise algebraic curves. Probably the most famous of these is ‘squaring the circle’, which refers to the impossible task of constructing a … Continue reading

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Bolzano-Weierstrass

A particularly useful result in real analysis is, remarkably, applicable to combinatorics problems where reals are not even mentioned. It is the fabled Bolzano-Weierstrass theorem. The statement of the theorem is that ‘every bounded sequence has a convergent subsequence’. It … Continue reading

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Cipher 6: Puzzling

This particular cipher comes in two components (an image and some ciphertext), both of which you’ll need to successfully solve the challenge. If you delve deeper, you may find more hidden clues and secret images to help you decrypt this beast of … Continue reading

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Adenovirus

Unfortunately, I am currently being invaded by millions of microscopic icosahedra (at least, I hope this is the common cold). I apologise on their behalf for any slight lapse in the frequency of CP4space postings. Don’t worry; the sixth cipher was made ages … Continue reading

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Fat Cantor set

The ordinary Cantor set is obtained by removing the middle third of a unit line segment and iterating. The resulting set of points is uncountable, nowhere dense and has zero measure. It transpires that the construction can be modified to give … Continue reading

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