# Monthly Archives: February 2013

Consider the Gaussian function . This gives the standard normal distribution, which has zero mean, unit variance, and points of inflection located at ±1. Note the scaling term , which is included so that the integral is 1 (necessary for a … Continue reading

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## Cipher 18: Enigma

This was, as suggested by the title, inspired by the Enigma machine used to encode run-of-the-mill messages during the Second World War (more high-security messages were encoded with the Lorenz cipher). The Enigma machine was relatively easy to operate, and … Continue reading

## 27 lines on a cubic

Some of you may have noticed a particularly queer post on cp4space yesterday (since deleted), which was written by an impostor. Specifically, I was hosting several people (including, but by no means limited to, the daughter of Kjartan Poskitt). I … Continue reading

## The torus

The torus is a reasonably interesting object. It can be embedded in as a quartic surface bounding a doughnut, or obtained by identifying opposite edges of a square. An intermediate between these constructions is the Clifford torus, which is the … Continue reading

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## Cipher 17: Hallucinogen

After the last cipher, Joseph Myers has overtaken Sam Cappleman-Lynes into first place. Will it remain this way? Only time will tell… Good luck.

## What constitutes an explicit example?

Some proofs of existence provide explicit examples. For instance, a proof of a composite Fermat number is as simple as noting that . On the other hand, some existence proofs are highly non-constructive, and do not provide explicit examples. The … Continue reading

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## Tournament dice

In an earlier cp4space post, I presented a set of five 5-sided dice. We can draw a directed graph associated with this set of dice: Each vertex represents a die. If die A beats die B with a probability greater … Continue reading

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## Magic squares of squares

In 1770, Leonhard Euler sent this particular curiosity to Joseph Lagrange. It’s a 4-by-4 magic square, all of whose entries are perfect squares. Martin Gardner offered a prize for finding a 3-by-3 magic square of squares. Lee Sallows found a … Continue reading

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## Cipher 16: The scenic route

Cipher Tuesday has been massively successful at coinciding with special occasions. We’ve had Christmas and New Year ciphers, and now this one lands on Shrove Tuesday (on reflection, I realise that will trivially happen every year!). So, to commemorate a rather exciting … Continue reading