# 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

## 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

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## 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

## 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

## 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

## 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