# Monthly Archives: August 2013

## Cipher 41: Caesar cipher

I’ve incorporated a few classical ciphers before, but generally avoided the Caesar cipher due to how trivial it is to brute-force. This one should present more difficulty: When you have the password, use it to access the protected area.

## Influential mathematicians

It has come to my attention that there is a maths camp taking place at Balliol College, Oxford, with the intention of subjecting young aspiring mathematicians to new ideas. Since one of the volunteers at the camp is advertising cp4space … Continue reading

## Growth of recursive string substitution

A Lindenmeyer system, or L-system, involves a recursive procedure applied to a string of symbols, where each symbol in the string is simultaneously replaced with a string, dependent on that symbol. For example, one of my favourite examples involves Easter eggs … Continue reading

## Analysing Escher

I have just been involved in the production of an action thriller about the International Mathematical Olympiad. Since certain intervals of time were inactive and unthrilling, I decided to pass the time by writing a few cp4space articles, amongst other … Continue reading

## Polynomials and Hamming weights

Let P(x) be a polynomial of degree n. Let H(i) represent the number of `1’s in the binary expansion of the integer i. Although reasonably easy to prove, it may seem surprising that the following identity holds: Does this theorem have a … Continue reading

## Cipher 40: Leversha’s paradise

Occasionally, mathematical olympiads contain no classical Euclidean geometry. One such example is the IMO paper in the action thriller X+Y, which encompasses discrete combinatorics, additive combinatorics and algebra. To compensate for this, I have designed a cipher based entirely on Euclidean plane … Continue reading

## Symmetric geometry theorems

Clark Kimberling’s Encyclopedia of Triangle Centres contains several thousand triangle centres, many of which are defined as intersections of three concurrent lines. For example, we have: The three medians of a triangle intersect at the centroid; The three altitudes of … Continue reading

## Kaleidoscopes

For the third time on cp4space, I’m going to refer to my Wythoffian polyhedron generator. This constructs a polyhedron by the use of some two-dimensional fundamental region, bounded by mirrors meeting at predetermined angles. For example, a triangle with internal … Continue reading