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In three dimensions, an aperiodic monotile is a solid capable of tiling space, but not in such a way that admits translational symmetry. The question of existence of aperiodic monotiles stems from a weaker question, which formed part of Hilbert’s … Continue reading →

I am proud to announce that Complex Projective 4-Space is celebrating its first anniversary today. This is an excellent opportunity to quantitatively summarise what has happened on cp4space in the last year: Complex Projective 4-Space has been viewed 104125 times since its … Continue reading →

What do the Sydney Opera House, the Human Papillomavirus and the following model of artificial life have in common? The history of artificial life has been a long one, and few would argue that it originated with the Hungarian-American mathematician … Continue reading →

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 →

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 →

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 →

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 →

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 →

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 →

(I’m testing out the functionality of the cp4space Facebook page. Hopefully, this post should be automatically published there.) In most familiar board games, cubic dice are used on the basis that each face is equally likely to face upwards. In … Continue reading →