The word “quincunx” refers to a pattern of four objects arranged in a square with a fifth in the centre, like the spots on a dice. Although it’s an obscure word today, it has resonances and survivals in subjects as diverse as garden design, architecture and various aspects of religious and mystical symbolism. It’s also […]

## Numbers Stations

Some people seem to think anything involving numbers must be mathematical, which is a lot more generous than most mathematicians would ask them to be. But numbers stations — an eerie sound from the Cold War era — do have a little bit of real mathematics in them. Numbers stations are shortwave AM radio frequencies […]

## Magic and Latin Squares

A “magic square” is a grid of numbers that add up to the same total across every row, every column and both long diagonals: The main picture for this post shows a detail from Albrecht Durer’s engaving Melencolia I, which includes (among many other symbols of sixteenth century mathematical learning) a 4×4 magic square whose […]

## Exploring Strange Spaces with Games

On this year’s Strange Spaces course, which came to an end last week, we were able to show off a visualization of 2-dimensional hyperbolic space thanks to the indie game HyperRogue. Below the fold is a video of someone wandering around on HyperRogue’s space, which students who followed the course might recognise as a Poincare […]

## Off On A Tangent

This week in Strange Spaces we looked at thread constructions, pursuit curves, tangents and — at last — came up with a handwaving account of curvature for 1-manifolds. We started with thread constructions, in which we create the illusion of curves by drawing only straight lines. For illustrative purposes we created a simple parabola, but […]

## Counting Backwards

We’re excited to report that this year’s Big Space exhibition will give Fine Art students at Central Saint Martins a chance to explore and demonstrate how their practice relates to a wide range of mathematical topics. Students have been invited to submit proposals that reflect on the role of mathematics within their practice, whether it […]

## Cartography

Mapmaking involves many disciplines at once: it is cultural, philosophical, visual and also mathematical. This last aspect reveals itself in the simple difficulty of transferring a pattern — in this case the pattern of the continents — from a roughly spherical surface to a flat one. It turns out that making a perfect map is […]

## Choosing a Representation

One of the things mathematicians like to do with their objects to make representations of them. Sometimes these are purely symbolic; sometimes they’re diagrams or drawings. We like to have lots of different ways to represent them because each one shows us different aspects of the object and makes different kinds of manipulation easy or […]

## Strange Spaces

Next Wednesday we’ll begin our course Strange Spaces, a gentle introduction to topology and non-Euclidean geometry. These are interesting subjects in maths because although they can include calculation and algebraic symbol-juggling, they don’t have to. The concepts and many of the problems are qualitative in nature — they ask for answers in words, not numbers. […]

## Space, Time and Music

The modern picture of mathematical space was invented by Descartes and his contemporaries in the first half of the seventeenth century.The key idea is to represent each point in space by some numbers called “coordinates”, indicating the way you need to travel from some fixed origin to get to the point in question. It so […]