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 […]

## Height, Heat and Topology

Cartographers often want to capture the way the height of an expanse of land changes. This is a “third dimension” of information, but usually they’re working on a two-dimensional, flat page, whether physical or digital. One solution is to use colour to represent height, as in this image of part of the Czech Republic. In […]

## Algorithmic Botany

Sometimes it’s easy to feel like you’ve missed your calling. If only the careers advisor at my school had told me I could become an algorithmic botanist, I might have taken biology classes a bit more seriously. To be fair to them, this job probably didn’t exist back then, but it does now: the University […]

## A Space of Farris Designs

We’ve just learned of a new book on mathematical design: Creating Symmetry: The Artful Mathematics of Wallpaper Patterns by Frank Farris; we came across it thanks to this article. As often happens, some questionable notions of “art” and “beauty” are being tossed around here, but that isn’t the main reason to mention it.The article points […]

## Visual & Spatial Maths

What is creative practice? “A vision that decants little by little over months and years, bringing to light the ‘obvious’ thing that no one had seen, taking form in an ‘obvious’ assertion of which no one had dreamed” That’s how Alexander Grothendieck, one of the great geometers of the last 100 years saw it. Did […]