How do Shapes Fill Space?

Books:

Popular:

All the authors listed here have several books worth investigating. Here I suggest one each, but there is plenty more to explore!

The Mathematical Tourist

I have to lead off with the book that introduced me to the Penrose tiling. A wander through various mathematical topics, from string theory to chaos. Its a little long in the tooth now, originally published in 1988 and with a second edition 10 years later, but still wonderful writing.

Annotated Flatland: A Romance of Many Dimensions

From a old book to an older one. Flatland is a satire of Victorian society set in a 2d world. Thinking about how the 2d inhabitants consider 3d, can help understand the mysteries of 4d. This edition with modern mathematical commentry from Ian Stewart. There is also now Flatland - The Movie version with Martin Sheen!

Professor Stewart's Cabinet of Mathematical Curiosities

Ian Stewart (mentioned above) has for many years been the star of British poplular mathematics. Along with the Mathematical Tourist his books made me want to become a mathematician. This book from last year is a fascinating collection from all over mathematics.

Finding Moonshine: A Mathematician's Journey Through Symmetry

If Ian Stewart has been the star, Marcus Du Sautoy is now giving serious competition, getting "The Story of Maths" on television and having a, sadly ended, column in the Times on "Sexy Maths". In this book he takes ideas about symmetry that come directly from simple questions about shapes and shows how they have been taken to incredible deep mathematics.

Jews in Hyperspace

Just as Flatland was originally a political book, satirising society as much as it describes mathematics, prolific maths and science writer Clifford Pickover mixes a plea for religious harmony with a trip into four dimensions. For his more standard writings on mathematics check out The Math Book.

Mathematics: A Very Short Introduction

As you can see from above mathematics has been well served by creative mathematicians writing about their subject. Even so this book is special, Tim Gowers is a winner of the Fields medal, the mathematical Nobel prize. He is also known for the simplicity and expository nature of his work. You could not therefore ask for a better account of what mathematics is, from one of its modern masters.

The Colossal Book of Mathematics

Martin Gardner generated a huge amount of popular mathematics content and is probably responsible for bringing more people to mathematics than anyone else alive. Amongst many other achievements he was the first to publish the Penrose tilings in his Scientific American article. This book brings together a broad collection of his work.

Fermat's Last Theorem

To finish, no list like this could be complete without mentioning Simon Singh's masterpiece on the fascinating historical and mathematical story of Fermat's Last theorem. A note in a margin that lead to a 350 year quest, finally solved by Andrew Wiles in 1995.

More mathematical:

For the more ambitious who want to look at the mathematics in more detail, here are some more books.

The Symmetries of Things

It is written in a very approachable style and takes the mathematics of symmetry from first principles through to modern research. In fact beyond the images the final section of the book is primarily of interest to researchers, and contains work that pushes forward the cutting edge in this field.

Indra's Pearls: The Vision of Felix Klein

Another maths book stuffed full of great pictures. This treads a different path to the generalisation of geometry that started with the genius of Felix Klein in the nineteenth century. More recently, thanks to computers, we can actually explore some stunning images that come out of these beautiful mathematical ideas.

Tilings and Patterns

This has been a bible on tilings since it was published, and after several years being hard to find it will be reissued by Dover this winter. Though some sections of it have been put a little out of date by Symmetries of Things it is still a beautiful very visual book with masses of details to dig through.

The Princeton Companion to Mathematics

For the very ambitious this pulls no punches, attempting to cover the whole of modern mathematics in a way accessible to anyone with A-level mathematics. By its own admission it does not make this goal, but it does cover most of the big ideas in an incredibly accessible way.

Materials:

As well as reading you might want to follow up the exhibit with more practical activities. There are wonderful toys available for this. Firstly I should mention the wonderful Polydron and Zometool who sponsored our exhibit. You will have seen their products on display!

Other toys, posters and so on are available from Tessellations, Tarquin books and Grand Illusions.

Finally the Institute of Figuring has a mission to enhance public understanding of figures and models that has a big intersection with mathematics. They are perhaps most famous for the hyperbolic crochet patterns and we saw a couple of beautiful example brought along to the exhibit.

Podcasts:

To conclude if you would rather sit back and listen there are some great podcasts on mathematics available.

Mathfactor

Mathematical puzzles, interviews and explanations, from Chaim Goodman-Strauss in Arkansas.

Travels in a mathematical world

Peter Rowlett of the IMA travels round Britain for his job as university liason officer. On the way he interviews many of the people he meets.