An Atlas of Symmetry is divided (like All Gaul, as my classics teacher used to say) into three parts.
- In one part I shall describe how to recognise and use the many different kinds of symmetry that can be found in patterns and other types of artwork. I shall also be attempting to convey, in a non-technical way, key aspects of the mathematics needed for creating images like the ones in this book. This part mathematicians might be tempted to skip, but I hope they will not, because I shall be taking aim at them from time to time, and querying why they do things the way they do. I'm not supposing it will get them to mend their ways, but I think an insight into how things might be if they were different is often very helpful in understanding why they are like they are. There will also be a good deal of less/non-mathematical content in this part - bits of history or just so stories, and sideways glances at how non-mathematicians have made use of artistic use of mathematics in the past.
- In the second part I will be going into the mathematics in a lot more detail, not always in a very rigorous way, but in enough detail to give anyone who might be interested in writing their own computer programs a good start.
- In the third part I shall largely let the images speak for themselves. There will be a bestiary, or atlas, with examples of patterns with almost every possible kind of symmetry.
As this will be a book designed to be looked at and read on a computer these parts won't necessarily be separated chapter by chapter. Instead you will be able to take your own route through the book, skipping over bits that seen too hard or too dull, and going into greater depth in the parts that awaken your interest.
Before we begin in earnest, it might be as well for me to write something about what mathematics actually is, and I'm going to start by asking the question "What is Mathematics?".