From our recent correspondence:
I’ve just been reading a book titled The Symmetries of Things by John H. Conway, Heidi Burgiel, and Chaim Goodman-Strauss.
It has really superb illustrations of the many different kinds of symmetries, as well as some designs offered as exercises. (The exercises are always important in mathematics. It’s never enough to say things like ‘sure, that makes sense,’ or ‘yeah, I follow you.’ You have to learn how to do it yourself or you don’t really get it, and as things move along further, you will quickly lose yourself in the dust.)
Meantime, if you’re not interested in the mathematics of the subject or the exercises, the pictures are still fascinating.
I don’t know how far I’m going to get, or how fast (how slowly, more likely), but the journey itself is enjoyable — and I will never look at a brick wall (or anything else with a pattern or symmetry: a frieze, wallpaper, sports balls, furniture, tilings, cobblestones, etc. etc.) the same way again. The brick wall that bounds my deck, in the simple pattern known as a ‘running bond,’ is notated as 2*22….
I just looked down at my kitchen floor this morning and, with my now symmetry-conscious eyes, I discovered that it has a repeating pattern with no symmetries: it’s a wonder! (In this case, “wonder” is a technical term for a repeating pattern with no mirror or rotational symmetries or rotational mappings. Its notational symbol is, unsurprisingly, o.)
I urge both my readers to find a copy of this book and look at it. Warning: it’s expensive, with all that glossy paper and those many, many illustrations. Worth looking at, though. So, if you wish only to browse through it, find a copy in a library or a bookstore that you can look at. Then, if you’re as fascinated as I am — and you may well be, since the book is amazingly accessible, especially in the first few chapters — you can always buy a copy for yourself. It’s worth whatever investment of time and mind you care to make.
