Yes, "Flatterland", by Ian Stewart, is a brilliant modernisation of Abbot's 19th-century book.
It has a female heroine, Victoria "(Vikki") Line. She's a young, trendy, 2-D gal. She still keeps, for strictly sentimental reasons, her childhood toys such as "My Little Polygon". But after placacating her grumpy Square dad "Grosvener", by bringing him a rectangle of lager, she goes off to surf the "Interline", and eventually discovers a new multi-dimensional Universe.
"Flatterland" is quite a long book. It has lot of witty detail, and scientific ideas. Yet, somehow it lacks the charm of Abbot's sparse original. Thus while I've re-read Abbot many times, and can keep doing so, I never feel like re-reading "Flatterland".
A much better book is A K Dewdney's "The Planiverse". This is a vivid account of a living, functional 2-D Universe, with - most importantly - marvellous illustrations which bring it to life.
For anyone interested in 2-D, I thoroughly recommend "The Planiverse".
