yes, but..
woven material has less stretch--unless you use it crosswise (bias) which ends up wasting a lot of the cloth.
which is why people used strips, and wrapped.
there is a book on the history of knitting (richard Rutt) i have read chapters, but not the whole book. i own and have read No idle hands,a history of knitting in america, (anne McDonald) which includes an out line of knitting history (from rutt's book) there are also books on traditional knitted garments (fisherman's jersey's or gansey's, scandinavian sweaters and latvian mittens (some of which copy design from anatolian socks! the anatolian socks meanwhile copy designs from woven rugs!)
and there has been a lot written on different styles of knitting
ataturk, in modernize turkey, destroyed a 1500 year old tradition of turkish socks (more like slippers than socks)most turks today knit immitating european styles of socks.
there are several styles/processes for shaping (turning is the knitting term) the heel- the traditional turkish style has been almost completely abandon in turkey, (and western knitters have taken it up!) i'll come back and edit, and include links to images of 'french' (most common western style) heel and to turkish style socks and (and heels)
OP
