JOHN N CROTHERS
ANTHONY G SHANNON
All symbols employed in this monograph which represent numbers are symbols representing integers. The term natural number, symbolised by N will mean the numbers 1, 2, 3, …, and so on, thus excluding the number zero. The term s–lattice will mean simple 19integer coordinate lattice The reference to ′simple′ is derived from a unique correspondence between any such lattice and two finite simple continued fractions, one with respect to the forward sense of the partial quotients < a , a , …a > and the other with 1 2 n respect to the reverse sense of these partial quotients. Such connections are however not developed here.(Definitions 1 and 2). The term lattice is often used here in place of ′slattice′ because it is a more familiar term and because a two variable s–lattice graph visually exemplifies the original and more universally understood meaning associated with the term ′lattice′, but it is not intended that this term should refer to any other form of lattice other than an s–lattice.