Lattice multiplication

It is mathematically identical to the more commonly used long multiplication algorithm, but it breaks the process into smaller steps, which some practitioners find easier to use.

The grid diagonal through the intersection of these two lines then determines the position of the decimal point in the result.

It is sometimes erroneously stated that lattice multiplication was described by Muḥammad ibn Mūsā al-Khwārizmī (Baghdad, c. 825) or by Fibonacci in his Liber Abaci (Italy, 1202, 1228).

In Chapter 3 of his Liber Abaci, Fibonacci does describe a related technique of multiplication by what he termed quadrilatero in forma scacherii (“rectangle in the form of a chessboard”).

Swetz[9] compares and contrasts multiplication by gelosia (lattice), by scacherii (chessboard), and other tableau methods.

Other notable historical uses of lattice multiplication include:[6] Derivations of this method also appeared in the 16th century works Umdet-ul Hisab by Ottoman-Bosnian polymath Matrakçı Nasuh.

[11] The same principle described by Matrakçı Nasuh underlay the later development of the calculating rods known as Napier's bones (Scotland, 1617) and Genaille–Lucas rulers (France, late 1800s).