A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Lars Bergman
Date: 2020 Sep 27, 12:50 -0700
Crelle's table is some 450 pages, and it gives the result directly for the multiplication of two integers less than 1000. With slightly more work, but only two and a half pages for a similar range, a table of "quarter squares" does the same job. Such a table (of total 14 pages covering integers up to 5100) is included in Chamber's Seven-Figure Mathematical Tables. It works on the fact that
a·b = (a+b)2/4 - (a-b)2/4
Find out a+b and a-b, look up their quarter squares in the table and take their difference.