NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Crelle's tables
From: Bill Ritchie
Date: 2020 Sep 27, 22:55 +0100
From: Bill Ritchie
Date: 2020 Sep 27, 22:55 +0100
Fabulous, Lars. This had me recalling schoolboy algebra expansions to realise that all the terms cancelled except for 2a.b/4 + 2a.b/4, which equals a.b.
Snippets like this one are great, adding to the library of quality information on NavList from Frank and so many knowledgeable contributors.
Regards,
Bill Ritchie.
On Sun, Sep 27, 2020 at 10:01 PM Lars Bergman <NoReply_Bergman@fer3.com> wrote:
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.
Lars
