Comments on: A 26th way to multiply. Sort of. 12 tables, 24 chairs, and plenty of chalk Mon, 20 Feb 2017 17:59:50 +0000 hourly 1 By: watchmath Tue, 04 Aug 2009 16:19:47 +0000 I tutor an 8th grader by using a Singapore Math book. Here is an exercise from that book that need to solved by using the method that you mentioned on your post.

\displaystyle \frac{236}{236^2-(238\times 234)}

By: Samantha Tue, 04 Aug 2009 15:47:36 +0000 That is a very cute method! Certainly it’s easier to have a list of perfect squares than to have a 100×100 multiplications table.

I wonder if that is idea is part of what sparked Fermat-Euler’s method of the sum of two squares. They said if p is prime and p = 1 mod 4 (or 2) then p is expressible as p = a^2 + b^2 for some integers a, b. The proof is much more complicated than the proof for this formula is and requires imaginary numbers, but that makes sense because we are dealing with addition inside the squares instead of subtraction.

Nice explanation!