source file: mills2.txt
Date: Fri, 13 Oct 1995 06:57:23 -0700

Subject: RE: 12-tet in China

From: COUL@ezh.nl (Manuel Op de Coul)

The algorithm for calculating a root is actually not so difficult.
This calculates a square root:

    Answer := Of_Number;
    loop
       Delta := (Of_Number / Answer) - Answer;
       if abs Delta <= Answer * Epsilon then
          return Answer;
       end if;
       Answer := Answer + 0.5 * Delta;
    end loop;

Epsilon indicates the required precision and is the smallest number that
makes a difference.
I suppose that modifying this to do the twelfth root of 2 is easy.
It converges very rapidly so it's doable by hand. It's very elementary
so it must have been known for a very long time.

Manuel Op de Coul    coul@ezh.nl

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