I recently discussed the traditional algorithms for computing square and cube roots in my History of Math class. Our reading, on mathematics in ancient China, gave both algorithms as a set of rules for manipulating number rods. For me, it was fascinating to see past the text: the rules as given would transfer directly to an abacus/soroban calculation, and were essentially the same as the rules that prior generations of American schoolchildren would have been drilled on in school.

My students (mostly high school math teachers) found the book’s explanation of the method obscure; the key is to view the process geometrically, rather than as a mechanical set of rules for manipulating digits.

I make no claim of originality in what follows; I offer it here in part because I can’t find any lucent discussions along these lines on the web. (more…)