30 - Roots, Rocks, and Newton-Raphson Algorithms for Approximating √2 3000 Years Apart pp. 229-240By Clemency Montelle
Mathematical Time Capsules
Online ISBN: 9780883859841
Chapter DOI: http://dx.doi.org/10.5948/UPO9780883859841.031
One of the classic examples to demonstrate the so-called Newton-Raphson method in undergraduate calculus is to apply it to the second-degree polynomial equation x2 – 2 = 0 to find an approximation to the square-root of two. After several iterations the solution converges quite quickly. Indeed, √2 has fascinated mathematicians since ancient times, and one of its earliest expressions is found on a cuneiform tablet written, it is supposed, some time in the first third of the second millennium B.C.E by a trainee scribe in southern Mesopotamia. While keeping this mathematical artifact firmly in its original archaeological and mathematical context, we look at the similarities and differences it shares with modern mathematical techniques, 3000 years distant.
Observing that mathematical knowledge is, to a certain extent, culturally dependent can be revelatory to students. Modern mathematical pedagogy is generally based around a cumulative approach which allows little room for lateral breadth, as it focuses on the acquisition of skills, often with scant regard for the actual manifestation or circumstances of mathematical knowledge itself. Students may have never been exposed to other contexts in which mathematics flourished, nor encountered different mathematical traditions thus far in their studies, much less non-western ones. Yet, such exposure can give them a vital and nuanced perspective on their own mathematical circumstances. Though many a mathematical problem posed may be universal, the ways in which various mathematically literate cultures attacked them and solved them are diverse, depending on many other factors related to the broader intellectual environment. This is an important observation to bequeath to future mathematically-literate generations. However, at the same time, the universality of mathematics should not be forgotten.
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