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| Sir Isaac Newton |
A non-traditional technique
Square, cube and fifth roots can be solved on the abacus using Newton's method. It is not a traditional method, but it is very old, so much so that it is also called the Babylonian method when it comes to square roots, although there is no evidence that it was actually used by the ancient Babylonians. What does matter is its effectiveness and the fact that it is very compact on the abacus.
Why practice cube or fifth roots? The truth is that they are not as frequent in applications as square roots, but their practice through the Newton method on the abacus is not a waste of time for the amateur abacist of the 21st century since, in reality, the process is fundamentally a repeated exercise of division and, being division a key piece of bead arithmetic, all the practice one can do will never be too much.
By comparison to traditional techniques and according to my own experience, Newton's method does not present a special advantage for square roots in terms of efficiency, difficulty or opportunities for error, but it does for cube roots, where the differences are notable. For fifth roots, as up to now I do not know of any traditional technique for the abacus, I have no possibility of comparison; Perhaps, Newton's method opens in this case a new opportunity for advanced calculation with the abacus.
You can find the full article on jccAbacus Web.
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