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| Sir Isaac Newton |
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.
I have just uploaded a first draft of my own elaboration on the traditional methods described by Knott for obtaining roots. Focusing mainly on cube roots, I offer several examples including obtaining four digits extending to 7-8 on a 13-rod abacus as anticipated in a previous post. I hope to finish writing it over the next few days.
It seems that while I was actively working at jccAbacus Web, Google changed its policy on Google Sites, now considered more as a tool for working in group than as a creator of web portals. The fact is that months go by and jccAbacus Web remains without being indexed by Google Search Engine and I'm afraid it never will be. It seems that I simply put the contents in the wrong place, or at the wrong time, and that I should consider moving them to another place.
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| Cover from Robert Flower's The Radix. A New Way of Making Logarithms (London 1771) |
The following list corresponds to the content of jccAbacus Web as of today. From now on, the current status of the Web will appear on an accessory page on this blog.
Ancient abacuses, both Japanese style (soroban) and Chinese style (suanpan), used to have five beads on the lower deck even though this is unnecessary from the point of view of representing decimal numbers.
What was the purpose of this additional fifth bead?
We have to look for the answer in ancient books.
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| Pánzhū Suànfǎ illustration showing the use of the 5th lower bead |
Txt-abacus is a simple python 3 module I wrote to cover my own needs for illustrating abacus diagrams on my jccAbacus website. The diagrams are based on text using a monospaced font instead of graphics, so the result is not particularly beautiful but it is lightweight, allowing a large number of diagrams to be included in a document without taking up too much disk space.
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| A 2:5 soroban/suanpan diagram |
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...
