Some advanced and especial calculations on the abacus, soroban, suanpan...
 |
| Newton's method |
Newton's method for abacus: square, cubic and fifth roots
Not a traditional method but very old and effective to obtain square, cubic and fifth roots with paper and pencil ... and, in a very compact way, with the abacus.
The radix method for logarithms
If you wish, your abacus can have the [LOG] and [EXP] keys that will expand its use to arbitrary powers and roots, Time Value of Money problems, etc.
The special methods for multiplication and division by numbers slightly greater than one used in the article are explained in Takashi Kojima’s book, Advanced Abacus, Theory and Practice (Charles E. Tuttle, 1963) and also on Totton Heffelfinger's website
To know more about radices and logs...
Tide abacus
Based on the "oni, oni, nishi" method for the Age of the Moon by the Japanese astronomer Prof. Gen'ichiro Hori (堀源一郎) , it allows estimating the time of oceanic high and low tides anywhere by simply adjusting a single local parameter.
Julian day
Some calendrical calculations from 4713 BCE to the distant future. Mainly an exercise in multiplication and division by 365.25! (which deserves to use specialized tools if you are going to do it many times). See Wikipedia.
DMS↔D.DDDD (In project)
Minutes and seconds to/from decimals
The hidden advantage of Kato's method (In project)
Numerical and statistical considerations show a decided advantage during the practice of the Kato's method (半九九法) over other traditional methods to obtain square roots; however, that advantage almost evaporates when it comes to real-world numbers.
Abbreviated operations
Some old arithmetic manuals include a chapter on how to abbreviate the most common operations in manual calculation. This can also be carried over to the abacus.
The twelfth root of 2
To 8 digits on a 13 rods 2:5 abacus. Prince Zhū Zàiyù (朱載堉) of the Ming dynasty used a 2:5 abacus pair of 81 rods each to obtain the 12th root of 2 to 26 digits
