Advanced abacus algorithms

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.

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.

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.

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.

In project

Minutes and seconds to/from decimals

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.

In project

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.

to 8 digits on a 13 rods 2:5 abacus

Both my daughter's vintage TI-83 and the wonderful Free42 app have provided me with an inexhaustible stream of random exercises for the abacus with the help of very simple programs.

In project