Slonimskyapos;s Multiplying Device, an impressive Example for Applied Mathematics：（Slonimskyapos;增加设备,应用数学的一个令人印象深刻的例子）.pdfVIP

Slonimskys Multiplying Device, an impressive Example for Applied Mathematics Stephan Weiss Summary This article presents multiplying devices from the middle of the 19th century, which are based on the so called Theorem of Slonimsky. With his theorem Slonimsky succeeded in solving the problem of tens carry in a simple device with no gears. He did it in a surprising way, but at the same time the multiplying device is an interesting and impressive example of application and usage of a rather complicated statement in numerical mathematics. The inventor and the base problem Hayyim Selig Slonimsky1 (*1810 in Byelostok or Belostok, Russian Empire, now Bialystok, Poland , †1904 in Warsaw) was a knowledgeable Talmudist and author of science books about mathematics and astronomy in Hebrew for Jewish people. As a publisher he produced the science magazine Hazefirah (Ha-Tsefira) from 1862 on, also in Hebrew, which continued until 1931. Furthermore Slonimsky invented at least two calculating aids, an adding device and a multiplying device. The article in the Leipziger Illustrierte Zeitung from 1845 [2] mentions a third calculating instrument, similar to an abacus. It is worth noting that the clockmaker and inventor of a calculating machine Abraham Jacob Stern was his father-in-law. For a better understanding of what is new in Slonimskys invention, I consider it useful to repeat briefly some historic methods for tens carry in multiplying devices. In his Rabdologia John Napier (1550 – 1617) broke a simple multiplying table into vertical columns. With these stripes, mounted on square rods which were called Napiers rods or bones, multiplication tables for any multiplicand may be composed (fig. 1, to ease comparison here I continuously use the multiplicand 274). Figures of the partial products are arranged in triangles so that the user may obtain the required