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Slonimski's Theorem
Slonimski's Theorem is an observation by Hayyim Selig Slonimski that the sequence of carry digits in a multiplication table is the Farey sequence. This observation allowed Slonimski to create very compact multiplication tables for use in hand calculations. He received several awards for different devices for presenting these tables. The most common format were Joffe Bars similar to Napier's Rods Napier's bones is a manually-operated calculating device created by John Napier of Merchiston, Scotland for the calculation of products and quotients of numbers. The method was based on lattice multiplication, and also called ''rabdology'', a word .... Joffe Bars were popular in Eastern Europe in the late 19th and early 20th century. References *. Provides a derivation of Slonimski's theorem, and some details on the calculating machine. *. Provides a complete set of tables. *{{citation, mr=3111378 , last=Monnier, first= Valéry, last2=Szrek, first2= Walter, last3= Zalewski, first3= Janu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hayyim Selig Slonimski
Ḥayyim Selig ben Ya'akov Slonimski () (March 31, 1810 – May 15, 1904), also known by his acronym ḤaZaS (), was a Hebrew publisher, mathematician, astronomer, inventor, science writer, and rabbi. He was among the first to write books on science for a broad Jewish audience, and was the founder of ''Ha-Tsfira'', the first Hebrew-language newspaper with an emphasis on the sciences. Biography Ḥayyim Selig Slonimski was born in Bialystok, in the Grodno Governorate of the Russian Empire (present-day Poland), the oldest son of Rabbi Avraham Ya'akov Bishka and Leah (Neches) Bishka. His father belonged to a family of rabbis, writers, publishers and printers, and his mother was the daughter of Rabbi Yeḥiel Neches, an owner of a well-known beit midrash in Bialystok. Slonimski had a traditional Jewish upbringing and Talmudic education; without a formal secular education, Slonimski taught himself mathematics, astronomy, and foreign languages. An advocate for the education of Eastern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Farey Sequence
In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ..., the Farey sequence of order ''n'' is the sequence of completely reduced fractions, either between 0 and 1, or without this restriction, which when in lowest terms have denominators less than or equal to ''n'', arranged in order of increasing size. With the restricted definition, each Farey sequence starts with the value 0, denoted by the fraction , and ends with the value 1, denoted by the fraction (although some authors omit these terms). A ''Farey sequence'' is sometimes called a Farey series (mathematics), ''series'', which is not strictly correct, because the terms are not summed. Examples The Farey sequences of orders 1 to 8 are : :''F''1 = :''F''2 = :''F''3 = :''F''4 = :''F''5 = :''F''6 = :''F''7 = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joffe Bars
Slonimski's Theorem is an observation by Hayyim Selig Slonimski that the sequence of carry digits in a multiplication table is the Farey sequence. This observation allowed Slonimski to create very compact multiplication tables for use in hand calculations. He received several awards for different devices for presenting these tables. The most common format were Joffe Bars similar to Napier's Rods Napier's bones is a manually-operated calculating device created by John Napier of Merchiston, Scotland for the calculation of products and quotients of numbers. The method was based on lattice multiplication, and also called ''rabdology'', a word .... Joffe Bars were popular in Eastern Europe in the late 19th and early 20th century. References *. Provides a derivation of Slonimski's theorem, and some details on the calculating machine. *. Provides a complete set of tables. *{{citation, mr=3111378 , last=Monnier, first= Valéry, last2=Szrek, first2= Walter, last3= Zalewski, first3= Janu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Napier's Rods
Napier's bones is a manually-operated calculating device created by John Napier of Merchiston, Scotland for the calculation of products and quotients of numbers. The method was based on lattice multiplication, and also called ''rabdology'', a word invented by Napier. Napier published his version in 1617. It was printed in Edinburgh and dedicated to his patron Alexander Seton. Using the multiplication tables embedded in the rods, multiplication can be reduced to addition operations and division to subtractions. Advanced use of the rods can extract square roots. Napier's bones are not the same as logarithms, with which Napier's name is also associated, but are based on dissected multiplication tables. The complete device usually includes a base board with a rim; the user places Napier's rods inside the rim to conduct multiplication or division. The board's left edge is divided into nine squares, holding the numbers 1 to 9. In Napier's original design, the rods are made of metal, wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanical Calculators
Mechanical may refer to: Machine * Machine (mechanical), a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement * Mechanical calculator, a device used to perform the basic operations of arithmetic * Mechanical energy, the sum of potential energy and kinetic energy * Mechanical system, a system that manages the power of forces and movements to accomplish a task * Mechanism (engineering), a portion of a mechanical device Other * Mechanical (character), one of several characters in Shakespeare's ''A Midsummer Night's Dream'' * A kind of typeface in the VOX-ATypI classification See also * Machine, especially in opposition to an electronic item * ''Mechanical Animals'', the third full-length studio release by Marilyn Manson * Manufactured or artificial, especially in opposition to a biological or natural component * Automation, using machine decisions and processing instead of human * Mechanization, using machine labor inst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
