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A mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically, or (historically) a simulation such as an analog computer or a slide rule.
Simple slide rules will have a C and D scale for multiplication and division, most likely an A and B for squares and square roots, and possibly CI and K for reciprocals and cubes. [8] In the early days of slide rules few scales were provided and no labelling was necessary. However, gradually the number of scales tended to increase.
The abacus was much faster for addition, somewhat faster for multiplication, but Feynman was faster at division. When the abacus was used for more complex operations, i.e. cube roots, Feynman won easily. However, the number chosen at random was close to a number Feynman happened to know was an exact cube, allowing him to use approximate methods ...
Proportion wheels are simple circular slide rules used in graphic design to calculate aspect ratios. Lining up the original and desired size values on the inner and outer wheels will display their ratio as a percentage in a small window. Though not as common since the advent of computerized layout, they are still made and used. [citation needed]
The steam-powered automatic flute described by the Book of Ingenious Devices (850) by the Persian-Baghdadi Banū Mūsā brothers may have been the first programmable device. [10] Other early mechanical devices used to perform one or another type of calculations include the planisphere and other mechanical computing devices invented by Al-Biruni ...
A small number is chosen, usually 2 through 9, by which to multiply the large number. In this example the small number by which to multiply the larger is 6. The horizontal row in which this number stands is the only row needed to perform the remaining calculations and may now be viewed in isolation. Second step of solving 6 x 425
The Roman abacus was the first portable calculating device for engineers, merchants, and presumably tax collectors. It greatly reduced the time needed to perform the basic operations of arithmetic using Roman numerals. [citation needed] Karl Menninger said:
Ch. III The book also has a discussion of theorems in spherical trigonometry, usually known as Napier's Rules of Circular Parts. Modern English translations of both Napier's books on logarithms and their description can be found on the web, as well as a discussion of Napier's bones and Promptuary (another early calculating device). [11]