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Some of the algorithms Trachtenberg developed are ones for general multiplication, division and addition. Also, the Trachtenberg system includes some specialised methods for multiplying small numbers between 5 and 13. The section on addition demonstrates an effective method of checking calculations that can also be applied to multiplication.
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
In the particular counting-out game that gives rise to the Josephus problem, a number of people are standing in a circle waiting to be executed. Counting begins at a specified point in the circle and proceeds around the circle in a specified direction. After a specified number of people are skipped, the next person is executed.
Skip counting is a mathematics technique taught as a kind of multiplication in reform mathematics textbooks such as TERC. In older textbooks, this technique is called counting by twos (threes, fours, etc.). In skip counting by twos, a person can count to 10 by only naming every other even number: 2, 4, 6, 8, 10. [1]
The Chisanbop system. When a finger is touching the table, it contributes its corresponding number to a total. Chisanbop or chisenbop (from Korean chi (ji) finger + sanpŏp (sanbeop) calculation [1] 지산법/指算法), sometimes called Fingermath, [2] is a finger counting method used to perform basic mathematical operations.
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
An abacus (pl. abaci or abacuses), also called a counting frame, is a hand-operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Hindu–Arabic numeral system. [1] An abacus consists of a two-dimensional array of slidable beads (or similar objects). In their ...
A Leibniz wheel or stepped drum is a cylinder with a set of teeth of incremental lengths which, when coupled to a counting wheel, can be used in the calculating engine of a class of mechanical calculators. Invented by Leibniz in 1673, it was used for three centuries until the advent of the electronic calculator in the mid-1970s.