ComputerA computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These programs enable computers to perform a wide range of tasks. A computer system is a nominally complete computer that includes the hardware, operating system (main software), and peripheral equipment needed and used for full operation.
Division (mathematics)Division is one of the four basic operations of arithmetic. The other operations are addition, subtraction, and multiplication. What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient. At an elementary level the division of two natural numbers is, among other possible interpretations, the process of calculating the number of times one number is contained within another. This number of times need not be an integer.
Mechanical calculatorA 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. Most mechanical calculators were comparable in size to small desktop computers and have been rendered obsolete by the advent of the electronic calculator and the digital computer. Surviving notes from Wilhelm Schickard in 1623 reveal that he designed and had built the earliest of the modern attempts at mechanizing calculation.
AdditionAddition (usually signified by the plus symbol ) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows two columns of three apples and two apples each, totaling at five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").
Common logarithmIn mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as standard logarithm. Historically, it was known as logarithmus decimalis or logarithmus decadis. It is indicated by log(x), log10 (x), or sometimes Log(x) with a capital L (however, this notation is ambiguous, since it can also mean the complex natural logarithmic multi-valued function).
Square rootIn mathematics, a square root of a number x is a number y such that ; in other words, a number y whose square (the result of multiplying the number by itself, or ) is x. For example, 4 and −4 are square roots of 16 because . Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by where the symbol "" is called the radical sign or radix. For example, to express the fact that the principal square root of 9 is 3, we write .
Scientific calculatorA scientific calculator is an electronic calculator, either desktop or handheld, designed to perform calculations using basic (addition, subtraction, multiplication, division) and complex (trigonometric, hyperbolic, etc.) mathematical operations and functions. They have completely replaced slide rules and are used in both educational and professional settings. In some areas of study scientific calculators have been replaced by graphing calculators and financial calculators which have the capabilities of a scientific calculator along with the capability to graph input data and functions.
William OughtredWilliam Oughtred (5 March 1574 – 30 June 1660), also Owtred, Uhtred, etc., was an English mathematician and Anglican clergyman. After John Napier invented logarithms and Edmund Gunter created the logarithmic scales (lines, or rules) upon which slide rules are based, Oughtred was the first to use two such scales sliding by one another to perform direct multiplication and division. He is credited with inventing the slide rule in about 1622. He also introduced the "×" symbol for multiplication and the abbreviations "sin" and "cos" for the sine and cosine functions.
CORDICCORDIC (for "coordinate rotation digital computer"), also known as Volder's algorithm, or: Digit-by-digit method Circular CORDIC (Jack E. Volder), Linear CORDIC, Hyperbolic CORDIC (John Stephen Walther), and Generalized Hyperbolic CORDIC (GH CORDIC) (Yuanyong Luo et al.), is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots, multiplications, divisions, and exponentials and logarithms with arbitrary base, typically converging with one digit (or bit) per iteration.
Analog computerAn analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities (analog signals) to model the problem being solved. In contrast, digital computers represent varying quantities symbolically and by discrete values of both time and amplitude (digital signals). Analog computers can have a very wide range of complexity.
Mechanical computerA mechanical computer is a computer built from mechanical components such as levers and gears rather than electronic components. The most common examples are adding machines and mechanical counters, which use the turning of gears to increment output displays. More complex examples could carry out multiplication and division—Friden used a moving head which paused at each column—and even differential analysis. One model, the Ascota 170 accounting machine sold in the 1960s calculated square roots.
Logarithmic scaleA logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way. As opposed to a linear number line in which every unit of distance corresponds to adding by the same amount, on a logarithmic scale, every unit of length corresponds to multiplying the previous value by the same amount. Hence, such a scale is nonlinear: the numbers 1, 2, 3, 4, 5, and so on, are not equally spaced. Rather, the numbers 10, 100, 1000, 10000, and 100000 would be equally spaced.
RoundingRounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing with, the fraction 312/937 with 1/3, or the expression with . Rounding is often done to obtain a value that is easier to report and communicate than the original. Rounding can also be important to avoid misleadingly precise reporting of a computed number, measurement, or estimate; for example, a quantity that was computed as but is known to be accurate only to within a few hundred units is usually better stated as "about ". Methods of computing square rootsMethods of computing square roots are numerical analysis algorithms for approximating the principal, or non-negative, square root (usually denoted , , or ) of a real number. Arithmetically, it means given , a procedure for finding a number which when multiplied by itself, yields ; algebraically, it means a procedure for finding the non-negative root of the equation ; geometrically, it means given two line segments, a procedure for constructing their geometric mean. Every real number except zero has two square roots.
Number lineIn elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point. The integers are often shown as specially-marked points evenly spaced on the line. Although the image only shows the integers from –3 to 3, the line includes all real numbers, continuing forever in each direction, and also numbers that are between the integers.
Sector (instrument)The sector, also known as a proportional compass or military compass, was a major calculating instrument in use from the end of the sixteenth century until the nineteenth century. It is an instrument consisting of two rulers of equal length joined by a hinge. A number of scales are inscribed upon the instrument which facilitate various mathematical calculations. It was used for solving problems in proportion, multiplication and division, geometry, and trigonometry, and for computing various mathematical functions, such as square roots and cube roots.
LogarithmIn mathematics, the logarithm is the inverse function to exponentiation. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 103, the logarithm base 10 of 1000 is 3, or log10 (1000) = 3. The logarithm of x to base b is denoted as logb (x), or without parentheses, logb x, or even without the explicit base, log x, when no confusion is possible, or when the base does not matter such as in big O notation.
CalculatorAn electronic calculator is typically a portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics. The first solid-state electronic calculator was created in the early 1960s. Pocket-sized devices became available in the 1970s, especially after the Intel 4004, the first microprocessor, was developed by Intel for the Japanese calculator company Busicom. Modern electronic calculators vary from cheap, give-away, credit-card-sized models to sturdy desktop models with built-in printers.
Multiplication algorithmA multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient than others. Efficient multiplication algorithms have existed since the advent of the decimal system. If a positional numeral system is used, a natural way of multiplying numbers is taught in schools as long multiplication, sometimes called grade-school multiplication, sometimes called the Standard Algorithm: multiply the multiplicand by each digit of the multiplier and then add up all the properly shifted results.
AbacusThe abacus (: abaci or abacuses), also called a counting frame, is a hand-operated calculating tool of unknown origin used since ancient times in the ancient Near East, Europe, China, and Russia, millennia before the adoption of the Hindu-Arabic numeral system. The abacus consists of multiple columns of slidable beads (or similar objects). In their earliest designs, the columns of beads could be loose on a flat surface or sliding in grooves. Later the beads were made to slide on rods and built into a frame, allowing faster manipulation.
