1.
Microsoft Windows
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Microsoft Windows is a metafamily of graphical operating systems developed, marketed, and sold by Microsoft. It consists of families of operating systems, each of which cater to a certain sector of the computing industry with the OS typically associated with IBM PC compatible architecture. Active Windows families include Windows NT, Windows Embedded and Windows Phone, defunct Windows families include Windows 9x, Windows 10 Mobile is an active product, unrelated to the defunct family Windows Mobile. Microsoft introduced an operating environment named Windows on November 20,1985, Microsoft Windows came to dominate the worlds personal computer market with over 90% market share, overtaking Mac OS, which had been introduced in 1984. Apple came to see Windows as an encroachment on their innovation in GUI development as implemented on products such as the Lisa. On PCs, Windows is still the most popular operating system, however, in 2014, Microsoft admitted losing the majority of the overall operating system market to Android, because of the massive growth in sales of Android smartphones. In 2014, the number of Windows devices sold was less than 25% that of Android devices sold and this comparison however may not be fully relevant, as the two operating systems traditionally target different platforms. As of September 2016, the most recent version of Windows for PCs, tablets, smartphones, the most recent versions for server computers is Windows Server 2016. A specialized version of Windows runs on the Xbox One game console, Microsoft, the developer of Windows, has registered several trademarks each of which denote a family of Windows operating systems that target a specific sector of the computing industry. It now consists of three operating system subfamilies that are released almost at the time and share the same kernel. Windows, The operating system for personal computers, tablets. The latest version is Windows 10, the main competitor of this family is macOS by Apple Inc. for personal computers and Android for mobile devices. Windows Server, The operating system for server computers, the latest version is Windows Server 2016. Unlike its clients sibling, it has adopted a strong naming scheme, the main competitor of this family is Linux. Windows PE, A lightweight version of its Windows sibling meant to operate as an operating system, used for installing Windows on bare-metal computers. The latest version is Windows PE10.0.10586.0, Windows Embedded, Initially, Microsoft developed Windows CE as a general-purpose operating system for every device that was too resource-limited to be called a full-fledged computer. The following Windows families are no longer being developed, Windows 9x, Microsoft now caters to the consumers market with Windows NT. Windows Mobile, The predecessor to Windows Phone, it was a mobile operating system
2.
Software calculator
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A software calculator is a calculator that has been implemented as a computer program, rather than as a physical hardware device. They are among the simpler interactive software tools, and, as such, they, can be used to perform any process that consists of a sequence of steps each of which applies one of these operations. As a calculator, rather than a computer, they usually, perform short processes that are not compute intensive. Do not accept large amounts of data or produce many results. Software calculators are available for different platforms, and they can be. A program implemented as server or client-side scripting within a web page, also complex software may have calculator-like dialogs, sometimes with the full calculator functionality, to enter data into the system. Computers as we know them today first emerged in the 1940s and 1950s, the software that they ran was naturally used to perform calculations, but it was specially designed for a substantial application that was not limited to simple calculations. For example, the LEO computer was designed to run application software such as payroll. This was VisiCalc and it was called an interactive visible calculator, but it was actually a spreadsheet, the Unix version released in 1979, V7 Unix, contained a command-line accessible calculator. Calculators have been used since ancient times and until the advent of software calculators they were physical, the most recent hardware calculators are electronic hand-held devices with buttons for digits and operations, and a small window for inputs and results. The first software calculators imitated these hardware calculators by implementing the same functionality with mouse-operated, rather than finger-operated, such software calculators first emerged in the 1980s as part of the Windows operating system, Windows 1.0. Some software calculators directly simulate one of the calculators, by presenting an image that looks like the calculator. There is now a wide range of software calculators. Software calculators are provided on the Internet which are customizable to use any conceivable algebraic expression, no longer limited to a set of trigonometric and simple algebraic expressions, versions of the software calculator are now tailored to any and all topical applications. Every type of hardware calculator has been implemented in software, including conversion, financial, graphing, programmable, other numerical calculators that do not imitate hardware calculators include, Formula calculators Windows-based calculators Specialised calculators. Windows-based calculators present a dialog box allows users to enter data, rather than data and operations. There are many examples of such calculators in finance, mathematics, science, there are software calculators that contain operations relevant to a specific application area and profession, including automotive, construction and electrical engineering. Formula weight calculator, The input is a molecular formula, using the periodic-table symbols and notation
3.
Calculator
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An electronic calculator is a small, portable electronic device used to perform operations ranging from basic arithmetic to complex mathematics. The first solid state electronic calculator was created in the 1960s, building on the history of tools such as the abacus. It was developed in parallel with the computers of the day. The pocket sized devices became available in the 1970s, especially after the first microprocessor and they later became used commonly within the petroleum industry. Modern electronic calculators vary, from cheap, give-away, credit-card-sized models to sturdy desktop models with built-in printers and they became popular in the mid-1970s. By the end of decade, calculator prices had reduced to a point where a basic calculator was affordable to most. In addition to general purpose calculators, there are designed for specific markets. For example, there are scientific calculators which include trigonometric and statistical calculations, some calculators even have the ability to do computer algebra. Graphing calculators can be used to graph functions defined on the real line, as of 2016, basic calculators cost little, but the scientific and graphing models tend to cost more. In 1986, calculators still represented an estimated 41% of the worlds general-purpose hardware capacity to compute information, by 2007, this diminished to less than 0. 05%. Modern 2016 electronic calculators contain a keyboard with buttons for digits and arithmetical operations, most basic calculators assign only one digit or operation on each button, however, in more specific calculators, a button can perform multi-function working with key combinations. Large-sized figures and comma separators are used to improve readability. Various symbols for function commands may also be shown on the display, fractions such as 1⁄3 are displayed as decimal approximations, for example rounded to 0.33333333. Also, some fractions can be difficult to recognize in decimal form, as a result, Calculators also have the ability to store numbers into computer memory. Basic types of these only one number at a time. The variables can also be used for constructing formulas, some models have the ability to extend memory capacity to store more numbers, the extended memory address is termed an array index. Power sources of calculators are, batteries, solar cells or mains electricity, some models even have no turn-off button but they provide some way to put off. Crank-powered calculators were also common in the computer era
4.
Windows 1.0
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Windows 1.0 is a graphical personal computer operating environment developed by Microsoft. Windows 1.0 was released on November 20,1985 and it runs as a graphical, 16-bit multi-tasking shell on top of an existing MS-DOS installation. It provides an environment which can run graphical programs designed for Windows and its development was spearheaded by the company founder Bill Gates after he saw a demonstration of a similar software suite known as Visi On at COMDEX. Despite positive responses to its early presentations and support from a number of hardware and software makers, critics felt Windows 1.0 did not meet their expectations. In particular, they felt that Windows 1, despite these criticisms, Windows 1.0 was an important milestone for Microsoft, as it introduced the Microsoft Windows line, and in computer history in general. Windows 1.0 was declared obsolete and Microsoft stopped providing support, the development of Windows began after Microsoft founder Bill Gates saw a demonstration at COMDEX1982 of VisiCorps Visi On, a graphical user interface software suite for IBM PC compatible computers. Microsoft first presented Windows to the public on November 10,1983, requiring two floppy disk drives and 192 KB of RAM, Microsoft described the software as a device driver for MS-DOS2.0. Many manufacturers of MS-DOS computers such as Compaq, Zenith, and DEC promised to support, as did software companies such as Ashton-Tate. From early in Windows history Gates viewed it as Microsofts future, were also saying that only applications that take advantage of Windows will be competitive in the long run. IBM was notably absent from Microsofts announcement, and by late 1984 the press reported a War of the Windows between Windows, IBMs TopView, and Digital Researchs Graphics Environment Manager. Microsoft had promised in November 1983 to ship Windows by April 1984, but subsequently denied that it had announced a release date, and predicted that Windows would ship by June 1985. Deemphasizing multitasking, the stated that Windows purpose, unlike that of TopView, was to turn the computer into a graphics-rich environment while using less memory. Windows 1.0 was officially released on November 20,1985, version 1.01, released in 1985, was the first point-release after Windows 1.00. Version 1.02, released in May 1986, was an international release, version 1.03, released in August 1986, included enhancements that made it consistent with the international release. It included drivers for European keyboards and additional screen and printer drivers, version 1.04, released in April 1987, added support for the new IBM PS/2 computers, although no support for PS/2 mice or new VGA graphics modes was provided. At the same time, Microsoft and IBM announced the introduction of OS/2 and its graphical OS/2 Presentation Manager, in November 1987, Windows 1.0 was succeeded by Windows 2.0. Microsoft supported Windows 1.0 for 16 years, until December 31,2001 – the longest out of all versions of Windows. Windows 1.0 offers limited multitasking of existing MS-DOS programs and concentrates on creating a paradigm, an execution model
5.
Windows 3.0
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Windows 3.0, a graphical environment, is the third major release of Microsoft Windows, and was released on May 22,1990. It became the first widely successful version of Windows and a rival to Apple Macintosh and it was followed by Windows 3.1. Windows 3.0 originated in 1989 when David Weise and Murray Sargent independently decided to develop a protected mode Windows as an experiment and they cobbled together a rough prototype and presented it to company executives, who were impressed enough to approve it as an official project. However, this was of limited use for the home market, the MS-DOS Executive file manager/program launcher was replaced with the icon-based Program Manager and the list-based File Manager, splitting files and programs. The Control Panel, previously available as an applet, was re-modeled after the one in the classic Mac OS. It centralized system settings, including control over the scheme of the interface. A number of applications were included, such as the text editor Notepad and the word processor Write, a macro recorder, the paint program Paintbrush. Also, the earlier Reversi game was complemented with the card game Microsoft Solitaire, 256-color VGA and MCGA modes were supported for the first time. Windows 3.0 includes a Protected/Enhanced mode which allows Windows applications to use memory in a more painless manner than their DOS counterparts could. It can run in any of Real, Standard, or 386 Enhanced modes, Windows 3.0 tries to auto detect which mode to run in, although it can be forced to run in a specific mode using the switches, /r, /s and /3 respectively. Since Windows 3.0 runs in 16-bit 286 protected mode and not 32-bit 386 protected mode, however, on 32-bit CPUs, the programmer had access to larger memory pointers and so it was possible to expand program segments to whatever size was desired. Because of this, Windows 3.0 can access only 16 MB total of RAM and this was the first version to run Windows programs in protected mode, although the 386 enhanced mode kernel was an enhanced version of the protected mode kernel for Windows/286. The official system requirements for Windows 3.1 or higher Also, Windows 3.0 cannot run in full color on most 8086/88 machines, as the built-in 640×350 EGA and 640×480 VGA drivers contained Intel 80186 instructions. MCGA 320×200 and 640×480 drivers did not contain these instructions and this could be worked around by installing the Windows 2. x EGA/VGA drivers, replacing the CPU with an NEC V20/V30, or by using a modified VGA driver that supports the 8086/88. Real mode primarily existed as a way to run Windows 2. x applications and it was removed in Windows 3. 1x. Almost all applications designed for Windows 3.0 had to be run in standard or 386 enhanced modes, however, it was necessary to load Windows 3.0 in real mode to run SWAPFILE. EXE, which allowed users to change virtual memory settings. Officially, Microsoft stated that an 8Mhz turbo 8086 was the minimum CPU needed to run Windows 3.0 and it could be run on 4.77 MHz 8088 machines, but performance is so slow as to render the OS almost unusable. Up to 4 MB of EMS memory is supported in real mode, Standard mode was used most often as its requirements were more in-line with an average PC of that era — an 80286 processor with at least 1 MB of memory
6.
Exponentiation
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Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent n. The exponent is usually shown as a superscript to the right of the base, Some common exponents have their own names, the exponent 2 is called the square of b or b squared, the exponent 3 is called the cube of b or b cubed. The exponent −1 of b, or 1 / b, is called the reciprocal of b, when n is a positive integer and b is not zero, b−n is naturally defined as 1/bn, preserving the property bn × bm = bn + m. The definition of exponentiation can be extended to any real or complex exponent. Exponentiation by integer exponents can also be defined for a variety of algebraic structures. The term power was used by the Greek mathematician Euclid for the square of a line, archimedes discovered and proved the law of exponents, 10a 10b = 10a+b, necessary to manipulate powers of 10. In the late 16th century, Jost Bürgi used Roman numerals for exponents, early in the 17th century, the first form of our modern exponential notation was introduced by Rene Descartes in his text titled La Géométrie, there, the notation is introduced in Book I. Nicolas Chuquet used a form of notation in the 15th century. The word exponent was coined in 1544 by Michael Stifel, samuel Jeake introduced the term indices in 1696. In the 16th century Robert Recorde used the square, cube, zenzizenzic, sursolid, zenzicube, second sursolid. Biquadrate has been used to refer to the power as well. Some mathematicians used exponents only for greater than two, preferring to represent squares as repeated multiplication. Thus they would write polynomials, for example, as ax + bxx + cx3 + d, another historical synonym, involution, is now rare and should not be confused with its more common meaning. In 1748 Leonhard Euler wrote consider exponentials or powers in which the exponent itself is a variable and it is clear that quantities of this kind are not algebraic functions, since in those the exponents must be constant. With this introduction of transcendental functions, Euler laid the foundation for the introduction of natural logarithm as the inverse function for y = ex. The expression b2 = b ⋅ b is called the square of b because the area of a square with side-length b is b2, the expression b3 = b ⋅ b ⋅ b is called the cube of b because the volume of a cube with side-length b is b3. The exponent indicates how many copies of the base are multiplied together, for example,35 =3 ⋅3 ⋅3 ⋅3 ⋅3 =243. The base 3 appears 5 times in the multiplication, because the exponent is 5
7.
Nth root
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A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred by using numbers, as in fourth root, twentieth root. For example,2 is a root of 4, since 22 =4. −2 is also a root of 4, since 2 =4. A real number or complex number has n roots of degree n. While the roots of 0 are not distinct, the n nth roots of any real or complex number are all distinct. If n is odd and x is real, one nth root is real and has the sign as x. Finally, if x is not real, then none of its nth roots is real. Roots are usually using the radical symbol or radix or √, with x or √ x denoting the square root, x 3 denoting the cube root, x 4 denoting the fourth root. In the expression x n, n is called the index, is the sign or radix. For example, −8 has three roots, −2,1 + i √3 and 1 − i √3. Out of these,1 + i √3 has the least argument,4 has two square roots,2 and −2, having arguments 0 and π respectively. So 2 is considered the root on account of having the lesser argument. An unresolved root, especially one using the symbol, is often referred to as a surd or a radical. Nth roots can also be defined for complex numbers, and the roots of 1 play an important role in higher mathematics. The origin of the root symbol √ is largely speculative, some sources imply that the symbol was first used by Arab mathematicians. One of those mathematicians was Abū al-Hasan ibn Alī al-Qalasādī, legend has it that it was taken from the Arabic letter ج, which is the first letter in the Arabic word جذر. However, many scholars, including Leonhard Euler, believe it originates from the letter r, the symbol was first seen in print without the vinculum in the year 1525 in Die Coss by Christoff Rudolff, a German mathematician
8.
Logarithm
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In mathematics, the logarithm is the inverse operation to exponentiation. That means the logarithm of a number is the exponent to which another fixed number, in simple cases the logarithm counts factors in multiplication. For example, the base 10 logarithm of 1000 is 3, the logarithm of x to base b, denoted logb, is the unique real number y such that by = x. For example, log2 =6, as 64 =26, the logarithm to base 10 is called the common logarithm and has many applications in science and engineering. The natural logarithm has the e as its base, its use is widespread in mathematics and physics. The binary logarithm uses base 2 and is used in computer science. Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations and they were rapidly adopted by navigators, scientists, engineers, and others to perform computations more easily, using slide rules and logarithm tables. The present-day notion of logarithms comes from Leonhard Euler, who connected them to the function in the 18th century. Logarithmic scales reduce wide-ranging quantities to tiny scopes, for example, the decibel is a unit quantifying signal power log-ratios and amplitude log-ratios. In chemistry, pH is a measure for the acidity of an aqueous solution. Logarithms are commonplace in scientific formulae, and in measurements of the complexity of algorithms and they describe musical intervals, appear in formulas counting prime numbers, inform some models in psychophysics, and can aid in forensic accounting. In the same way as the logarithm reverses exponentiation, the logarithm is the inverse function of the exponential function applied to complex numbers. The discrete logarithm is another variant, it has uses in public-key cryptography, the idea of logarithms is to reverse the operation of exponentiation, that is, raising a number to a power. For example, the power of 2 is 8, because 8 is the product of three factors of 2,23 =2 ×2 ×2 =8. It follows that the logarithm of 8 with respect to base 2 is 3, the third power of some number b is the product of three factors equal to b. More generally, raising b to the power, where n is a natural number, is done by multiplying n factors equal to b. The n-th power of b is written bn, so that b n = b × b × ⋯ × b ⏟ n factors, exponentiation may be extended to by, where b is a positive number and the exponent y is any real number. For example, b−1 is the reciprocal of b, that is, the logarithm of a positive real number x with respect to base b, a positive real number not equal to 1, is the exponent by which b must be raised to yield x
9.
Factorial
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In mathematics, the factorial of a non-negative integer n, denoted by n. is the product of all positive integers less than or equal to n. =5 ×4 ×3 ×2 ×1 =120, the value of 0. is 1, according to the convention for an empty product. The factorial operation is encountered in areas of mathematics, notably in combinatorics, algebra. Its most basic occurrence is the fact there are n. ways to arrange n distinct objects into a sequence. This fact was known at least as early as the 12th century, fabian Stedman, in 1677, described factorials as applied to change ringing. After describing a recursive approach, Stedman gives a statement of a factorial, Now the nature of these methods is such, the factorial function is formally defined by the product n. = ∏ k =1 n k, or by the relation n. = {1 if n =0. The factorial function can also be defined by using the rule as n. All of the above definitions incorporate the instance 0, =1, in the first case by the convention that the product of no numbers at all is 1. This is convenient because, There is exactly one permutation of zero objects, = n. ×, valid for n >0, extends to n =0. It allows for the expression of many formulae, such as the function, as a power series. It makes many identities in combinatorics valid for all applicable sizes, the number of ways to choose 0 elements from the empty set is =0. More generally, the number of ways to choose n elements among a set of n is = n. n, the factorial function can also be defined for non-integer values using more advanced mathematics, detailed in the section below. This more generalized definition is used by advanced calculators and mathematical software such as Maple or Mathematica, although the factorial function has its roots in combinatorics, formulas involving factorials occur in many areas of mathematics. There are n. different ways of arranging n distinct objects into a sequence, often factorials appear in the denominator of a formula to account for the fact that ordering is to be ignored. A classical example is counting k-combinations from a set with n elements, one can obtain such a combination by choosing a k-permutation, successively selecting and removing an element of the set, k times, for a total of n k _ = n ⋯ possibilities. This however produces the k-combinations in an order that one wishes to ignore, since each k-combination is obtained in k. different ways. This number is known as the coefficient, because it is also the coefficient of Xk in n
10.
Trigonometry
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Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies, Trigonometry is also the foundation of surveying. Trigonometry is most simply associated with planar right-angle triangles, thus the majority of applications relate to right-angle triangles. One exception to this is spherical trigonometry, the study of triangles on spheres, surfaces of constant positive curvature, Trigonometry on surfaces of negative curvature is part of hyperbolic geometry. Trigonometry basics are often taught in schools, either as a course or as a part of a precalculus course. Sumerian astronomers studied angle measure, using a division of circles into 360 degrees, the ancient Nubians used a similar method. In 140 BC, Hipparchus gave the first tables of chords, analogous to modern tables of sine values, in the 2nd century AD, the Greco-Egyptian astronomer Ptolemy printed detailed trigonometric tables in Book 1, chapter 11 of his Almagest. Ptolemy used chord length to define his trigonometric functions, a difference from the sine convention we use today. The modern sine convention is first attested in the Surya Siddhanta and these Greek and Indian works were translated and expanded by medieval Islamic mathematicians. By the 10th century, Islamic mathematicians were using all six trigonometric functions, had tabulated their values, at about the same time, Chinese mathematicians developed trigonometry independently, although it was not a major field of study for them. At the same time, another translation of the Almagest from Greek into Latin was completed by the Cretan George of Trebizond, Trigonometry was still so little known in 16th-century northern Europe that Nicolaus Copernicus devoted two chapters of De revolutionibus orbium coelestium to explain its basic concepts. Driven by the demands of navigation and the growing need for maps of large geographic areas. Bartholomaeus Pitiscus was the first to use the word, publishing his Trigonometria in 1595, gemma Frisius described for the first time the method of triangulation still used today in surveying. It was Leonhard Euler who fully incorporated complex numbers into trigonometry, the works of the Scottish mathematicians James Gregory in the 17th century and Colin Maclaurin in the 18th century were influential in the development of trigonometric series. Also in the 18th century, Brook Taylor defined the general Taylor series, if one angle of a triangle is 90 degrees and one of the other angles is known, the third is thereby fixed, because the three angles of any triangle add up to 180 degrees. The two acute angles therefore add up to 90 degrees, they are complementary angles, the shape of a triangle is completely determined, except for similarity, by the angles. Once the angles are known, the ratios of the sides are determined, if the length of one of the sides is known, the other two are determined. Sin A = opposite hypotenuse = a c, Cosine function, defined as the ratio of the adjacent leg to the hypotenuse
