99-637: The TI-7 MathMate is a basic educational calculator by Texas Instruments , designed for students in grades K–3. The MathMate was unique in that it automatically performed order of operations . The MathMate slotted in between the TI-108 and the TI-12 Math Explorer . The TI-7 MathMate was eventually replaced by the TI-10 , which features a two-line display. MathMate by Texas Instruments - US and Canada This microcomputer - or microprocessor -related article
198-513: A Sanskrit word Shunye or shunya to refer to the concept of void . In mathematics texts this word often refers to the number zero. In a similar vein, Pāṇini (5th century BC) used the null (zero) operator in the Ashtadhyayi , an early example of an algebraic grammar for the Sanskrit language (also see Pingala ). There are other uses of zero before Brahmagupta, though the documentation
297-525: A numeral is not clearly distinguished from the number that it represents. In mathematics, the notion of number has been extended over the centuries to include zero (0), negative numbers , rational numbers such as one half ( 1 2 ) {\displaystyle \left({\tfrac {1}{2}}\right)} , real numbers such as the square root of 2 ( 2 ) {\displaystyle \left({\sqrt {2}}\right)} and π , and complex numbers which extend
396-404: A , b positive and the other negative. The incorrect use of this identity, and the related identity in the case when both a and b are negative even bedeviled Euler . This difficulty eventually led him to the convention of using the special symbol i in place of − 1 {\displaystyle {\sqrt {-1}}} to guard against this mistake. The 18th century saw
495-592: A base 4, base 5 "finger" abacus. By 130 AD, Ptolemy , influenced by Hipparchus and the Babylonians, was using a symbol for 0 (a small circle with a long overbar) within a sexagesimal numeral system otherwise using alphabetic Greek numerals . Because it was used alone, not as just a placeholder, this Hellenistic zero was the first documented use of a true zero in the Old World. In later Byzantine manuscripts of his Syntaxis Mathematica ( Almagest ),
594-410: A basic calculator was affordable to most and they became common in schools. In addition to general purpose calculators, there are those 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
693-407: A button can perform multi-function working with key combinations . Calculators usually have liquid-crystal displays (LCD) as output in place of historical light-emitting diode (LED) displays and vacuum fluorescent displays (VFD); details are provided in the section Technical improvements . Large-sized figures are often used to improve readability; while using decimal separator (usually
792-399: A calculator could be made using just a few chips of low power consumption, allowing portable models powered from rechargeable batteries. The first handheld calculator was a 1967 prototype called Cal Tech , whose development was led by Jack Kilby at Texas Instruments in a research project to produce a portable calculator. It could add, multiply, subtract, and divide, and its output device
891-669: A development from the "Cal-Tech" project. It had no traditional display; numerical output was on thermal paper tape. Sharp put in great efforts in size and power reduction and introduced in January 1971 the Sharp EL-8 , also marketed as the Facit 1111, which was close to being a pocket calculator. It weighed 1.59 pounds (721 grams), had a vacuum fluorescent display , rechargeable NiCad batteries, and initially sold for US$ 395. However, integrated circuit development efforts culminated in early 1971 with
990-588: A full single chip calculator IC for the Monroe Royal Digital III calculator. Pico was a spinout by five GI design engineers whose vision was to create single chip calculator ICs. Pico and GI went on to have significant success in the burgeoning handheld calculator market. The first truly pocket-sized electronic calculator was the Busicom LE-120A "HANDY", which was marketed early in 1971. Made in Japan, this
1089-439: A given direction is postulated to converge to the corresponding ideal point. This is closely related to the idea of vanishing points in perspective drawing. The earliest fleeting reference to square roots of negative numbers occurred in the work of the mathematician and inventor Heron of Alexandria in the 1st century AD , when he considered the volume of an impossible frustum of a pyramid . They became more prominent when in
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#17331057246531188-447: A notable expansion. The idea of the graphic representation of complex numbers had appeared, however, as early as 1685, in Wallis 's De algebra tractatus . In the same year, Gauss provided the first generally accepted proof of the fundamental theorem of algebra , showing that every polynomial over the complex numbers has a full set of solutions in that realm. Gauss studied complex numbers of
1287-447: A part from infinity or add a part to infinity, still what remains is infinity." Infinity was a popular topic of philosophical study among the Jain mathematicians c. 400 BC. They distinguished between five types of infinity: infinite in one and two directions, infinite in area, infinite everywhere, and infinite perpetually. The symbol ∞ {\displaystyle {\text{∞}}}
1386-499: A placeholder digit in representing another number as was done by the Babylonians or as a symbol for a lack of quantity as was done by Ptolemy and the Romans. The use of 0 as a number should be distinguished from its use as a placeholder numeral in place-value systems . Many ancient texts used 0. Babylonian and Egyptian texts used it. Egyptians used the word nfr to denote zero balance in double entry accounting . Indian texts used
1485-485: A pocket calculator. Launched in early 1972, it was unlike the other basic four-function pocket calculators then available in that it was the first pocket calculator with scientific functions that could replace a slide rule . The $ 395 HP-35 , along with nearly all later HP engineering calculators, uses reverse Polish notation (RPN), also called postfix notation. A calculation like "8 plus 5" is, using RPN, performed by pressing 8 , Enter↑ , 5 , and + ; instead of
1584-428: A point rather than a comma ) instead of or in addition to vulgar fractions . 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 (such as 1 ⁄ 7 , which is 0.14285714285714 ; to 14 significant figures ) can be difficult to recognize in decimal form; as
1683-437: A result, many scientific calculators are able to work in vulgar fractions or mixed numbers . Calculators also have the ability to save numbers into computer memory . Basic calculators usually store only one number at a time; more specific types are able to store many numbers represented in variables . Usually these variables are named ans or ans(0). The variables can also be used for constructing formulas . Some models have
1782-425: A rigorous method of treating the ideas about infinite and infinitesimal numbers that had been used casually by mathematicians, scientists, and engineers ever since the invention of infinitesimal calculus by Newton and Leibniz . A modern geometrical version of infinity is given by projective geometry , which introduces "ideal points at infinity", one for each spatial direction. Each family of parallel lines in
1881-420: A series of separate identical seven-segment displays to build a metering circuit, for example. If the numeric quantity were stored and manipulated as pure binary, interfacing to such a display would require complex circuitry. Therefore, in cases where the calculations are relatively simple, working throughout with BCD can lead to a simpler overall system than converting to and from binary. (For example, CDs keep
1980-671: A system that used combinations of letters from the Roman alphabet, remained dominant in Europe until the spread of the superior Hindu–Arabic numeral system around the late 14th century, and the Hindu–Arabic numeral system remains the most common system for representing numbers in the world today. The key to the effectiveness of the system was the symbol for zero , which was developed by ancient Indian mathematicians around 500 AD. The first known documented use of zero dates to AD 628, and appeared in
2079-474: A way to swap true roots and false roots as well. At the same time, the Chinese were indicating negative numbers by drawing a diagonal stroke through the right-most non-zero digit of the corresponding positive number's numeral. The first use of negative numbers in a European work was by Nicolas Chuquet during the 15th century. He used them as exponents , but referred to them as "absurd numbers". As recently as
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#17331057246532178-451: Is a stub . You can help Misplaced Pages by expanding it . Calculator An 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 ,
2277-444: Is a subset of the next one. So, for example, a rational number is also a real number, and every real number is also a complex number. This can be expressed symbolically as A more complete list of number sets appears in the following diagram. The most familiar numbers are the natural numbers (sometimes called whole numbers or counting numbers): 1, 2, 3, and so on. Traditionally, the sequence of natural numbers started with 1 (0
2376-691: Is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system , which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system , which allows for the representation of any non-negative integer using a combination of ten fundamental numeric symbols, called digits . In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with serial numbers ), and for codes (as with ISBNs ). In common usage,
2475-566: Is common for the Jain math sutra to include calculations of decimal-fraction approximations to pi or the square root of 2 . Similarly, Babylonian math texts used sexagesimal (base 60) fractions with great frequency. The earliest known use of irrational numbers was in the Indian Sulba Sutras composed between 800 and 500 BC. The first existence proofs of irrational numbers is usually attributed to Pythagoras , more specifically to
2574-419: Is common in electronic systems where a numeric value is to be displayed, especially in systems consisting solely of digital logic, and not containing a microprocessor. By employing BCD, the manipulation of numerical data for display can be greatly simplified by treating each digit as a separate single sub-circuit. This matches much more closely the physical reality of display hardware—a designer might choose to use
2673-538: Is largely due to Ernst Kummer , who also invented ideal numbers , which were expressed as geometrical entities by Felix Klein in 1893. In 1850 Victor Alexandre Puiseux took the key step of distinguishing between poles and branch points, and introduced the concept of essential singular points . This eventually led to the concept of the extended complex plane . Prime numbers have been studied throughout recorded history. They are positive integers that are divisible only by 1 and themselves. Euclid devoted one book of
2772-467: Is needed to fit all the desired functions in the limited memory space available in the calculator chip , with acceptable calculation time. The first known tools used to aid arithmetic calculations were: bones (used to tally items), pebbles, and counting boards , and the abacus , known to have been used by Sumerians and Egyptians before 2000 BC. Except for the Antikythera mechanism (an "out of
2871-576: Is not as complete as it is in the Brāhmasphuṭasiddhānta . Records show that the Ancient Greeks seemed unsure about the status of 0 as a number: they asked themselves "How can 'nothing' be something?" leading to interesting philosophical and, by the Medieval period, religious arguments about the nature and existence of 0 and the vacuum. The paradoxes of Zeno of Elea depend in part on
2970-405: Is notably different from the layout of telephone Touch-Tone keypads which have the 1 - 2 - 3 keys on top and 7 - 8 - 9 keys on the third row. In general, a basic electronic calculator consists of the following components: Clock rate of a processor chip refers to the frequency at which the central processing unit (CPU) is running. It is used as an indicator of
3069-405: Is often used to represent an infinite quantity. Aristotle defined the traditional Western notion of mathematical infinity. He distinguished between actual infinity and potential infinity —the general consensus being that only the latter had true value. Galileo Galilei 's Two New Sciences discussed the idea of one-to-one correspondences between infinite sets. But the next major advance in
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3168-434: Is the first book that mentions zero as a number, hence Brahmagupta is usually considered the first to formulate the concept of zero. He gave rules of using zero with negative and positive numbers, such as "zero plus a positive number is a positive number, and a negative number plus zero is the negative number". The Brāhmasphuṭasiddhānta is the earliest known text to treat zero as a number in its own right, rather than as simply
3267-598: Is the first calculator in the world which includes the square root function. Later that same year were released the ELKA 22 (with a luminescent display) and the ELKA 25, with an built-in printer. Several other models were developed until the first pocket model, the ELKA 101 , was released in 1974. The writing on it was in Roman script , and it was exported to western countries. The first desktop programmable calculators were produced in
3366-502: Is transcendental and Lindemann proved in 1882 that π is transcendental. Finally, Cantor showed that the set of all real numbers is uncountably infinite but the set of all algebraic numbers is countably infinite , so there is an uncountably infinite number of transcendental numbers. The earliest known conception of mathematical infinity appears in the Yajur Veda , an ancient Indian script, which at one point states, "If you remove
3465-559: The Brāhmasphuṭasiddhānta , the main work of the Indian mathematician Brahmagupta . He treated 0 as a number and discussed operations involving it, including division . By this time (the 7th century) the concept had clearly reached Cambodia as Khmer numerals , and documentation shows the idea later spreading to China and the Islamic world . Brahmagupta's Brāhmasphuṭasiddhānta
3564-677: The Elements to the theory of primes; in it he proved the infinitude of the primes and the fundamental theorem of arithmetic , and presented the Euclidean algorithm for finding the greatest common divisor of two numbers. In 240 BC, Eratosthenes used the Sieve of Eratosthenes to quickly isolate prime numbers. But most further development of the theory of primes in Europe dates to the Renaissance and later eras. In 1796, Adrien-Marie Legendre conjectured
3663-774: The Pythagorean Hippasus of Metapontum , who produced a (most likely geometrical) proof of the irrationality of the square root of 2 . The story goes that Hippasus discovered irrational numbers when trying to represent the square root of 2 as a fraction. However, Pythagoras believed in the absoluteness of numbers, and could not accept the existence of irrational numbers. He could not disprove their existence through logic, but he could not accept irrational numbers, and so, allegedly and frequently reported, he sentenced Hippasus to death by drowning, to impede spreading of this disconcerting news. The 16th century brought final European acceptance of negative integral and fractional numbers. By
3762-726: The complex number system. In modern mathematics, number systems are considered important special examples of more general algebraic structures such as rings and fields , and the application of the term "number" is a matter of convention, without fundamental significance. Bones and other artifacts have been discovered with marks cut into them that many believe are tally marks . These tally marks may have been used for counting elapsed time, such as numbers of days, lunar cycles or keeping records of quantities, such as of animals. A tallying system has no concept of place value (as in modern decimal notation), which limits its representation of large numbers. Nonetheless, tallying systems are considered
3861-585: The prime number theorem , describing the asymptotic distribution of primes. Other results concerning the distribution of the primes include Euler's proof that the sum of the reciprocals of the primes diverges, and the Goldbach conjecture , which claims that any sufficiently large even number is the sum of two primes. Yet another conjecture related to the distribution of prime numbers is the Riemann hypothesis , formulated by Bernhard Riemann in 1859. The prime number theorem
3960-461: The 16th century closed formulas for the roots of third and fourth degree polynomials were discovered by Italian mathematicians such as Niccolò Fontana Tartaglia and Gerolamo Cardano . It was soon realized that these formulas, even if one was only interested in real solutions, sometimes required the manipulation of square roots of negative numbers. This was doubly unsettling since they did not even consider negative numbers to be on firm ground at
4059-467: The 17th century, mathematicians generally used decimal fractions with modern notation. It was not, however, until the 19th century that mathematicians separated irrationals into algebraic and transcendental parts, and once more undertook the scientific study of irrationals. It had remained almost dormant since Euclid . In 1872, the publication of the theories of Karl Weierstrass (by his pupil E. Kossak), Eduard Heine , Georg Cantor , and Richard Dedekind
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4158-577: The 18th century, it was common practice to ignore any negative results returned by equations on the assumption that they were meaningless. It is likely that the concept of fractional numbers dates to prehistoric times . The Ancient Egyptians used their Egyptian fraction notation for rational numbers in mathematical texts such as the Rhind Mathematical Papyrus and the Kahun Papyrus . Classical Greek and Indian mathematicians made studies of
4257-597: The 3rd century AD in Greece. Diophantus referred to the equation equivalent to 4 x + 20 = 0 (the solution is negative) in Arithmetica , saying that the equation gave an absurd result. During the 600s, negative numbers were in use in India to represent debts. Diophantus' previous reference was discussed more explicitly by Indian mathematician Brahmagupta , in Brāhmasphuṭasiddhānta in 628, who used negative numbers to produce
4356-507: The ANITA was superseded in June 1963 by the U.S. manufactured Friden EC-130, which had an all-transistor design, a stack of four 13-digit numbers displayed on a 5-inch (13 cm) cathode-ray tube (CRT), and introduced Reverse Polish Notation (RPN) to the calculator market for a price of $ 2200, which was about three times the cost of an electromechanical calculator of the time. Like Bell Punch, Friden
4455-590: The Autumn of 1971, with four functions and an eight-digit red LED display, for US$ 240 , while in August 1972 the four-function Sinclair Executive became the first slimline pocket calculator measuring 5.4 by 2.2 by 0.35 inches (137.2 mm × 55.9 mm × 8.9 mm) and weighing 2.5 ounces (71 g). It retailed for around £79 ( US$ 194 at the time). By the end of the decade, similar calculators were priced less than £5 ($ 6.85). Following protracted development over
4554-593: The Hellenistic zero had morphed into the Greek letter Omicron (otherwise meaning 70). Another true zero was used in tables alongside Roman numerals by 525 (first known use by Dionysius Exiguus ), but as a word, nulla meaning nothing , not as a symbol. When division produced 0 as a remainder, nihil , also meaning nothing , was used. These medieval zeros were used by all future medieval computists (calculators of Easter). An isolated use of their initial, N,
4653-687: The Mk VII for continental Europe and the Mk VIII for Britain and the rest of the world, both for delivery from early 1962. The Mk VII was a slightly earlier design with a more complicated mode of multiplication, and was soon dropped in favour of the simpler Mark VIII. The ANITA had a full keyboard, similar to mechanical comptometers of the time, a feature that was unique to it and the later Sharp CS-10A among electronic calculators. The ANITA weighed roughly 33 pounds (15 kg) due to its large tube system. Bell Punch had been producing key-driven mechanical calculators of
4752-493: 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 (for old models), turning on with a switch or button. Some models even have no turn-off button but they provide some way to put off (for example, leaving no operation for a moment, covering solar cell exposure, or closing their lid ). Crank -powered calculators were also common in
4851-413: The adding machine as a means of completing this operation. There is a debate about whether Pascal or Shickard should be credited as the known inventor of a calculating machine due to the differences (like the different aims) of both inventions. Schickard and Pascal were followed by Gottfried Leibniz who spent forty years designing a four-operation mechanical calculator, the stepped reckoner , inventing in
4950-552: The algebraic infix notation : 8 , + , 5 , = . It had 35 buttons and was based on Mostek Mk6020 chip. The first Soviet scientific pocket-sized calculator the "B3-18" was completed by the end of 1975. In 1973, Texas Instruments (TI) introduced the SR-10 , ( SR signifying slide rule ) an algebraic entry pocket calculator using scientific notation for $ 150. Shortly after the SR-11 featured an added key for entering pi (π). It
5049-415: The comptometer type under the names "Plus" and "Sumlock", and had realised in the mid-1950s that the future of calculators lay in electronics. They employed the young graduate Norbert Kitz, who had worked on the early British Pilot ACE computer project, to lead the development. The ANITA sold well since it was the only electronic desktop calculator available, and was silent and quick. The tube technology of
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#17331057246535148-524: The course of two years including a botched partnership with Texas Instruments, Eldorado Electrodata released five pocket calculators in 1972. One called the Touch Magic was "no bigger than a pack of cigarettes" according to Administrative Management . The first Soviet Union made pocket-sized calculator, the Elektronika B3-04 was developed by the end of 1973 and sold at the start of 1974. One of
5247-416: The development of Greek mathematics , stimulating the investigation of many problems in number theory which are still of interest today. During the 19th century, mathematicians began to develop many different abstractions which share certain properties of numbers, and may be seen as extending the concept. Among the first were the hypercomplex numbers , which consist of various extensions or modifications of
5346-428: The early computer era. The following keys are common to most pocket calculators. While the arrangement of the digits is standard, the positions of other keys vary from model to model; the illustration is an example. The arrangement of digits on calculator and other numeric keypads with the 7 - 8 - 9 keys two rows above the 1 - 2 - 3 keys is derived from calculators and cash registers . It
5445-493: The eve of the industrial revolution made large scale production of more compact and modern units possible. The Arithmometer , invented in 1820 as a four-operation mechanical calculator, was released to production in 1851 as an adding machine and became the first commercially successful unit; forty years later, by 1890, about 2,500 arithmometers had been sold plus a few hundreds more from two arithmometer clone makers (Burkhardt, Germany, 1878 and Layton, UK, 1883) and Felt and Tarrant,
5544-461: 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. They became popular in the mid-1970s as the incorporation of integrated circuits reduced their size and cost. By the end of that decade, prices had dropped to the point where
5643-463: The first Japanese one) was the Casio (AL-1000) produced in 1967. It featured a nixie tubes display and had transistor electronics and ferrite core memory. The Monroe Epic programmable calculator came on the market in 1967. A large, printing, desk-top unit, with an attached floor-standing logic tower, it could be programmed to perform many computer-like functions. However, the only branch instruction
5742-483: The first direct multiplication machine in 1834: this was also the second key-driven machine in the world, following that of James White (1822). It was not until the 19th century and the Industrial Revolution that real developments began to occur. Although machines capable of performing all four arithmetic functions existed prior to the 19th century, the refinement of manufacturing and fabrication processes during
5841-641: The first kind of abstract numeral system. The first known system with place value was the Mesopotamian base 60 system ( c. 3400 BC) and the earliest known base 10 system dates to 3100 BC in Egypt . Numbers should be distinguished from numerals , the symbols used to represent numbers. The Egyptians invented the first ciphered numeral system, and the Greeks followed by mapping their counting numbers onto Ionian and Doric alphabets. Roman numerals,
5940-552: The first low-cost calculators was the Sinclair Cambridge , launched in August 1973. It retailed for £29.95 ($ 41.03), or £5 ($ 6.85) less in kit form, and later models included some scientific functions. The Sinclair calculators were successful because they were far cheaper than the competition; however, their design led to slow and less accurate computations of transcendental functions (maximum three decimal places of accuracy). Meanwhile, Hewlett-Packard (HP) had been developing
6039-417: The form a + bi , where a and b are integers (now called Gaussian integers ) or rational numbers. His student, Gotthold Eisenstein , studied the type a + bω , where ω is a complex root of x − 1 = 0 (now called Eisenstein integers ). Other such classes (called cyclotomic fields ) of complex numbers derive from the roots of unity x − 1 = 0 for higher values of k . This generalization
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#17331057246536138-740: The general form quadratic formula that remains in use today. However, in the 12th century in India, Bhaskara gives negative roots for quadratic equations but says the negative value "is in this case not to be taken, for it is inadequate; people do not approve of negative roots". European mathematicians, for the most part, resisted the concept of negative numbers until the 17th century, although Fibonacci allowed negative solutions in financial problems where they could be interpreted as debts (chapter 13 of Liber Abaci , 1202) and later as losses (in Flos ). René Descartes called them false roots as they cropped up in algebraic polynomials yet he found
6237-579: The idea of a cut (Schnitt) in the system of real numbers , separating all rational numbers into two groups having certain characteristic properties. The subject has received later contributions at the hands of Weierstrass, Kronecker , and Méray. The search for roots of quintic and higher degree equations was an important development, the Abel–Ruffini theorem ( Ruffini 1799, Abel 1824) showed that they could not be solved by radicals (formulas involving only arithmetical operations and roots). Hence it
6336-603: The introduction of the first "calculator on a chip", the MK6010 by Mostek , followed by Texas Instruments later in the year. Although these early hand-held calculators were very costly, these advances in electronics, together with developments in display technology (such as the vacuum fluorescent display , LED , and LCD ), led within a few years to the cheap pocket calculator available to all. In 1971, Pico Electronics and General Instrument also introduced their first collaboration in ICs,
6435-547: The logic circuits, appeared in the 1940s and 1950s. Electronic circuits developed for computers also had application to electronic calculators. The Casio Computer Company, in Japan , released the Model 14-A calculator in 1957, which was the world's first all-electric (relatively) compact calculator. It did not use electronic logic but was based on relay technology, and was built into a desk. The IBM 608 plugboard programmable calculator
6534-619: The mid-1960s. They included the Mathatronics Mathatron (1964) and the Olivetti Programma 101 (late 1965) which were solid-state, desktop, printing, floating point, algebraic entry, programmable, stored-program electronic calculators. Both could be programmed by the end user and print out their results. The Programma 101 saw much wider distribution and had the added feature of offline storage of programs via magnetic cards. Another early programmable desktop calculator (and maybe
6633-695: The only other competitor in true commercial production, had sold 100 comptometers . It wasn't until 1902 that the familiar push-button user interface was developed, with the introduction of the Dalton Adding Machine, developed by James L. Dalton in the United States . In 1921, Edith Clarke invented the "Clarke calculator", a simple graph-based calculator for solving line equations involving hyperbolic functions. This allowed electrical engineers to simplify calculations for inductance and capacitance in power transmission lines . The Curta calculator
6732-422: The power grid, was released at the start of the 1970s. The electronic calculators of the mid-1960s were large and heavy desktop machines due to their use of hundreds of transistors on several circuit boards with a large power consumption that required an AC power supply. There were great efforts to put the logic required for a calculator into fewer and fewer integrated circuits (chips) and calculator electronics
6831-421: The process his leibniz wheel , but who couldn't design a fully operational machine. There were also five unsuccessful attempts to design a calculating clock in the 17th century. The 18th century saw the arrival of some notable improvements, first by Poleni with the first fully functional calculating clock and four-operation machine, but these machines were almost always one of a kind . Luigi Torchi invented
6930-631: The processor's speed, and is measured in clock cycles per second or hertz (Hz) . For basic calculators, the speed can vary from a few hundred hertz to the kilohertz range. A basic explanation as to how calculations are performed in a simple four-function calculator: To perform the calculation 25 + 9 , one presses keys in the following sequence on most calculators: 2 5 + 9 = . Other functions are usually performed using repeated additions or subtractions. Most pocket calculators do all their calculations in binary-coded decimal (BCD) rather than binary. BCD
7029-504: The properties of numbers. Besides their practical uses, numbers have cultural significance throughout the world. For example, in Western society, the number 13 is often regarded as unlucky , and " a million " may signify "a lot" rather than an exact quantity. Though it is now regarded as pseudoscience , belief in a mystical significance of numbers, known as numerology , permeated ancient and medieval thought. Numerology heavily influenced
7128-508: The real line, or higher-dimensional Euclidean space . As of 2016 , basic calculators cost little, but scientific and graphing models tend to cost more. Computer operating systems as far back as early Unix have included interactive calculator programs such as dc and hoc , and interactive BASIC could be used to do calculations on most 1970s and 1980s home computers. Calculator functions are included in most smartphones , tablets , and personal digital assistant (PDA) type devices. With
7227-403: The real numbers with a square root of −1 (and its combinations with real numbers by adding or subtracting its multiples). Calculations with numbers are done with arithmetical operations, the most familiar being addition , subtraction , multiplication , division , and exponentiation . Their study or usage is called arithmetic , a term which may also refer to number theory , the study of
7326-603: The same time). The Victor 3900 was the first to use integrated circuits in place of individual transistors , but production problems delayed sales until 1966. There followed a series of electronic calculator models from these and other manufacturers, including Canon , Mathatronics , Olivetti , SCM (Smith-Corona-Marchant), Sony , Toshiba , and Wang . The early calculators used hundreds of germanium transistors , which were cheaper than silicon transistors , on multiple circuit boards. Display types used were CRT, cold-cathode Nixie tubes , and filament lamps . Memory technology
7425-556: The theory of rational numbers, as part of the general study of number theory . The best known of these is Euclid's Elements , dating to roughly 300 BC. Of the Indian texts, the most relevant is the Sthananga Sutra , which also covers number theory as part of a general study of mathematics. The concept of decimal fractions is closely linked with decimal place-value notation; the two seem to have developed in tandem. For example, it
7524-408: The theory was made by Georg Cantor ; in 1895 he published a book about his new set theory , introducing, among other things, transfinite numbers and formulating the continuum hypothesis . In the 1960s, Abraham Robinson showed how infinitely large and infinitesimal numbers can be rigorously defined and used to develop the field of nonstandard analysis. The system of hyperreal numbers represents
7623-403: The time" astronomical device), development of computing tools arrived near the start of the 17th century: the geometric-military compass (by Galileo ), logarithms and Napier bones (by Napier ), and the slide rule (by Edmund Gunter ). The Renaissance saw the invention of the mechanical calculator by Wilhelm Schickard in 1623, and later by Blaise Pascal in 1642. A device that
7722-430: The time. When René Descartes coined the term "imaginary" for these quantities in 1637, he intended it as derogatory. (See imaginary number for a discussion of the "reality" of complex numbers.) A further source of confusion was that the equation seemed capriciously inconsistent with the algebraic identity which is valid for positive real numbers a and b , and was also used in complex number calculations with one of
7821-735: The track number in BCD, limiting them to 99 tracks.) The same argument applies when hardware of this type uses an embedded microcontroller or other small processor. Often, smaller code results when representing numbers internally in BCD format, since a conversion from or to binary representation can be expensive on such limited processors. For these applications, some small processors feature BCD arithmetic modes, which assist when writing routines that manipulate BCD quantities. Where calculators have added functions (such as square root, or trigonometric functions ), software algorithms are required to produce high precision results. Sometimes significant design effort
7920-569: The uncertain interpretation of 0. (The ancient Greeks even questioned whether 1 was a number.) The late Olmec people of south-central Mexico began to use a symbol for zero, a shell glyph , in the New World, possibly by the 4th century BC but certainly by 40 BC, which became an integral part of Maya numerals and the Maya calendar . Maya arithmetic used base 4 and base 5 written as base 20. George I. Sánchez in 1961 reported
8019-643: The very wide availability of smartphones and the like, dedicated hardware calculators, while still widely used, are less common than they once were. In 1986, calculators still represented an estimated 41% of the world's general-purpose hardware capacity to compute information. By 2007, this had diminished to less than 0.05%. Electronic calculators contain a keyboard with buttons for digits and arithmetical operations; some even contain "00" and "000" buttons to make larger or smaller numbers easier to enter. Most basic calculators assign only one digit or operation on each button; however, in more specific calculators,
8118-420: The work of Abraham de Moivre and Leonhard Euler . De Moivre's formula (1730) states: while Euler's formula of complex analysis (1748) gave us: The existence of complex numbers was not completely accepted until Caspar Wessel described the geometrical interpretation in 1799. Carl Friedrich Gauss rediscovered and popularized it several years later, and as a result the theory of complex numbers received
8217-472: The writings of Joseph Louis Lagrange . Other noteworthy contributions have been made by Druckenmüller (1837), Kunze (1857), Lemke (1870), and Günther (1872). Ramus first connected the subject with determinants , resulting, with the subsequent contributions of Heine, Möbius , and Günther, in the theory of Kettenbruchdeterminanten . The existence of transcendental numbers was first established by Liouville (1844, 1851). Hermite proved in 1873 that e
8316-616: Was IBM's first all-transistor product, released in 1957; this was a console type system, with input and output on punched cards, and replaced the earlier, larger, vacuum-tube IBM 603 . In October 1961, the world's first all-electronic desktop calculator, the British Bell Punch /Sumlock Comptometer ANITA ( A N ew I nspiration T o A rithmetic/ A ccounting) was announced. This machine used vacuum tubes , cold-cathode tubes and Dekatrons in its circuits, with 12 cold-cathode "Nixie" tubes for its display. Two models were displayed,
8415-571: Was a manufacturer of mechanical calculators that had decided that the future lay in electronics. In 1964 more all-transistor electronic calculators were introduced: Sharp introduced the CS-10A , which weighed 25 kilograms (55 lb) and cost 500,000 yen ($ 4555.81), and Industria Macchine Elettroniche of Italy introduced the IME 84, to which several extra keyboard and display units could be connected so that several people could make use of it (but apparently not at
8514-568: Was a paper tape. As a result of the "Cal-Tech" project, Texas Instruments was granted master patents on portable calculators. The first commercially produced portable calculators appeared in Japan in 1970, and were soon marketed around the world. These included the Sanyo ICC-0081 "Mini Calculator", the Canon Pocketronic, and the Sharp QT-8B "micro Compet". The Canon Pocketronic was
8613-541: Was also the first calculator to use an LED display, the first hand-held calculator to use a single integrated circuit (then proclaimed as a "calculator on a chip"), the Mostek MK6010, and the first electronic calculator to run off replaceable batteries. Using four AA-size cells the LE-120A measures 4.9 by 2.8 by 0.9 inches (124 mm × 71 mm × 23 mm). The first European-made pocket-sized calculator, DB 800
8712-419: Was an implied unconditional branch (GOTO) at the end of the operation stack, returning the program to its starting instruction. Thus, it was not possible to include any conditional branch (IF-THEN-ELSE) logic. During this era, the absence of the conditional branch was sometimes used to distinguish a programmable calculator from a computer. The first Soviet programmable desktop calculator ISKRA 123 , powered by
8811-436: Was at times somewhat over-promoted as being able to perform all four arithmetic operations with minimal human intervention. Pascal's calculator could add and subtract two numbers directly and thus, if the tedium could be borne, multiply and divide by repetition. Schickard's machine, constructed several decades earlier, used a clever set of mechanised multiplication tables to ease the process of multiplication and division with
8910-456: Was brought about. In 1869, Charles Méray had taken the same point of departure as Heine, but the theory is generally referred to the year 1872. Weierstrass's method was completely set forth by Salvatore Pincherle (1880), and Dedekind's has received additional prominence through the author's later work (1888) and endorsement by Paul Tannery (1894). Weierstrass, Cantor, and Heine base their theories on infinite series, while Dedekind founds his on
9009-470: Was developed in 1948 and, although costly, became popular for its portability. This purely mechanical hand-held device could do addition, subtraction, multiplication and division. By the early 1970s electronic pocket calculators ended manufacture of mechanical calculators, although the Curta remains a popular collectable item. The first mainframe computers, initially using vacuum tubes and later transistors in
9108-539: Was finally proved by Jacques Hadamard and Charles de la Vallée-Poussin in 1896. Goldbach and Riemann's conjectures remain unproven and unrefuted. Numbers can be classified into sets , called number sets or number systems , such as the natural numbers and the real numbers . The main number systems are as follows: N 0 {\displaystyle \mathbb {N} _{0}} or N 1 {\displaystyle \mathbb {N} _{1}} are sometimes used. Each of these number systems
9207-596: Was followed the next year by the SR-50 which added log and trig functions to compete with the HP-35, and in 1977 the mass-marketed TI-30 line which is still produced. Number A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals ; for example, "5"
9306-581: Was made in May 1971 by Digitron in Buje , Croatia (former Yugoslavia ) with four functions and an eight-digit display and special characters for a negative number and a warning that the calculation has too many digits to display. The first American-made pocket-sized calculator, the Bowmar 901B (popularly termed The Bowmar Brain ), measuring 5.2 by 3.0 by 1.5 inches (132 mm × 76 mm × 38 mm), came out in
9405-434: Was necessary to consider the wider set of algebraic numbers (all solutions to polynomial equations). Galois (1832) linked polynomial equations to group theory giving rise to the field of Galois theory . Simple continued fractions , closely related to irrational numbers (and due to Cataldi, 1613), received attention at the hands of Euler , and at the opening of the 19th century were brought into prominence through
9504-424: Was not even considered a number for the Ancient Greeks.) However, in the 19th century, set theorists and other mathematicians started including 0 ( cardinality of the empty set , i.e. 0 elements, where 0 is thus the smallest cardinal number ) in the set of natural numbers. Today, different mathematicians use the term to describe both sets, including 0 or not. The mathematical symbol for
9603-608: Was one of the leading edges of semiconductor development. U.S. semiconductor manufacturers led the world in large scale integration (LSI) semiconductor development, squeezing more and more functions into individual integrated circuits. This led to alliances between Japanese calculator manufacturers and U.S. semiconductor companies: Canon Inc. with Texas Instruments , Hayakawa Electric (later renamed Sharp Corporation ) with North-American Rockwell Microelectronics (later renamed Rockwell International ), Busicom with Mostek and Intel , and General Instrument with Sanyo . By 1970,
9702-507: Was used in a table of Roman numerals by Bede or a colleague about 725, a true zero symbol. The abstract concept of negative numbers was recognized as early as 100–50 BC in China. The Nine Chapters on the Mathematical Art contains methods for finding the areas of figures; red rods were used to denote positive coefficients , black for negative. The first reference in a Western work was in
9801-744: Was usually based on the delay-line memory or the magnetic-core memory , though the Toshiba "Toscal" BC-1411 appears to have used an early form of dynamic RAM built from discrete components. Already there was a desire for smaller and less power-hungry machines. Bulgaria's ELKA 6521 , introduced in 1965, was developed by the Central Institute for Calculation Technologies and built at the Elektronika factory in Sofia . The name derives from EL ektronen KA lkulator , and it weighed around 8 kg (18 lb). It
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