115-646: The HP-67 is a magnetic card-programmable handheld calculator , introduced by Hewlett-Packard in 1976 at an MSRP of $ 450. A desktop version with built-in thermal printer was sold as the HP-97 at a price of $ 750. Collectively, they are known as the HP-67/97 . Marketed as improved successors to the HP-65 , the HP-67/97 were based on the technology of the "20-series" of calculators ( HP-25 , HP-19C etc.) introduced
230-591: A set whose elements are unspecified, of operations acting on the elements of the set, and rules that these operations must follow. The scope of algebra thus grew to include the study of algebraic structures. This object of algebra was called modern algebra or abstract algebra , as established by the influence and works of Emmy Noether . Some types of algebraic structures have useful and often fundamental properties, in many areas of mathematics. Their study became autonomous parts of algebra, and include: The study of types of algebraic structures as mathematical objects
345-407: 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
460-399: 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
575-613: A designated corner. In addition to software and support from HP, an active user community supported the HP-67/97 as well as the other HP programmables of the era. The group was called PPC and produced the PPC Journal . One of the notable contributions of the group was the development of a "Blackbox" that allowed pseudo-alphanumeric displays. A version adapted to support an additional backward-facing display manufactured by Educational Calculator Devices named EduCALC 67 GD existed as well. In 1977, HP introduced an extended version of
690-684: 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
805-614: A foundation for all mathematics). Mathematics involves the description and manipulation of abstract objects that consist of either abstractions from nature or—in modern mathematics—purely abstract entities that are stipulated to have certain properties, called axioms . Mathematics uses pure reason to prove properties of objects, a proof consisting of a succession of applications of deductive rules to already established results. These results include previously proved theorems , axioms, and—in case of abstraction from nature—some basic properties that are considered true starting points of
920-669: A fruitful interaction between mathematics and science , to the benefit of both. Mathematical discoveries continue to be made to this very day. According to Mikhail B. Sevryuk, in the January ;2006 issue of the Bulletin of the American Mathematical Society , "The number of papers and books included in the Mathematical Reviews (MR) database since 1940 (the first year of operation of MR)
1035-609: 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
1150-404: A mathematical problem. In turn, the axiomatic method allows for the study of various geometries obtained either by changing the axioms or by considering properties that do not change under specific transformations of the space . Today's subareas of geometry include: Algebra is the art of manipulating equations and formulas. Diophantus (3rd century) and al-Khwarizmi (9th century) were
1265-422: A mathematical statement that is taken to be true without need of proof. If a mathematical statement has yet to be proven (or disproven), it is termed a conjecture . Through a series of rigorous arguments employing deductive reasoning , a statement that is proven to be true becomes a theorem. A specialized theorem that is mainly used to prove another theorem is called a lemma . A proven instance that forms part of
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#17327980860191380-402: A more general finding is termed a corollary . Numerous technical terms used in mathematics are neologisms , such as polynomial and homeomorphism . Other technical terms are words of the common language that are used in an accurate meaning that may differ slightly from their common meaning. For example, in mathematics, " or " means "one, the other or both", while, in common language, it
1495-485: 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
1610-428: 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
1725-535: A population mean with a given level of confidence. Because of its use of optimization , the mathematical theory of statistics overlaps with other decision sciences , such as operations research , control theory , and mathematical economics . Computational mathematics is the study of mathematical problems that are typically too large for human, numerical capacity. Numerical analysis studies methods for problems in analysis using functional analysis and approximation theory ; numerical analysis broadly includes
1840-437: 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
1955-411: A separate branch of mathematics until the seventeenth century. At the end of the 19th century, the foundational crisis in mathematics and the resulting systematization of the axiomatic method led to an explosion of new areas of mathematics. The 2020 Mathematics Subject Classification contains no less than sixty-three first-level areas. Some of these areas correspond to the older division, as
2070-420: 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
2185-424: A single unknown , which were called algebraic equations (a term still in use, although it may be ambiguous). During the 19th century, mathematicians began to use variables to represent things other than numbers (such as matrices , modular integers , and geometric transformations ), on which generalizations of arithmetic operations are often valid. The concept of algebraic structure addresses this, consisting of
2300-418: A statistical action, such as using a procedure in, for example, parameter estimation , hypothesis testing , and selecting the best . In these traditional areas of mathematical statistics , a statistical-decision problem is formulated by minimizing an objective function , like expected loss or cost , under specific constraints. For example, designing a survey often involves minimizing the cost of estimating
2415-477: A wide expansion of mathematical logic, with subareas such as model theory (modeling some logical theories inside other theories), proof theory , type theory , computability theory and computational complexity theory . Although these aspects of mathematical logic were introduced before the rise of computers , their use in compiler design, formal verification , program analysis , proof assistants and other aspects of computer science , contributed in turn to
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#17327980860192530-456: A year earlier. The two models are functionally equivalent, and programs on magnetic cards can be interchanged between them. The 67/97 provide a complete set of scientific, statistical and engineering operations, including trigonometric , logarithmic and exponential functions, coordinate conversions, average/ standard deviation etc. The HP-67/97 series featured a program memory of 224 eight-bit words . The two extra bits per word compared to
2645-703: Is Fermat's Last Theorem . This conjecture was stated in 1637 by Pierre de Fermat, but it was proved only in 1994 by Andrew Wiles , who used tools including scheme theory from algebraic geometry , category theory , and homological algebra . Another example is Goldbach's conjecture , which asserts that every even integer greater than 2 is the sum of two prime numbers . Stated in 1742 by Christian Goldbach , it remains unproven despite considerable effort. Number theory includes several subareas, including analytic number theory , algebraic number theory , geometry of numbers (method oriented), diophantine equations , and transcendence theory (problem oriented). Geometry
2760-419: 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
2875-403: Is commonly used for advanced parts. Analysis is further subdivided into real analysis , where variables represent real numbers , and complex analysis , where variables represent complex numbers . Analysis includes many subareas shared by other areas of mathematics which include: Discrete mathematics, broadly speaking, is the study of individual, countable mathematical objects. An example
2990-513: Is defined by the set of all similar objects and the properties that these objects must have. For example, in Peano arithmetic , the natural numbers are defined by "zero is a number", "each number has a unique successor", "each number but zero has a unique predecessor", and some rules of reasoning. This mathematical abstraction from reality is embodied in the modern philosophy of formalism , as founded by David Hilbert around 1910. The "nature" of
3105-407: Is either ambiguous or means "one or the other but not both" (in mathematics, the latter is called " exclusive or "). Finally, many mathematical terms are common words that are used with a completely different meaning. This may lead to sentences that are correct and true mathematical assertions, but appear to be nonsense to people who do not have the required background. For example, "every free module
3220-493: Is in Babylonian mathematics that elementary arithmetic ( addition , subtraction , multiplication , and division ) first appear in the archaeological record. The Babylonians also possessed a place-value system and used a sexagesimal numeral system which is still in use today for measuring angles and time. In the 6th century BC, Greek mathematics began to emerge as a distinct discipline and some Ancient Greeks such as
3335-586: Is mostly used for numerical calculations . Number theory dates back to ancient Babylon and probably China . Two prominent early number theorists were Euclid of ancient Greece and Diophantus of Alexandria. The modern study of number theory in its abstract form is largely attributed to Pierre de Fermat and Leonhard Euler . The field came to full fruition with the contributions of Adrien-Marie Legendre and Carl Friedrich Gauss . Many easily stated number problems have solutions that require sophisticated methods, often from across mathematics. A prominent example
3450-473: 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
3565-404: Is not sufficient to verify by measurement that, say, two lengths are equal; their equality must be proven via reasoning from previously accepted results ( theorems ) and a few basic statements. The basic statements are not subject to proof because they are self-evident ( postulates ), or are part of the definition of the subject of study ( axioms ). This principle, foundational for all mathematics,
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3680-405: 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
3795-1192: Is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs." Mathematical notation is widely used in science and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. This notation consists of symbols used for representing operations , unspecified numbers, relations and any other mathematical objects, and then assembling them into expressions and formulas. More precisely, numbers and other mathematical objects are represented by symbols called variables, which are generally Latin or Greek letters, and often include subscripts . Operation and relations are generally represented by specific symbols or glyphs , such as + ( plus ), × ( multiplication ), ∫ {\textstyle \int } ( integral ), = ( equal ), and < ( less than ). All these symbols are generally grouped according to specific rules to form expressions and formulas. Normally, expressions and formulas do not appear alone, but are included in sentences of
3910-547: Is often held to be Archimedes ( c. 287 – c. 212 BC ) of Syracuse . He developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series , in a manner not too dissimilar from modern calculus. Other notable achievements of Greek mathematics are conic sections ( Apollonius of Perga , 3rd century BC), trigonometry ( Hipparchus of Nicaea , 2nd century BC), and
4025-433: Is one of the oldest branches of mathematics. It started with empirical recipes concerning shapes, such as lines , angles and circles , which were developed mainly for the needs of surveying and architecture , but has since blossomed out into many other subfields. A fundamental innovation was the ancient Greeks' introduction of the concept of proofs , which require that every assertion must be proved . For example, it
4140-567: Is sometimes mistranslated as a condemnation of mathematicians. The apparent plural form in English goes back to the Latin neuter plural mathematica ( Cicero ), based on the Greek plural ta mathēmatiká ( τὰ μαθηματικά ) and means roughly "all things mathematical", although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after
4255-610: 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
4370-418: Is the purpose of universal algebra and category theory . The latter applies to every mathematical structure (not only algebraic ones). At its origin, it was introduced, together with homological algebra for allowing the algebraic study of non-algebraic objects such as topological spaces ; this particular area of application is called algebraic topology . Calculus, formerly called infinitesimal calculus,
4485-405: Is the set of all integers. Because the objects of study here are discrete, the methods of calculus and mathematical analysis do not directly apply. Algorithms —especially their implementation and computational complexity —play a major role in discrete mathematics. The four color theorem and optimal sphere packing were two major problems of discrete mathematics solved in the second half of
4600-508: Is true regarding number theory (the modern name for higher arithmetic ) and geometry. Several other first-level areas have "geometry" in their names or are otherwise commonly considered part of geometry. Algebra and calculus do not appear as first-level areas but are respectively split into several first-level areas. Other first-level areas emerged during the 20th century or had not previously been considered as mathematics, such as mathematical logic and foundations . Number theory began with
4715-586: The Babylonians and Egyptians began using arithmetic, algebra, and geometry for taxation and other financial calculations, for building and construction, and for astronomy. The oldest mathematical texts from Mesopotamia and Egypt are from 2000 to 1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical concept after basic arithmetic and geometry. It
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4830-768: The Golden Age of Islam , especially during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics. The most notable achievement of Islamic mathematics was the development of algebra . Other achievements of the Islamic period include advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarizmi , Omar Khayyam and Sharaf al-Dīn al-Ṭūsī . The Greek and Arabic mathematical texts were in turn translated to Latin during
4945-511: The Pythagoreans appeared to have considered it a subject in its own right. Around 300 BC, Euclid organized mathematical knowledge by way of postulates and first principles, which evolved into the axiomatic method that is used in mathematics today, consisting of definition, axiom, theorem, and proof. His book, Elements , is widely considered the most successful and influential textbook of all time. The greatest mathematician of antiquity
5060-536: The Renaissance , mathematics was divided into two main areas: arithmetic , regarding the manipulation of numbers, and geometry , regarding the study of shapes. Some types of pseudoscience , such as numerology and astrology , were not then clearly distinguished from mathematics. During the Renaissance, two more areas appeared. Mathematical notation led to algebra which, roughly speaking, consists of
5175-446: The controversy over Cantor's set theory . In the same period, various areas of mathematics concluded the former intuitive definitions of the basic mathematical objects were insufficient for ensuring mathematical rigour . This became the foundational crisis of mathematics. It was eventually solved in mainstream mathematics by systematizing the axiomatic method inside a formalized set theory . Roughly speaking, each mathematical object
5290-400: The 17th century, when René Descartes introduced what is now called Cartesian coordinates . This constituted a major change of paradigm : Instead of defining real numbers as lengths of line segments (see number line ), it allowed the representation of points using their coordinates , which are numbers. Algebra (and later, calculus) can thus be used to solve geometrical problems. Geometry
5405-405: The 19th century, mathematicians discovered non-Euclidean geometries , which do not follow the parallel postulate . By questioning that postulate's truth, this discovery has been viewed as joining Russell's paradox in revealing the foundational crisis of mathematics . This aspect of the crisis was solved by systematizing the axiomatic method, and adopting that the truth of the chosen axioms is not
5520-532: The 20th century. The P versus NP problem , which remains open to this day, is also important for discrete mathematics, since its solution would potentially impact a large number of computationally difficult problems. Discrete mathematics includes: The two subjects of mathematical logic and set theory have belonged to mathematics since the end of the 19th century. Before this period, sets were not considered to be mathematical objects, and logic , although used for mathematical proofs, belonged to philosophy and
5635-515: 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
5750-598: 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
5865-466: The HP-65's six allowed the designers to store any program instruction in a single memory cell ("fully merged keycodes") even if it required multiple keystrokes to enter. Programs could include 20 labels, subroutines (3 levels deep), four flag registers , 8 comparison functions , and extended index and loop control functions. At 15 digits, the display was wider than those of the predecessor models, although
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#17327980860195980-637: The Middle Ages and made available in Europe. During the early modern period , mathematics began to develop at an accelerating pace in Western Europe , with innovations that revolutionized mathematics, such as the introduction of variables and symbolic notation by François Viète (1540–1603), the introduction of logarithms by John Napier in 1614, which greatly simplified numerical calculations, especially for astronomy and marine navigation ,
6095-696: 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
6210-472: The ability to combine data from multiple cards. The same magnetic card format was later used for the HP-41C which offered compatibility to the 67/97 through software in the card reader. HP offered a library of programs supplied on packs of pre-recorded magnetic cards for many applications including surveying , medicine, as well as civil and electrical engineering . Cards could be write protected by cutting off
6325-493: 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
6440-413: 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
6555-560: 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
6670-583: The beginnings of algebra (Diophantus, 3rd century AD). The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics . Other notable developments of Indian mathematics include the modern definition and approximation of sine and cosine , and an early form of infinite series . During
6785-415: 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
6900-511: The concept of a proof and its associated mathematical rigour first appeared in Greek mathematics , most notably in Euclid 's Elements . Since its beginning, mathematics was primarily divided into geometry and arithmetic (the manipulation of natural numbers and fractions ), until the 16th and 17th centuries, when algebra and infinitesimal calculus were introduced as new fields. Since then,
7015-538: 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
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#17327980860197130-399: The current language, where expressions play the role of noun phrases and formulas play the role of clauses . Mathematics has developed a rich terminology covering a broad range of fields that study the properties of various abstract, idealized objects and how they interact. It is based on rigorous definitions that provide a standard foundation for communication. An axiom or postulate is
7245-515: The decimal point was displayed on its own digit position. The HP-67 keys carry up to four functions each, accessed through "f", "g" and "h" prefix keys (gold, blue and black labels, respectively). The model 97 had more (and larger) keys, therefore only two functions were assigned to each key. When interchanging magnetic cards between the HP-67 and the HP-97, the calculators' software took care of converting
7360-569: The derived expression mathēmatikḗ tékhnē ( μαθηματικὴ τέχνη ), meaning ' mathematical science ' . It entered the English language during the Late Middle English period through French and Latin. Similarly, one of the two main schools of thought in Pythagoreanism was known as the mathēmatikoi (μαθηματικοί)—which at the time meant "learners" rather than "mathematicians" in the modern sense. The Pythagoreans were likely
7475-491: The desktop model as the HP-97S which featured an extra parallel I/O port (40 lines for 10 4-bit BCD digits, plus 5 control lines) for collecting data from external hardware, at a price of $ 1,375. Handheld 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
7590-428: 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
7705-472: The end of that decade, prices had dropped to the point where 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
7820-493: 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,
7935-428: The expansion of these logical theories. The field of statistics is a mathematical application that is employed for the collection and processing of data samples, using procedures based on mathematical methods especially probability theory . Statisticians generate data with random sampling or randomized experiments . Statistical theory studies decision problems such as minimizing the risk ( expected loss ) of
8050-467: 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
8165-492: 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
8280-560: 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
8395-567: The first to constrain the use of the word to just the study of arithmetic and geometry. By the time of Aristotle (384–322 BC) this meaning was fully established. In Latin and English, until around 1700, the term mathematics more commonly meant " astrology " (or sometimes " astronomy ") rather than "mathematics"; the meaning gradually changed to its present one from about 1500 to 1800. This change has resulted in several mistranslations: For example, Saint Augustine 's warning that Christians should beware of mathematici , meaning "astrologers",
8510-491: The interaction between mathematical innovations and scientific discoveries has led to a correlated increase in the development of both. At the end of the 19th century, the foundational crisis of mathematics led to the systematization of the axiomatic method , which heralded a dramatic increase in the number of mathematical areas and their fields of application. The contemporary Mathematics Subject Classification lists more than sixty first-level areas of mathematics. Before
8625-400: The introduction of coordinates by René Descartes (1596–1650) for reducing geometry to algebra, and the development of calculus by Isaac Newton (1643–1727) and Gottfried Leibniz (1646–1716). Leonhard Euler (1707–1783), the most notable mathematician of the 18th century, unified these innovations into a single corpus with a standardized terminology, and completed them with the discovery and
8740-610: 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,
8855-445: The key codes, and emulated the 97's print functions through the 67's display. The HP-67 is powered by a pack of three AA-sized nickel-cadmium rechargeable batteries. Owing to the power requirements of the built-in thermal printer, the HP-97 employs a larger battery pack and more powerful charger. Of the 26- register data memory, the first ten ("primary registers") could be accessed directly, ten more as an alternate register set, and
8970-555: 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
9085-409: The manipulation of numbers , that is, natural numbers ( N ) , {\displaystyle (\mathbb {N} ),} and later expanded to integers ( Z ) {\displaystyle (\mathbb {Z} )} and rational numbers ( Q ) . {\displaystyle (\mathbb {Q} ).} Number theory was once called arithmetic, but nowadays this term
9200-637: 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
9315-400: The natural numbers, there are theorems that are true (that is provable in a stronger system), but not provable inside the system. This approach to the foundations of mathematics was challenged during the first half of the 20th century by mathematicians led by Brouwer , who promoted intuitionistic logic , which explicitly lacks the law of excluded middle . These problems and debates led to
9430-536: The objects defined this way is a philosophical problem that mathematicians leave to philosophers, even if many mathematicians have opinions on this nature, and use their opinion—sometimes called "intuition"—to guide their study and proofs. The approach allows considering "logics" (that is, sets of allowed deducing rules), theorems, proofs, etc. as mathematical objects, and to prove theorems about them. For example, Gödel's incompleteness theorems assert, roughly speaking that, in every consistent formal system that contains
9545-711: 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
9660-521: The pattern of physics and metaphysics , inherited from Greek. In English, the noun mathematics takes a singular verb. It is often shortened to maths or, in North America, math . In addition to recognizing how to count physical objects, prehistoric peoples may have also known how to count abstract quantities, like time—days, seasons, or years. Evidence for more complex mathematics does not appear until around 3000 BC , when
9775-422: 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
9890-421: 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
10005-631: 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
10120-658: The proof of numerous theorems. Perhaps the foremost mathematician of the 19th century was the German mathematician Carl Gauss , who made numerous contributions to fields such as algebra, analysis, differential geometry , matrix theory , number theory, and statistics . In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems , which show in part that any consistent axiomatic system—if powerful enough to describe arithmetic—will contain true propositions that cannot be proved. Mathematics has since been greatly extended, and there has been
10235-508: 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
10350-432: The remaining six through the user defined keys A-E and as an index register . Using the latter, a program could access all 26 registers as a single indexed array. Data memory is not permanent as in later models, i.e. register contents and program are lost when powering off. The alternate register set was also used by statistical functions. The built-in magnetic card reader/writer could be used to save programs and data, with
10465-603: 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
10580-657: The study and the manipulation of formulas . Calculus , consisting of the two subfields differential calculus and integral calculus , is the study of continuous functions , which model the typically nonlinear relationships between varying quantities, as represented by variables . This division into four main areas—arithmetic, geometry, algebra, and calculus —endured until the end of the 19th century. Areas such as celestial mechanics and solid mechanics were then studied by mathematicians, but now are considered as belonging to physics. The subject of combinatorics has been studied for much of recorded history, yet did not become
10695-568: The study of approximation and discretization with special focus on rounding errors . Numerical analysis and, more broadly, scientific computing also study non-analytic topics of mathematical science, especially algorithmic- matrix -and- graph theory . Other areas of computational mathematics include computer algebra and symbolic computation . The word mathematics comes from the Ancient Greek word máthēma ( μάθημα ), meaning ' something learned, knowledge, mathematics ' , and
10810-672: The theory under consideration. Mathematics is essential in the natural sciences , engineering , medicine , finance , computer science , and the social sciences . Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation. Some areas of mathematics, such as statistics and game theory , are developed in close correlation with their applications and are often grouped under applied mathematics . Other areas are developed independently from any application (and are therefore called pure mathematics ) but often later find practical applications. Historically,
10925-403: 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
11040-487: The title of his main treatise . Algebra became an area in its own right only with François Viète (1540–1603), who introduced the use of variables for representing unknown or unspecified numbers. Variables allow mathematicians to describe the operations that have to be done on the numbers represented using mathematical formulas . Until the 19th century, algebra consisted mainly of the study of linear equations (presently linear algebra ), and polynomial equations in
11155-738: 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
11270-508: The two main precursors of algebra. Diophantus solved some equations involving unknown natural numbers by deducing new relations until he obtained the solution. Al-Khwarizmi introduced systematic methods for transforming equations, such as moving a term from one side of an equation into the other side. The term algebra is derived from the Arabic word al-jabr meaning 'the reunion of broken parts' that he used for naming one of these methods in
11385-643: 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,
11500-624: 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,
11615-578: 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
11730-589: 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
11845-553: 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
11960-419: 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
12075-436: 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
12190-574: 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. They became popular in the mid-1970s as the incorporation of integrated circuits reduced their size and cost. By
12305-474: 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
12420-462: Was first elaborated for geometry, and was systematized by Euclid around 300 BC in his book Elements . The resulting Euclidean geometry is the study of shapes and their arrangements constructed from lines, planes and circles in the Euclidean plane ( plane geometry ) and the three-dimensional Euclidean space . Euclidean geometry was developed without change of methods or scope until
12535-783: 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. Mathematics Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of continuous changes), and set theory (presently used as
12650-414: Was introduced independently and simultaneously by 17th-century mathematicians Newton and Leibniz . It is fundamentally the study of the relationship of variables that depend on each other. Calculus was expanded in the 18th century by Euler with the introduction of the concept of a function and many other results. Presently, "calculus" refers mainly to the elementary part of this theory, and "analysis"
12765-592: 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
12880-437: Was not specifically studied by mathematicians. Before Cantor 's study of infinite sets , mathematicians were reluctant to consider actually infinite collections, and considered infinity to be the result of endless enumeration . Cantor's work offended many mathematicians not only by considering actually infinite sets but by showing that this implies different sizes of infinity, per Cantor's diagonal argument . This led to
12995-608: 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,
13110-571: Was split into two new subfields: synthetic geometry , which uses purely geometrical methods, and analytic geometry , which uses coordinates systemically. Analytic geometry allows the study of curves unrelated to circles and lines. Such curves can be defined as the graph of functions , the study of which led to differential geometry . They can also be defined as implicit equations , often polynomial equations (which spawned algebraic geometry ). Analytic geometry also makes it possible to consider Euclidean spaces of higher than three dimensions. In
13225-767: 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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