A combination lock is a type of locking device in which a sequence of symbols numbers, is used to open the lock. The sequence may be entered using a single rotating dial which interacts with several discs or cams, by using a set of several rotating discs with inscribed symbols which directly interact with the locking mechanism, or through an electronic or mechanical keypad. Types range from inexpensive three-digit luggage locks to high-security safes. Unlike ordinary padlocks, combination locks do not use keys; the earliest known combination lock was excavated in a Roman period tomb on the Athens. Attached to a small box, it featured several dials instead of keyholes. In 1206, the Muslim engineer Al-Jazari documented a combination lock in his book al-Ilm Wal-Amal al-Nafi Fi Sina'at al-Hiyal. Muhammad al-Astrulabi made combination locks, two of which are kept in Copenhagen and Boston Museums. Gerolamo Cardano described a combination lock in the 16th century. In 1878 a German man by the name of Joseph Loch was said to have invented the modern combination lock for Tiffany's Jewelers in New York City, from the 1870s to the early 1900s made many more improvements in the designs and functions of such locks.
The first commercially-viable single-dial combination lock was patented on 1 February 1910 by John Junkunc, owner of American Lock Company. One of the simplest types of combination lock seen in low-security bicycle locks and in briefcases, uses several rotating discs with notches cut into them; the lock is secured by a pin with several teeth on it. When the notches in the discs align with the teeth on the pin, the lock can be opened; this lock is considered to be one of the least secure types of combination lock. Opening one in this fashion depends on slight irregularities in the machining of the parts. Unless the lock is machined when the pin is pulled outward, one of the teeth will pull more than the others on its corresponding disc; this disc is rotated until a slight click is heard, indicating that the tooth has settled into the notch. The procedure is repeated for the remaining discs, resulting in an open lock, a correct combination, in little time. Combination locks found on padlocks, lockers, or safes may use a single dial which interacts with several parallel discs or cams.
Customarily, a lock of this type is opened by rotating the dial clockwise to the first numeral, counterclockwise to the second, so on in an alternating fashion until the last numeral is reached. The cams have an indentation or notch, when the correct combination is entered, the notches align, allowing the latch to fit into them and open the lock. Depending on the quality of the lock, some single-dial combination locks can be defeated easily. Typical padlocks are manufactured with generous tolerances, allowing two, three or more digits of'play' in the correct access sequence. Given a 60-number dial with three cams and three digits of play, the search space is reduced from 60 × 60 × 60 to 20 × 20 × 20, a 96% reduction in potential combinations. Additionally, if testing the mechanism to open the lock does not modify the state of the lock, multiple combinations can be tried sequentially, drastically reducing the brute force search time; the first two digits are entered once starting from the second digit, the dial is rotated sequentially through the digits, testing the lock on each.
If it takes three seconds to input the first digit, two seconds for the second digit, one second for the third digit the normal search time for a 60-number dial with three cams would be × 60³. The reduced search time would be × a reduction of nearly 82 % from 360 hours to 65 hours; this strategy can be extended to the second digit as well reducing the search time further. When these two strategies are combined on a lock with the properties given above, the brute force search time is reduced by greater than 99%; this is still better security than multiple-dial locks and many keyed locks, but unacceptable for high security applications. Inexpensive padlocks are also susceptible to direct mechanical attacks, such as the use of a padlock shim which can release the shackle without entering a combination. Early combination padlocks made by Master Lock could be cracked by pulling on the shackle of the lock and turning the dial until it stopped. More recent models of Master padlocks with a 40-position dial have a mechanical weakness that can give away the last numeral in the combination, the first two numerals have a mathematical relationship with the last number.
This weakness reduces the number of possible combinations from 64,000 to a mere 100, which can be tried in a short time. In 1978 a combination lock which could be set by the user to a sequence of his own choosing was invented by Andrew Elliot Rae. At this time the electronic keypad was invented and he was unable to get any manufacturers to back his mechanical lock for lockers, luggage, or brief-cases; the silicon chip locks never became popular due to the need for battery power to maintain their integrity. The patent expired and the original mechanical invention was manufactured and sold worldwide for luggage and hotel safes, it is now a standard part of the luggage used by travellers. Many doors use combination locks which require the user to enter a numeric sequence on a keypad to gain entry; these s
Arrow keys or cursor movement keys are buttons on a computer keyboard that are either programmed or designated to move the cursor in a specified direction. The term "cursor movement key" is distinct from "arrow key" in that the former term may refer to any of various keys on a computer keyboard designated for cursor movement, whereas "arrow keys" refers to one of four specific keys marked with arrows. Arrow keys are located at the bottom of the keyboard to the left side of the numeric keypad arranged in an inverted-T layout but found in diamond shapes and linear shapes. Arrow keys are used for navigating around documents and for playing games; the inverted-T layout was popularized by the Digital Equipment Corporation LK201 keyboard from 1982. Before the computer mouse was widespread, arrow keys were the primary way of moving a cursor on screen. Mouse keys is a feature. A feature echoed in the Amiga whereby holding the Amiga key would allow a person to move the pointer with the arrow keys in the Workbench, but most games require a mouse or joystick.
The use of arrow keys in games has come back into fashion from the late 1980s and early 1990s when joysticks were a must, were used in preference to arrow keys with some games not supporting any keys. It can be used instead of WASD keys; the inverted-T layout was popularized by the Digital Equipment Corporation LK201 keyboard from 1982. Some Commodore 8-bit computers used two keys instead of four, with directions selected using the shift key; the original Apple Macintosh had no arrow keys at the insistence of Steve Jobs, who felt that people should use the mouse instead. They were deliberately excluded from the Macintosh launch design as a forcing device, acclimating users to the new mouse input device and inducing software developers to conform to mouse-driven design rather than porting previous terminal-based software to the new platform. Arrow keys were included in Apple keyboards. Early models with arrow keys but no middle section placed them in one line below the right-hand Shift key in an HJKL-like fashion.
Although the "arrow keys" provide one convention for cursor movement on computers, there are other conventions for cursor movement that use different keys. This layout dates back to Sinclair ZX80, Sinclair ZX81, Sinclair Spectrum software: the original Sinclair machines had cursor keys on the top row, keys 5, 6, 7, 8. Due to the unusual layout adopted by Sinclair, these keys were accessed either by using the ⇧ Shift key in conjunction with a numeric key or by the numeric key alone, depending on the program in use. WASD is a set of four keys on a QWERTY or QWERTZ computer keyboard which mimics the inverted-T configuration of the arrow keys; these keys are used to control the player character's movement in computer games, most first person games but in many driving and third person games. W/S control forward and backward, while A/D control strafing left and right. WASD is used to account for the fact that the arrow keys are not ergonomic to use in conjunction with a right-handed mouse. During the early days of gaming, this was not a problem.
However, the introduction of mouselook, a system that allowed the ability to use the mouse to look around both vertically and horizontally, enabled the player to perform techniques such as smooth circle strafing, although possible with the keyboard, was difficult to perform and resulted in jagged movement. Since the mouse was now used for looking, the ← and → keys for looking would be redundant and thus were altered to become strafe keys; the style was popularized in competitive play in Quake and subsequently QuakeWorld, notably by professional gamer Dennis Fong, where the advantages of WASD and mouselook were recognised over a purely keyboard-based control system. In the same year that Castle Wolfenstein was released, 1981, the game Wizardry used the AWD keys for movement in a 3D dungeon. Both the programmers of Castle Wolfenstein and Wizardry were users of the earlier PLATO system where the game Moria used the AWD keys. Another advantage of WASD is that it allows the user to use the left hand thumb to press the space bar and the left hand little finger to press the Ctrl or ⇧ Shift keys, as opposed to the arrow keys which lack other keys in proximity to press.
Ctrl and ⇧ Shift were chosen because they are larger keys and thus easier to hit, but because in older systems the computer could only recognise a couple of alphanumeric key presses, a limitation circumvented by the use of modifier keys. In games, the usage of the E key to interact with items or open up the inventory was popularized due to its location next to the WASD keys, allowing players to reach it quickly. Dark Castle may be the first game to use WASD keys and mouse for control. Half-Life was one of the first games to use WASD by default. After being popularized by first-person shooters, WASD became more common in other computer game genres as well. Many of the games that have adopted this layout use a first-person or over-the-shoulder third-person perspective; some games that use overhead camera views use WASD to move the camera, such as some city-building games and economic simulation games. Th
Computer keyboards can be classified by the switch technology that they use. Computer alphanumeric keyboards have 80 to 110 durable switches one for each key; the choice of switch technology affects pre travel. Newer keyboard models use hybrids of various technologies to achieve greater cost savings. There are two types of membrane-based keyboards, flat-panel membrane keyboards and full-travel membrane keyboards: Flat-panel membrane keyboards are most found on appliances like microwave ovens or photocopiers. A common design consists of three layers; the top layer has the labels printed on its conductive stripes printed on the back. Under this it has a spacer layer, which holds the front and back layer apart so that they do not make electrical contact; the back layer has conductive stripes printed perpendicularly to those of the front layer. When placed together, the stripes form a grid; when the user pushes down at a particular position, their finger pushes the front layer down through the spacer layer to close a circuit at one of the intersections of the grid.
This indicates to the computer or keyboard control processor that a particular button has been pressed. Flat-panel membrane keyboards do not produce a noticeable physical feedback. Therefore, devices using these issue a beep or flash a light, they are used in harsh environments where water- or leak-proofing is desirable. Although used in the early days of the personal computer, they have been supplanted by the more tactile dome and mechanical switch keyboards. Full-travel membrane-based keyboards are the most common computer keyboards today, they have one-piece plastic keytop/switch plungers which press down on a membrane to actuate a contact in an electrical switch matrix. Dome-switch keyboards are a hybrid of mechanical-switch keyboards, they bring two circuit board traces together under a rubber or silicone keypad using either metal "dome" switches or polyurethane formed domes. The metal dome switches are formed pieces of stainless steel that, when compressed, give the user a crisp, positive tactile feedback.
These metal types of dome switches are common, are reliable to over 5 million cycles, can be plated in either nickel, silver or gold. The rubber dome switches, most referred to as polydomes, are formed polyurethane domes where the inside bubble is coated in graphite. While polydomes are cheaper than metal domes, they lack the crisp snap of the metal domes, have a lower life specification. Polydomes are considered quiet, but purists tend to find them "mushy" because the collapsing dome does not provide as much positive response as metal domes. For either metal or polydomes, when a key is pressed, it collapses the dome, which connects the two circuit traces and completes the connection to enter the character; the pattern on the PC board is gold-plated. Both are common switch technologies used in mass market keyboards today; this type of switch technology happens to be most used in handheld controllers, mobile phones, consumer electronics and medical devices. Dome-switch keyboards are called direct-switch keyboards.
A special case of the computer keyboard dome-switch is the scissor-switch. The keys are attached to the keyboard via two plastic pieces that interlock in a "scissor"-like fashion, snap to the keyboard and the key, it still uses rubber domes, but a special plastic'scissors' mechanism links the keycap to a plunger that depresses the rubber dome with a much shorter travel than the typical rubber dome keyboard. Scissor-switch keyboards employ 3-layer membranes as the electrical component of the switch, they usually have a shorter total key travel distance. This type of keyswitch is found on the built-in keyboards on laptops and keyboards marketed as'low-profile'; these keyboards are quiet and the keys require little force to press. Scissor-switch keyboards are slightly more expensive, they are harder to clean but less to get debris in them as the gaps between the keys are smaller. In this type of keyboard, pressing a key changes the capacitance of a pattern of capacitor pads; the pattern consists of two D-shaped capacitor pads for each switch, printed on a printed circuit board and covered by a thin, insulating film of soldermask which acts as a dielectric.
Despite the sophistication of the concept, the mechanism of capacitive switching is physically simple. The movable part ends with a flat foam element about the size of an aspirin tablet, finished with aluminum foil. Opposite the switch is a PCB with the capacitor pads; when the key is pressed, the foil clings to the surface of the PCB, forming a daisy chain of two capacitors between contact pads and itself separated with thin soldermask, thus "shorting" the contact pads with an detectable drop of capacitive reactance between them. This permits a pulse or pulse train to be sensed; because the switch doesn't have an actual electrical contact, there is no debouncing necessary. The keys do not need to be pressed to be actuated, which enables some people to type faster; the IBM Model F keyboard is mechanical-key design consisted of a buckling spring over a capacitive PCB to the Model M keyboard that used a membrane in p
Nokia Bell Labs is an industrial research and scientific development company owned by Finnish company Nokia. Its headquarters are located in New Jersey. Other laboratories are located around the world. Bell Labs has its origins in the complex past of the Bell System. In the late 19th century, the laboratory began as the Western Electric Engineering Department and was located at 463 West Street in New York City. In 1925, after years of conducting research and development under Western Electric, the Engineering Department was reformed into Bell Telephone Laboratories and under the shared ownership of American Telephone & Telegraph Company and Western Electric. Researchers working at Bell Labs are credited with the development of radio astronomy, the transistor, the laser, the photovoltaic cell, the charge-coupled device, information theory, the Unix operating system, the programming languages C, C++, S. Nine Nobel Prizes have been awarded for work completed at Bell Laboratories. In 1880, when the French government awarded Alexander Graham Bell the Volta Prize of 50,000 francs (approximately US$10,000 at that time for the invention of the telephone, he used the award to fund the Volta Laboratory in Washington, D.
C. in collaboration with Sumner Tainter and Bell's cousin Chichester Bell. The laboratory was variously known as the Volta Bureau, the Bell Carriage House, the Bell Laboratory and the Volta Laboratory, it focused on the analysis and transmission of sound. Bell used his considerable profits from the laboratory for further research and education to permit the " diffusion of knowledge relating to the deaf": resulting in the founding of the Volta Bureau, located at Bell's father's house at 1527 35th Street N. W. in Washington, D. C, its carriage house became their headquarters in 1889. In 1893, Bell constructed a new building close by at 1537 35th Street N. W. to house the lab. This building was declared a National Historic Landmark in 1972. After the invention of the telephone, Bell maintained a distant role with the Bell System as a whole, but continued to pursue his own personal research interests; the Bell Patent Association was formed by Alexander Graham Bell, Thomas Sanders, Gardiner Hubbard when filing the first patents for the telephone in 1876.
Bell Telephone Company, the first telephone company, was formed a year later. It became a part of the American Bell Telephone Company. American Telephone & Telegraph Company and its own subsidiary company, took control of American Bell and the Bell System by 1889. American Bell held a controlling interest in Western Electric whereas AT&T was doing research into the service providers. In 1884, the American Bell Telephone Company created the Mechanical Department from the Electrical and Patent Department formed a year earlier. In 1896, Western Electric bought property at 463 West Street to station their manufacturers and engineers, supplying AT&T with their product; this included everything from telephones, telephone exchange switches, transmission equipment. In 1925, Bell Laboratories was developed to better consolidate the research activities of the Bell System. Ownership was evenly split between Western Electric and AT&T. Throughout the next decade the AT&T Research and Development branch moved into West Street.
Bell Labs carried out consulting work for the Bell Telephone Company, U. S. government work, a few workers were assigned to basic research. The first president of research at Bell Labs was Frank B. Jewett who stayed there until 1940. By the early 1940s, Bell Labs engineers and scientists had begun to move to other locations away from the congestion and environmental distractions of New York City, in 1967 Bell Laboratories headquarters was relocated to Murray Hill, New Jersey. Among the Bell Laboratories locations in New Jersey were Holmdel, Crawford Hill, the Deal Test Site, Lincroft, Long Branch, Neptune, Piscataway, Red Bank and Whippany. Of these, Murray Hill and Crawford Hill remain in existence; the largest grouping of people in the company was in Illinois, at Naperville-Lisle, in the Chicago area, which had the largest concentration of employees prior to 2001. There were groups of employees in Indianapolis, Indiana. Since 2001, many of the former locations closed; the Holmdel site, a 1.9 million square foot structure set on 473 acres, was closed in 2007.
The mirrored-glass building was designed by Eero Saarinen. In August 2013, Somerset Development bought the building, intending to redevelop it into a mixed commercial and residential project. A 2012 article expressed doubt on the success of the newly named Bell Works site however several large tenants had announced plans to move in through 2016 and 2017 Bell Laboratories was, is, regarded by many as the premier research facility of its type, developing a wide range of revolutionary technologies, including radio astronomy, the transistor, the laser, information theory, the operating system Unix, the programming languages C and C++, solar cells, the CCD, floating-gate MOSFET, a whole host of optical and wired communications
The equals sign or equality sign is a mathematical symbol used to indicate equality. It was invented in 1557 by Robert Recorde. In an equation, the equals sign is placed between two expressions. In Unicode and ASCII, it is U+003D = EQUALS SIGN; the etymology of the word "equal" is from the Latin word "æqualis" as meaning "uniform", "identical", or "equal", from aequus. The "=" symbol, now universally accepted in mathematics for equality was first recorded by Welsh mathematician Robert Recorde in The Whetstone of Witte; the original form of the symbol was much wider than the present form. In his book Recorde explains his design of the "Gemowe lines": And to auoide the tediouſe repetition of theſe woordes: is equalle to: I will ſette as I doe in woorke vſe, a paire of paralleles, or Gemowe lines of one lengthe, thus: =, bicauſe noe.2. Thynges, can be moare equalle, and to avoid the tedious repetition of these words: is equal to: I will set as I do in work use, a pair of parallels, or Gemowe lines of one length, thus: =, because no 2 things, can be more equal.
According to Scotland's University of St Andrews History of Mathematics website: The symbol'=' was not popular. The symbol || was used by some and æ, from the Latin word aequalis meaning equal, was used into the 1700s. In mathematics, the equals sign can be used as a simple statement of fact in a specific case, or to create definitions, conditional statements, or to express a universal equivalence 2 = x2 + 2x + 1; the first important computer programming language to use the equals sign was the original version of Fortran, FORTRAN I, designed in 1954 and implemented in 1957. In Fortran, "=" serves as an assignment operator: X = 2 sets the value of X to 2; this somewhat resembles the use of "=" in a mathematical definition, but with different semantics: the expression following "=" is evaluated first and may refer to a previous value of X. For example, the assignment X = X + 2 increases the value of X by 2. A rival programming-language usage was pioneered by the original version of ALGOL, designed in 1958 and implemented in 1960.
ALGOL included a relational operator that tested for equality, allowing constructions like if x = 2 with the same meaning of "=" as the conditional usage in mathematics. The equals sign was reserved for this usage. Both usages have remained common in different programming languages into the early 21st century; as well as Fortran, "=" is used for assignment in such languages as C, Python and their descendants. But "=" is used for equality and not assignment in the Pascal family, Eiffel, APL, other languages. A few languages, such as BASIC and PL/I, have used the equals sign to mean both assignment and equality, distinguished by context. However, in most languages where "=" has one of these meanings, a different character or, more a sequence of characters is used for the other meaning. Following ALGOL, most languages that use "=" for equality use ":=" for assignment, although APL, with its special character set, uses a left-pointing arrow. Fortran did not have an equality operator until FORTRAN IV was released in 1962, since when it has used the four characters ".
The === operator may be defined arbitrarily for any given type. For example, a value of type Range is a range of integers, such as 1800..1899. == 1844 is false. Note that under these semantics, === is non-symmetric; the equals sign is sometimes used in Japanese as a separator between names. The equals sign is used as a grammatical tone letter in the orthographies of Budu in the Congo-Kinshasa, in Krumen and Dan in the Ivory Coast; the Unicode character used for the tone letter is different from the mathematical symbol. A unique case of the equals sign of European usage in a person's name in a double-barreled name, was by pioneer aviator Alberto Santos-Dumont, as he is known not only to have used an equals sign between his two surnames in place of a hyphen, but seems to have preferred that practice, to display equal respect for his father's French ethnicity and the Brazilian ethnicity of his mother. In linguistic interlinear
An electronic calculator is 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 after the Intel 4004, the first microprocessor, was developed by Intel for the Japanese calculator company Busicom, they became used within the petroleum industry. 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 a basic calculator was affordable to most and they became common in schools. Computer operating systems as far back as early Unix have included interactive calculator programs such as dc and hoc, calculator functions are included in all personal digital assistant type devices, the exceptions being a few dedicated address book and dictionary devices.
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 have the ability to do computer algebra. Graphing calculators can be used to graph functions defined on the real line, or higher-dimensional Euclidean space; as of 2016, basic calculators cost little. 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 arithmetical operations. Most basic calculators assign operation on each button. Calculators have liquid-crystal displays as output in place of historical light-emitting diode displays and vacuum fluorescent displays. Large-sized figures are used to improve readability. Various symbols for function commands may be shown on the display. Fractions such as 1⁄3 are displayed as decimal approximations, for example rounded to 0.33333333.
Some fractions can be difficult to recognize in decimal form. Calculators have the ability to store numbers into computer memory. Basic calculators store only one number at a time; the variables can be used for constructing formulas. Some models have the ability to extend memory capacity to store more numbers. Power sources of calculators are: batteries, solar cells or mains electricity, turning on with a switch or button; some models have no turn-off button but they provide some way to put off. Crank-powered calculators were common in 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. In general, a basic electronic calculator consists of the following components: Power source Keypad – consists of keys used to input numbers and function commands Display panel – displays input numbers and results. Liquid-crystal displays, vacuum fluorescent displays, light-emitting diode displays use seven segments to represent each digit in a basic calculator.
Advanced calculators may use dot matrix displays. A printing calculator, in addition to a display panel, has a printing unit that prints results in ink onto a roll of paper, using a printing mechanism. Processor chip. Clock rate of a processor chip refers to the frequency at which the central processing unit is running, it is used as an indicator of the processor's speed, is measured in clock cycles per second or the SI unit hertz. 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 =; when 2 5 is entered, it is picked up by the scanning unit. This "pushes" the first number out into the Y register.
Arithmetic is a branch of mathematics that consists of the study of numbers the properties of the traditional operations on them—addition, subtraction and division. Arithmetic is an elementary part of number theory, number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra and analysis; the terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory and are sometimes still used to refer to a wider part of number theory. The prehistory of arithmetic is limited to a small number of artifacts which may indicate the conception of addition and subtraction, the best-known being the Ishango bone from central Africa, dating from somewhere between 20,000 and 18,000 BC, although its interpretation is disputed; the earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations as early as 2000 BC. These artifacts do not always reveal the specific process used for solving problems, but the characteristics of the particular numeral system influence the complexity of the methods.
The hieroglyphic system for Egyptian numerals, like the Roman numerals, descended from tally marks used for counting. In both cases, this origin resulted in values that used a decimal base but did not include positional notation. Complex calculations with Roman numerals required the assistance of a counting board or the Roman abacus to obtain the results. Early number systems that included positional notation were not decimal, including the sexagesimal system for Babylonian numerals and the vigesimal system that defined Maya numerals; because of this place-value concept, the ability to reuse the same digits for different values contributed to simpler and more efficient methods of calculation. The continuous historical development of modern arithmetic starts with the Hellenistic civilization of ancient Greece, although it originated much than the Babylonian and Egyptian examples. Prior to the works of Euclid around 300 BC, Greek studies in mathematics overlapped with philosophical and mystical beliefs.
For example, Nicomachus summarized the viewpoint of the earlier Pythagorean approach to numbers, their relationships to each other, in his Introduction to Arithmetic. Greek numerals were used by Archimedes and others in a positional notation not different from ours; the ancient Greeks lacked a symbol for zero until the Hellenistic period, they used three separate sets of symbols as digits: one set for the units place, one for the tens place, one for the hundreds. For the thousands place they would reuse the symbols for the units place, so on, their addition algorithm was identical to ours, their multiplication algorithm was only slightly different. Their long division algorithm was the same, the digit-by-digit square root algorithm, popularly used as as the 20th century, was known to Archimedes, who may have invented it, he preferred it to Hero's method of successive approximation because, once computed, a digit doesn't change, the square roots of perfect squares, such as 7485696, terminate as 2736.
For numbers with a fractional part, such as 546.934, they used negative powers of 60 instead of negative powers of 10 for the fractional part 0.934. The ancient Chinese had advanced arithmetic studies dating from the Shang Dynasty and continuing through the Tang Dynasty, from basic numbers to advanced algebra; the ancient Chinese used a positional notation similar to that of the Greeks. Since they lacked a symbol for zero, they had one set of symbols for the unit's place, a second set for the ten's place. For the hundred's place they reused the symbols for the unit's place, so on, their symbols were based on the ancient counting rods. It is a complicated question to determine when the Chinese started calculating with positional representation, but it was before 400 BC; the ancient Chinese were the first to meaningfully discover and apply negative numbers as explained in the Nine Chapters on the Mathematical Art, written by Liu Hui. The gradual development of the Hindu–Arabic numeral system independently devised the place-value concept and positional notation, which combined the simpler methods for computations with a decimal base and the use of a digit representing 0.
This allowed the system to represent both large and small integers. This approach replaced all other systems. In the early 6th century AD, the Indian mathematician Aryabhata incorporated an existing version of this system in his work, experimented with different notations. In the 7th century, Brahmagupta established the use of 0 as a separate number and determined the results for multiplication, division and subtraction of zero and all other numbers, except for the result of division by 0, his contemporary, the Syriac bishop Severus Sebokht said, "Indians possess a method of calculation that no word can praise enough. Their rational system of mathematics, or of their method of calculation. I mean the system using nine symbols." The Arabs learned this new method and called it hesab. Although the Codex Vigilanus described an early form of Arabic numerals by 976 AD, Leonardo of Pisa was responsible for spreading their use throughout Europe after the publication of his book Liber Abaci in 1202, he wrote, "The method of the Indians surpasses any known method to compute.
It's a marvelous method. They do their computations using nine figures and symbol zero". In the Middle Ages, arithmetic was one of the seven