The slide rule (often nicknamed a "slipstick") was developed by William Oughtred and others (see history, below); it is a mechanical analog computer, consisting of at least two finely divided scales (rules), most often a fixed outer pair and a movable inner one, with a sliding window called the cursor. William Oughtred ( March 5, 1575 – June 30, 1660) was an English Mathematician. An analog computer (spelt analogue in British English is a form of Computer that uses continuous physical phenomena such as electrical mechanical The slide rule is used primarily for multiplication and division, and also for "scientific" functions such as roots, logarithms and trigonometry, but does not generally perform addition or subtraction. In Mathematics, especially in elementary Arithmetic, division is an arithmetic operation which is the inverse of Multiplication. In Mathematics, an n th root of a Number a is a number b such that bn = a. In Mathematics, the logarithm of a number to a given base is the power or Exponent to which the base must be raised in order to produce Circle-trig6svg|300px|thumb|right|All of the Trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Addition is the mathematical process of putting things together Subtraction is one of the four basic Arithmetic operations it is the inverse of Addition, meaning that if we start with any number and add any number and then subtract The Binary Slide Rule manufactured by Gilson in 1931 performed an addition and subtraction function limited to fractions. Year 1931 ( MCMXXXI) was a Common year starting on Thursday (link will display full 1931 calendar of the Gregorian calendar. In Mathematics, a fraction (from the Latin fractus, broken is a concept of a proportional relation between an object part and the object 
Before the advent of the pocket calculator, it was the most commonly used calculation tool in science and engineering. A calculator is device for performing mathematical calculations distinguished from a Computer by having a limited problem solving ability and an interface optimized for interactive Science (from the Latin scientia, meaning " Knowledge " or "knowing" is the effort to discover, and increase human understanding Engineering is the Discipline and Profession of applying technical and scientific Knowledge and The use of slide rules continued to grow through the 1950s and 1960s even as digital computing devices were being gradually introduced; but around 1974 the electronic scientific calculator made it largely obsolete and most suppliers exited the business. Year 1950 ( MCML) was a Common year starting on Sunday (link will display the full calendar of the Gregorian calendar. Year 1960 ( MCMLX) was a Leap year starting on Friday (link will display full calendar of the Gregorian calendar. A computer is a Machine that manipulates data according to a list of instructions. A scientific calculator is a type of electronic Calculator, usually but not always handheld designed to calculate problems in science (especially Physics
In its most basic form, the slide rule uses two logarithmic scales to allow rapid multiplication and division of numbers, common operations that can be time-consuming and error-prone when done on paper. More complex slide rules allow other calculations, such as square roots, exponentials, logarithms, and trigonometric functions. In Mathematics, a square root of a number x is a number r such that r 2 = x, or in words a number r whose
In general, mathematical calculations are performed by aligning a mark on the sliding central strip with a mark on one of the fixed strips, and then observing the relative positions of other marks on the strips. Numbers aligned with the marks give the approximate value of the product, quotient, or other calculated result. A number is an Abstract object, tokens of which are Symbols used in Counting and measuring. In Mathematics, a quotient is the result of a division. For example when dividing 6 by 3 the quotient is 2 while 6 is called the dividend, and 3 the
The user determines the location of the decimal point in the result, based on mental estimation. In a positional Numeral system, the decimal separator is a Symbol used to mark the boundary between the integral and the fractional Scientific notation is used to track the decimal point in more formal calculations. Scientific notation, also sometimes known as standard form or as exponential notation, is a way of writing numbers that accommodates values too large or small to be Addition and subtraction steps in a calculation are generally done mentally or on paper, not on the slide rule. Addition is the mathematical process of putting things together Subtraction is one of the four basic Arithmetic operations it is the inverse of Addition, meaning that if we start with any number and add any number and then subtract
Even the most basic student slide rules have more than two scales. Most consist of three linear strips of the same length, aligned in parallel and interlocked so that the central strip can be moved lengthwise relative to the other two. The outer two strips are fixed so that their relative positions do not change.
Some slide rules ("duplex" models) have scales on both sides of the rule and slide strip, others on one side of the outer strips and both sides of the slide strip, still others on one side only ("simplex" rules). A sliding cursor with a vertical alignment line is used to find corresponding points on scales that are not adjacent to each other or, in duplex models, are on the other side of the rule. The cursor can also record an intermediate result on any of the scales.
A logarithm transforms the operations of multiplication and division to addition and subtraction according to the rules log(xy) = log(x) + log(y) and log(x / y) = log(x) − log(y). Moving the top scale to the right by a distance of log(x), by matching the beginning of the top scale with the label x on the bottom, aligns each number y, at position log(y) on the top scale, with the number at position log(x) + log(y) on the bottom scale. Because log(x) + log(y) = log(xy), this position on the bottom scale gives xy, the product of x and y.
Operations may go "off the scale. " For example the diagram above shows that the slide rule has not positioned the 7 on the upper scale above any number on the lower scale, so it does not give any answer for 2×7. In such cases, the user may slide the upper scale to the left until its right index aligns with the 2, effectively multiplying by 0. 2 instead of by 2, as in the illustration below:
Here the user of the slide rule must remember to adjust the decimal point appropriately to correct the final answer. We wanted to find 2×7, but instead we calculated 0. 2×7=1. 4. So the true answer is not 1. 4 but 14. Resetting the slide is not the only way to handle multiplications that would result in off-scale results, such as 2×7; some other methods are:
Method 1 is easy to understand, but entails a loss of precision. Method 3 has the advantage that it only involves two scales.
The illustration below demonstrates the computation of 5. 5/2. The 2 on the top scale is placed over the 5. 5 on the bottom scale. The 1 on the top scale lies above the quotient, 2. 75. There is more than one method for doing division, however, the method presented here has the advantage that the final result cannot be off-scale, because one has a choice of using the 1 at either end.
In addition to the logarithmic scales, some slide rules have other mathematical functions encoded on other auxiliary scales. The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function The most popular were trigonometric, usually sine and tangent, common logarithm (log10) (for taking the log of a value on a multiplier scale), natural logarithm (ln) and exponential (ex) scales. The common logarithm is the Logarithm with base 10 It is also known as the decadic logarithm, named after its base The natural logarithm, formerly known as the Hyperbolic logarithm is the Logarithm to the base e, where e is an irrational The exponential function is a function in Mathematics. The application of this function to a value x is written as exp( x) Some rules include a Pythagorean scale, to figure sides of triangles, and a scale to figure circles. "Pythagoras of Samos" redirects here For the Samian statuary of the same name see Pythagoras (sculptor. Others feature scales for calculating hyperbolic functions. In Mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular functions On linear rules, the scales and their labeling are highly standardized, with variation usually occurring only in terms of which scales are included and in what order:
|A, B||two-decade logarithmic scales, used for finding square roots and squares of numbers|
|C, D||single-decade logarithmic scales|
|K||three-decade logarithmic scale, used for finding cube roots and cubes of numbers|
|CF, DF||"folded" versions of the C and D scales that start from π rather than from unity; these are convenient in two cases. IMPORTANT NOTICE Please note that Wikipedia is not a database to store the millions of digits of π please refrain from adding those to Wikipedia as it could cause technical problems First when the user guesses a product will be close to 10 but isn't sure whether it will be slightly less or slightly more than 10, the folded scales avoid the possibility of going off the scale. Second, by making the start π rather than the square root of 10, multiplying or dividing by π (as is common in science and engineering formulas) is simplified.|
|CI, DI, DIF||"inverted" scales, running from right to left, used to simplify 1/x steps|
|S||used for finding sines and cosines on the D scale|
|T||used for finding tangents and cotangents on the D and DI scales|
|ST, SRT||used for sines and tangents of small angles and degree–radian conversion|
|L||a linear scale, used along with the C and D scales for finding base-10 logarithms and powers of 10|
|LLn||a set of log-log scales, used for finding logarithms and exponentials of numbers|
|Ln||a linear scale, used along with the C and D scales for finding natural (base e) logarithms and ex|
|The scales on the front and back of a K&E 4081-3 slide rule.|
There are single-decade (C and D), double-decade (A and B), and triple-decade (K) scales. To compute x2, for example, locate x on the D scale and read its square on the A scale. Inverting this process allows square roots to be found, and similarly for the powers 3, 1/3, 2/3, and 3/2. Care must be taken when the base, x, is found in more than one place on its scale. For instance, there are two nines on the A scale; to find the square root of nine, use the first one; the second one gives the square root of 90. For xy problems, use the LL scales. There are often several, but we only need consider the one with x on it. First, align the leftmost 1 on the C scale with x on the LL scale. Then, find y on the C scale and go down to the LL scale with x on it. That scale will indicate the answer. If y is "off the scale," locate xy / 2 and square it using the A and B scales as described above.
The S, T, and ST scales are used for trig functions and multiples of trig functions, for angles in degrees.
For angles from around 5. 7 up to 90 degrees, sines are found by comparing the S scale with C. The S scale has a second set of angles (sometimes in a different color), which run in the opposite direction, and are used for cosines. Tangents are found by comparing the T scale with C or, for angles greater than 45 degrees, CI. Common forms such as k*sin(x) can be read directly from x on the S scale to the result on the D scale, when the C-scale index is set at k. For angles below 5. 7 degrees, sines, tangents, and radians are approximately equal, and are found on the ST or SRT (sines, radians, and tangents) scale, or simply divided by 57. 3 degrees/radian. The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57 Inverse trigonometric functions are found by reversing the process.
Many slide rules have S, T, and ST scales marked with degrees and minutes. So-called decitrig models use decimal fractions of degrees instead.
Base-10 logarithms and exponentials are found using the L scale, which is linear. Some slide rules have a Ln scale, which is for base e.
The Ln scale was invented by an 11th grade student, Stephen B. Cohen, in 1958. The original intent was to allow the user to select an exponent x (in the range 0 to 2. 3) on the Ln scale and read ex on the C (or D) scale and e–x on the CI (or DI) scale. Pickett, Inc. was given exclusive rights to the scale. Later, the inventor created a set of "marks" on the Ln scale to extend the range beyond the 2. 3 limit, but Pickett never incorporated these marks on any of its slide rules.
Addition and subtraction can be performed directly on a slide rule using two different techniques. 
The first method to perform addition and subtraction on the C and D (or any comparable scales) requires converting the problem into one of division. For addition, the quotient of the two variables plus one times the divisor equals their sum:
For subtraction, the quotient of the two variables minus one times the divisor equals their difference:
The second method utilizes a sliding linear L scale available on some models. Addition and subtraction are performed by sliding the cursor left (for subtraction) or right (for addition) then returning the slide to 0 to read the result.
The length of the slide rule is quoted in terms of the nominal length of the scales. Scales on the most common "10-inch" models are actually 25 cm in length, as they were made to metric standards, though some rules offer slightly extended scales to simplify manipulation when a result overflowed. A centimetre ( American spelling: centimeter, symbol cm) is a unit of Length in the Metric system, equal to one hundredth Pocket rules are typically 5 inches. Models a couple of meters long were sold to be hung in classrooms for teaching purposes. 
Typically the divisions mark a scale to a precision of two significant figures, and the user estimates the third figure. The significant figures (also called significant digits and abbreviated sig figs) of a number are those digits that carry meaning contributing to its accuracy Some high-end slide rules have magnifying cursors that make the markings easier to see. Such cursors can effectively double the accuracy of readings, permitting a 10-inch slide rule to serve as well as a 20-inch.
A number of tricks can be used to get more convenience. Trigonometric scales are sometimes dual-labeled, in black and red, with complementary angles, the so-called "Darmstadt" style. Duplex slide rules often duplicate some of the scales on the back. Scales are often "split" to get higher accuracy.
Specialized slide rules were invented for various forms of engineering, business and banking. These often had common calculations directly expressed as special scales, for example loan calculations, optimal purchase quantities, or particular engineering equations. For example, the Fisher Controls company distributed a customized slide rule adapted to solving the equations used for selecting the proper size of industrial flow control valves. Emerson Electric Company ( NYSE: EMR is a major Multinational corporation headquartered in St For other uses see Valve (disambiguation. For the electronic component see Thermionic valve.
Circular slide rules come in two basic types, one with two cursors (left), and another with a movable disk and a single cursor (right). The dual cursor versions perform multiplication and division by maintaining a fixed angle between the cursors as they are rotated around the dial. The single cursor version operates more like the standard slide rule through the appropriate alignment of the scales.
The basic advantage of a circular slide rule is that the longest dimension was reduced by a factor of about 3 (i. e. by π). IMPORTANT NOTICE Please note that Wikipedia is not a database to store the millions of digits of π please refrain from adding those to Wikipedia as it could cause technical problems For example, a 10 cm circular would have a maximum precision equal to a 30 cm ordinary slide rule. A centimetre ( American spelling: centimeter, symbol cm) is a unit of Length in the Metric system, equal to one hundredth At least one circular rule sacrificed some of the scales usually found in slide rules in order to obtain additional resolution in multiplication and division. It was the 8 3/8" in diameter Atlas slide rule, apparently made by Gilson in 1931, and was of the two-cursor variety. It functioned through the use of a spiral C scale, which was claimed to be 50 feet long and readable to five significant figures.  Circular slide rules also eliminate "off-scale" calculations, because the scales were designed to "wrap around"; they never have to be re-oriented when results are near 1. 0—the rule is always on scale. However, for non-cyclical non-spiral scales such as S, T, and LL's, the scale length is shortened to make room for end margins.
Circular slide rules are mechanically more rugged and smoother-moving, but their scale alignment precision is sensitive to the centering of a central pivot; a minute 0. 1 mm off-centre of the pivot can result in a 0. 2 mm worst case alignment error. The pivot, however, does prevent scratching of the face and cursors. The highest accuracy scales are placed on the outer rings. Rather than "split" scales, high-end circular rules use spiral scales for difficult things like log-of-log scales. One eight-inch premium circular rule had a 50 inch spiral log-log scale! Technically, a real disadvantage of circular slide rules is that less-important scales are closer to the center, and have lower precisions. The main disadvantages of circular slide rules are the difficulty in locating figures along a rotating disc, and limited number of scales. Most students learned slide rule use on the linear slide rules, and did not find reason to switch.
One slide rule remaining in daily use around the world is the E6B. StudentE6BFlightComputerjpg|thumb|An E6B flight computer commonly used by student pilots This is a circular slide rule first created in the 1930s for aircraft pilots to help with dead reckoning. The 1930s were described as an abrupt shift to more radical and conservative lifestyles as countries were struggling to find a solution to the Great Depression. Dead reckoning ( DR) is the process of estimating one's current position based upon a previously determined position or fix, and advancing that position based upon With the aid of scales printed on the frame it also helps with such miscellaneous tasks as converting time, distance, speed, and temperature values, compass errors, and calculating fuel use. A compass, magnetic compass or mariner's compass is a navigational instrument for determining direction relative to the earth's Magnetic poles It consists The so-called "prayer wheel" is still available in all flight shops, and remains widely used. While GPS has reduced the use of dead reckoning for aerial navigation, and handheld calculators have taken over many of its functions, the E6B remains widely used as a primary or backup device and the majority of flight schools demand that their students have some degree of its mastery. Basic concept of GPS operation A GPS receiver calculates its position by carefully timing the signals sent by the constellation of GPS Satellites high above the Earth Dead reckoning ( DR) is the process of estimating one's current position based upon a previously determined position or fix, and advancing that position based upon The principles of air navigation are the same for all Aircraft, big or Small. A calculator is device for performing mathematical calculations distinguished from a Computer by having a limited problem solving ability and an interface optimized for interactive StudentE6BFlightComputerjpg|thumb|An E6B flight computer commonly used by student pilots
In 1952, Swiss watch company Breitling introduced a pilot's wristwatch (above, left) with an integrated circular slide rule specialized for flight calculations: the Breitling Navitimer. Switzerland (English pronunciation; Schweiz Swiss German: Schwyz or Schwiiz Suisse Svizzera Svizra officially the Swiss Confederation Breitling is a brand of Swiss Watches from the Canton of Jura. A watch is a timepiece that is made to be worn on a person The term now usually refers to a wristwatch, which is worn on the wrist with a strap or Bracelet. The Navitimer circular rule, referred to by Breitling as a "navigation computer", featured airspeed, rate/time of climb/descent, flight time, distance, and fuel consumption functions, as well as kilometer–nautical mile and gallon–liter fuel amount conversion functions. Airspeed is the speed of an Aircraft relative to the air There are several different measures of airspeed indicated airspeed calibrated airspeed equivalent airspeed and true In Aerodynamics, the rate of climb RoC is the speed at which an Aircraft increases its Altitude. The kilometre ( American spelling: kilometer) symbol km is a unit of Length in the Metric system, equal to one thousand A nautical mile or sea mile is a unit of Length. It corresponds approximately to one minute of Latitude along any meridian. A gallon is a measure of Volume. It is in current use in the United States and still has limited use in many other English-speaking countries The litre or liter (see spelling differences) is a unit of Volume.
There are two main types of cylindrical slide rules: those with helical scales such as the Fuller, the Otis King and the Bygrave slide rule, and those with bars, such as the Thacher and some Loga models. Otis Carter Formby King (1876&ndash?? was a grocer and engineer in London who invented and produced a cylindrical Slide rule with helical scales primarily for business uses The Bygrave slide rule is a Slide rule named for its inventor Captain L In either case, the advantage is a much longer scale, and hence potentially higher accuracy, than a straight or circular rule.
Traditionally slide rules were made out of hard wood such as mahogany or boxwood with cursors of glass and metal. The name mahogany is used when referring to numerous varieties of dark-colored wood originally the wood of the species Swietenia mahagoni, known as West As noted below, at least one high precision instrument was made of steel. Steel is an Alloy consisting mostly of Iron, with a Carbon content between 0
In 1895, a Japanese firm, Hemmi, started to make them from bamboo, which had the advantages of being dimensionally stable, strong and naturally self-lubricating. Bamboo is a group of Woody perennial Evergreen Plants in the True grass family Poaceae, subfamily These bamboo slide rules were introduced in Sweden in the fall of 1933 , and probably only a little earlier in Germany. Scales were made of celluloid or plastic. Celluloid is the name of a class of compounds created from Nitrocellulose and Camphor, plus dyes and other agents Later slide rules were made of plastic, or aluminum painted with plastic. WikipediaNaming Later cursors were acrylics or polycarbonates sliding on Teflon bearings. In Organic chemistry, the acryl group is the Functional group with structure H 2 C =CH-C(= O)- it is the Acyl group In Chemistry, poly(tetrafluoroethene or poly(tetrafluoroethylene ( PTFE) is a synthetic Fluoropolymer which finds numerous applications
All premium slide rules had numbers and scales engraved, and then filled with paint or other resin. Resin, not to be confused with Rosin, is a Hydrocarbon Secretion of many Plants particularly coniferous trees. Painted or imprinted slide rules were viewed as inferior because the markings could wear off. Nevertheless, Pickett, probably America's most successful slide rule company, made all printed scales. Premium slide rules included clever catches so the rule would not fall apart by accident, and bumpers to protect the scales and cursor from rubbing on tabletops. The recommended cleaning method for engraved markings is to scrub lightly with steel-wool. For painted slide rules, and the faint of heart, use diluted commercial window-cleaning fluid and a soft cloth.
The slide rule was invented around 1620–1630, shortly after John Napier's publication of the concept of the logarithm. For other people with the same name see John Napier (disambiguation. In Mathematics, the logarithm of a number to a given base is the power or Exponent to which the base must be raised in order to produce Edmund Gunter of Oxford developed a calculating device with a single logarithmic scale, which, with additional measuring tools, could be used to multiply and divide. Edmund Gunter ( 1581 - December 10, 1626) English Mathematician, of Welsh descent was born in Hertfordshire in 1581 The first description of this scale was published in Paris in 1624 by Edmund Wingate (c. 1593 - 1656), an English Mathematician, in a book entitled “L'usage de la reigle de proportion en l'arithmetique & geometrie”. The book contains a double scale on one side of which is a logarithmic scale and on the other a tabular scale. In 1630, William Oughtred of Cambridge invented a circular slide rule, and in 1632 he combined two Gunter rules, held together with the hands, to make a device that is recognizably the modern slide rule. William Oughtred ( March 5, 1575 – June 30, 1660) was an English Mathematician. Like his contemporary at Cambridge, Isaac Newton, Oughtred taught his ideas privately to his students, but delayed in publishing them, and like Newton, he became involved in a vitriolic controversy over priority, with his one-time student Richard Delamain and the prior claims of Wingate. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements Oughtred's ideas were only made public in publications of his student William Forster in 1632 and 1653.
In 1677, Henry Coggeshall created a two-foot folding rule for timber measure, called the Coggeshall slide rule. In measurement the Coggeshall slide rule, also called a carpenter's slide rule, was a Slide rule designed by Henry Coggeshall in 1677 to facilitate His design and uses for the tool gave the slide rule purpose outside of mathematical inquiry.
In 1722, Warner introduced the two- and three-decade scales, and in 1755 Everard included an inverted scale; a slide rule containing all of these scales is usually known as a "polyphase" rule.
In 1815, Peter Roget invented the log log slide rule, which included a scale displaying the logarithm of the logarithm. Peter Mark Roget roʊˈʒeɪ ( January 18, 1779 &ndash September 12, 1869) was a British Physician, Natural theologian This allowed the user to directly perform calculations involving roots and exponents. This was especially useful for fractional powers.
The more modern form was created in 1859 by French artillery lieutenant Amédée Mannheim, "who was fortunate in having his rule made by a firm of national reputation and in having it adopted by the French Artillery. Amedie Mannheim ( 17 July, 1831 &ndash 11 December, 1906) was the inventor of the modern Slide rule. " It was around that time, as engineering became a recognized professional activity, that slide rules came into wide use in Europe. Engineering is the Discipline and Profession of applying technical and scientific Knowledge and They did not become common in the United States until 1881, when Edwin Thacher introduced a cylindrical rule there. The duplex rule was invented by William Cox in 1891, and was produced by Keuffel and Esser Co. of New York. The Keuffel and Esser Co (also known as K&E was a drafting company founded in 1867 by German immigrants William J ,
Astronomical work also required fine computations, and in 19th century Germany a steel slide rule about 2 meters long was used at one observatory. It had a microscope attached, giving it accuracy to six decimal places. A microscope ( Greek: ( micron) = small + ( skopein) = to look or see is an instrument for viewing objects that are
In World War II, bombardiers and navigators who required quick calculations often used specialized slide rules. World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including One office of the U.S. Navy actually designed a generic slide rule "chassis" with an aluminum body and plastic cursor into which celluloid cards (printed on both sides) could be placed for special calculations. The process was invented to calculate range, fuel use and altitude for aircraft, and then adapted to many other purposes. The E6-B Flight Computer, a circular sliderule with added features is still used today in aviation, particularly by student pilots. StudentE6BFlightComputerjpg|thumb|An E6B flight computer commonly used by student pilots
Throughout the 1950s and 1960s the slide rule was the symbol of the engineer's profession (in the same way that the stethoscope symbolized the medical profession). The 1950s Decade refers to the years of 1950 to 1959 inclusive The 1960s decade refers to the years from the beginning of 1960 to the end of 1969 The stethoscope (from Greek στηθοσκόπιο, of στήθος stéthos - chest and σκοπή skopé - examination) is an acoustic As an anecdote it can be mentioned that German rocket scientist Wernher von Braun brought two 1930s vintage Nestler slide rules with him when he moved to the U. Wernher Magnus Maximilian Freiherr von Braun (March 23 1912 &ndash June 16 1977 a German rocket physicist and astronautics engineer became one of the leading figures in S. after World War II to work on the American space program. Throughout his life he never used any other pocket calculating devices; slide rules obviously served him perfectly well for making quick estimates of rocket design parameters and other figures. Aluminum Pickett-brand slide rules were carried on five Apollo space missions, including to the moon, according to advertising on Pickett's N600 slide rule boxes . Pickett is a Surname, and may refer to Albert J Pickett Bill Pickett Blake Pickett
Some engineering students and engineers carried ten-inch slide rules in belt holsters, and even into the mid 1970s this was a common sight on campuses. Students also might keep a ten-or twenty-inch rule for precision work at home or the office while carrying a five-inch pocket slide rule around with them.
In 2004, education researchers David B. Sher and Dean C. Nataro conceived a new type of slide rule based on prosthaphaeresis, an algorithm for rapidly computing products that predates logarithms. Prosthaphaeresis was an Algorithm used in the late 16th century and early 17th century for approximate Multiplication and division using formulas from There has been little practical interest in constructing one beyond the initial prototype, however. 
The importance of the slide rule began to diminish as electronic computers, a new but very scarce resource in the 1950s, became widely available to technical workers during the 1960s. A computer is a Machine that manipulates data according to a list of instructions. The introduction of Fortran in 1957 made computers practical for solving modest size mathematical problems. Fortran (previously FORTRAN) is a general-purpose, procedural, imperative Programming language that is especially suited to IBM introduced a series of more affordable computers, the IBM 650 (1954), IBM 1620 (1959), IBM 1130 (1965) addressed to the science and engineering market. International Business Machines Corporation abbreviated IBM and nicknamed "Big Blue", is a multinational Computer Technology The IBM 650 ( photo was one of IBM ’s early Computers and the world’s first mass-produced ( photo computer The IBM 1620 was announced by IBM on October 21, 1959 and marketed as an inexpensive "scientific computer" The IBM 1130 Computing System was introduced in 1965. It was IBM 's least-expensive Computer to date and was aimed at price-sensitive computing-intensive John Kemeny's BASIC programming language (1964) made it easy for students to use computers. In Computer programming, BASIC (an Acronym for Beginner's All-purpose Symbolic Instruction Code) is a family of High-level programming languages The DEC PDP-8 minicomputer was introduced in 1965. The PDP-8 was the first successful commercial Minicomputer, produced by Digital Equipment Corporation (DEC in the 1960s
Computers also changed the nature of calculation. With slide rules, there was a great emphasis on working the algebra to get expressions into the most computable form. Small terms were approximated or dropped. Fortran allowed complicated formulas simply to be typed in from textbooks. Fortran (previously FORTRAN) is a general-purpose, procedural, imperative Programming language that is especially suited to A textbook is a manual of instruction or a standard book in any branch of study Numerical integration was often easier than trying to find closed form solutions. In Numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite Integral, and by extension More difficult problems could be solved. The young engineer asking for computer time to solve a problem that could have been done by a few swipes on the slide rule became a humorous cliché. Many computer centers had a framed slide rule hung on a wall with the note "In case of emergency, break glass. "
Another step toward the replacement of slide rules with electronics was the development of electronic calculators for scientific and engineering use. A calculator is device for performing mathematical calculations distinguished from a Computer by having a limited problem solving ability and an interface optimized for interactive The first included the Wang Laboratories LOCI-2,  introduced in 1965, which used logarithms for multiplication and division and the Hewlett-Packard HP-9100, introduced in 1968. Wang Laboratories was a computer company founded in 1951 by Dr In Mathematics, the logarithm of a number to a given base is the power or Exponent to which the base must be raised in order to produce  Some consider the HP-9100 the first true scientific calculator because it had trigonometric functions (sin, cos, tan) in addition to exponentials and logarithms. The HP-9100 used the CORDIC (coordinate rotation digital computer) algorithm,  which allows for calculation of trigonometric functions using only shift and add operations. CORDIC (digit-by-digit method Volder's algorithm (for CO ordinate R otation DI gital C omputer is a simple and efficient Algorithm This method facilitated the development of ever smaller scientific calculators.
The last nail in the coffin for the slide rule was the launch of pocket-sized scientific calculators, of which the 1972 Hewlett-Packard HP-35 was the first. The HP-35 was Hewlett-Packard 's first Pocket calculator and the world's first scientific pocket calculator (a calculator with trigonometric Such calculators became known as "slide rule" calculators since they could perform most or all of the functions on a slide rule. At several hundred dollars, even this was considered expensive for most students. While professional slide rules could also be quite expensive, drug stores often sold basic plastic models for under $20 USD. The United States dollar ( sign: $; code: USD) is the unit of Currency of the United States; it has also been But by 1975, basic four-function electronic calculators could be had for under $50. By 1976 the TI-30 offered a scientific calculator for under $25. The TI-30 is a series of scientific Calculators manufactured by Texas Instruments, the first of which was introduced in 1976. After this time, the market for slide rules dried up quickly as small scientific calculators became affordable. Somewhat ironically, most advanced high school mathematics classes now require graphing calculators that cost nearly $100 by the late 1990s as mathematics reform sought to leverage technology. A graphing calculator (also known as a graphic calculator or graphical calculator) typically refers to a class of handheld Calculators that are capable of
One advantage of using a slide rule in addition to an electronic calculator is that an important calculation can be checked by doing it on both; because the two instruments are so different, there is little chance of making the same mistake twice.
For reasons given above, some people still prefer a slide rule over an electronic calculator as a practical computing device. Many others keep their old slide rules out of a sense of nostalgia, or collect slide rules as a hobby.
A popular model is the Keuffel & Esser Deci-Lon, a premium scientific and engineering slide rule available both in a ten-inch "regular" (Deci-Lon 10) and a five-inch "pocket" (Deci-Lon 5) variant. The Keuffel and Esser Co (also known as K&E was a drafting company founded in 1867 by German immigrants William J Another prized American model is the eight-inch Scientific Instruments circular rule. Of European rules, Faber-Castell's high-end models are the most popular among collectors. Faber-Castell is a German manufacturer of writing instruments art supplies staplers and Slide rules founded in 1761 in Nuremberg by Kaspar
Although there is a large supply of slide rules circulating on the market, specimens in good condition tend to be surprisingly expensive. Many rules found for sale on online auction sites are damaged or have missing parts, and the seller may not know enough to supply the relevant information. Replacement parts are scarce, and therefore expensive, and are generally only available for separate purchase on individual collectors' web sites. The Keuffel and Esser rules from the period up to about 1950 are particularly problematic, because the end-pieces on the cursors, made of celluloid, tend to break down chemically over time. Celluloid is the name of a class of compounds created from Nitrocellulose and Camphor, plus dyes and other agents
In many cases, an economical method for obtaining a working slide rule is to buy more than one of the same model, and combine their parts.
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