Scientific calculator
Encyclopedia
Electronics
Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...
calculator
Calculator
An electronic calculator is a small, portable, usually inexpensive electronic device used to perform the basic operations of arithmetic. Modern calculators are more portable than most computers, though most PDAs are comparable in size to handheld calculators.The first solid-state electronic...
, usually but not always handheld, designed to calculate problems in science, engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
, and mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
. They have almost completely replaced slide rule
Slide rule
The slide rule, also known colloquially as a slipstick, is a mechanical analog computer. The slide rule is used primarily for multiplication and division, and also for functions such as roots, logarithms and trigonometry, but is not normally used for addition or subtraction.Slide rules come in a...
s in almost all traditional applications, and are widely used in both education and professional settings.
In certain contexts such as higher education, scientific calculators have been superseded by graphing calculator
Graphing calculator
A graphing calculator typically refers to a class of handheld calculators that are capable of plotting graphs, solving simultaneous equations, and performing numerous other tasks with variables...
s, which offer a superset of scientific calculator functionality along with the ability to graph input data and write and store programs for the device. There is also some overlap with the financial calculator market.
Functions
Modern scientific calculators generally have many more features than a standard four or five-function calculator, and the feature set differs between manufacturers and models; however, the defining features of a scientific calculator include:- scientific notationScientific notationScientific notation is a way of writing numbers that are too large or too small to be conveniently written in standard decimal notation. Scientific notation has a number of useful properties and is commonly used in calculators and by scientists, mathematicians, doctors, and engineers.In scientific...
- floating pointFloating pointIn computing, floating point describes a method of representing real numbers in a way that can support a wide range of values. Numbers are, in general, represented approximately to a fixed number of significant digits and scaled using an exponent. The base for the scaling is normally 2, 10 or 16...
arithmetic - logarithmLogarithmThe logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
ic functions, using both base 10 and base eE (mathematical constant)The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base... - trigonometricTrigonometryTrigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
functions (some including hyperbolic trigonometryHyperbolic trigonometryIn mathematics, hyperbolic trigonometry can mean:*The use of the hyperbolic functions*The use of gyrotrigonometry in hyperbolic geometry...
) - exponential functions and rootNth rootIn mathematics, the nth root of a number x is a number r which, when raised to the power of n, equals xr^n = x,where n is the degree of the root...
s beyond the square rootSquare rootIn mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x... - quick access to constants such as piPi' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
and eE (mathematical constant)The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...
In addition, high-end scientific calculators will include:
- hexadecimalHexadecimalIn mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...
, binaryBinary numeral systemThe binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...
, and octalOctalThe octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three...
calculations, including basic BooleanBoolean logicBoolean algebra is a logical calculus of truth values, developed by George Boole in the 1840s. It resembles the algebra of real numbers, but with the numeric operations of multiplication xy, addition x + y, and negation −x replaced by the respective logical operations of...
math - complex numberComplex numberA complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
s - fractionFractionIn common usage a fraction is any part of a unit.Fraction may also mean:*Fraction , one of more equal parts of something, eg...
s - statisticsStatisticsStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
and probabilityProbabilityProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
calculations - programmability — see Programmable calculatorProgrammable calculatorProgrammable calculators are calculators that can automatically carry out a sequence of operations under control of a stored program, much like a computer. The first programmable calculators such as the IBM CPC used punched cards or other media for program storage...
- equation solving
- calculusCalculusCalculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
- conversion of unitsConversion of unitsConversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.- Process :...
- physical constants
While most scientific models have traditionally used a single-line display similar to traditional pocket calculators, many of them have at the very least more digits (10 to 12), sometimes with extra digits for the floating point exponent. A few have multi-line displays, with some recent models from Hewlett-Packard
Hewlett-Packard
Hewlett-Packard Company or HP is an American multinational information technology corporation headquartered in Palo Alto, California, USA that provides products, technologies, softwares, solutions and services to consumers, small- and medium-sized businesses and large enterprises, including...
, Texas Instruments
Texas Instruments
Texas Instruments Inc. , widely known as TI, is an American company based in Dallas, Texas, United States, which develops and commercializes semiconductor and computer technology...
, Casio
Casio
is a multinational electronic devices manufacturing company founded in 1946, with its headquarters in Shibuya, Tokyo, Japan. Casio is best known for its electronic products, such as calculators, audio equipment, PDAs, cameras, musical instruments, and watches...
, Sharp
Sharp Corporation
is a Japanese multinational corporation that designs and manufactures electronic products. Headquartered in Abeno-ku, Osaka, Japan, Sharp employs more than 55,580 people worldwide as of June 2011. The company was founded in September 1912 and takes its name from one of its founder's first...
, and Canon using dot matrix
Dot matrix
A dot matrix is a 2-dimensional array of LED used to represent characters, symbols and images.Typically the dot matrix is used in older computer printers and many digital display devices. In printers, the dots are usually the darkened areas of the paper...
displays similar to those found on graphing calculator
Graphing calculator
A graphing calculator typically refers to a class of handheld calculators that are capable of plotting graphs, solving simultaneous equations, and performing numerous other tasks with variables...
s.
Uses
Scientific calculators are used widely in any situation where quick access to certain mathematical functions is needed, especially those such as trigonometric functions that were once traditionally looked up in tables; they are also used in situations requiring back-of-the-envelope calculations of very large numbers, as in some aspects of astronomyAstronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
, physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, and chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
.
They are very often required for math classes from the junior high school level through college, and are generally either permitted or required on many standardized test
Standardized test
A standardized test is a test that is administered and scored in a consistent, or "standard", manner. Standardized tests are designed in such a way that the questions, conditions for administering, scoring procedures, and interpretations are consistent and are administered and scored in a...
s covering math and science subjects; as a result, many are sold into educational markets to cover this demand, and some high-end models include features making it easier to translate the problem on a textbook page into calculator input, from allowing explicit operator precedence using parentheses to providing a method for the user to enter an entire problem in as it is written on the page using simple formatting tools.
History
The first scientific calculator that included all of the basic features above was the programmable Hewlett-PackardHewlett-Packard
Hewlett-Packard Company or HP is an American multinational information technology corporation headquartered in Palo Alto, California, USA that provides products, technologies, softwares, solutions and services to consumers, small- and medium-sized businesses and large enterprises, including...
HP-9100A
Hewlett-Packard 9100A
The Hewlett-Packard 9100A is an early computer , first appearing in 1968. HP called it a desktop calculator because, as Bill Hewlett said, "If we had called it a computer, it would have been rejected by our customers' computer gurus because it didn't look like an IBM...
, released in 1968, though the Wang
Wang Laboratories
Wang Laboratories was a computer company founded in 1951 by Dr. An Wang and Dr. G. Y. Chu. The company was successively headquartered in Cambridge , Tewksbury , and finally in Lowell, Massachusetts . At its peak in the 1980s, Wang Laboratories had annual revenues of $3 billion and employed over...
LOCI-2 and the Mathatronics Mathatron had some features later identified with scientific calculator designs. The HP-9100 series was built entirely from discrete transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...
logic with no integrated circuit
Integrated circuit
An integrated circuit or monolithic integrated circuit is an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material...
s, and was one of the first uses of the CORDIC
CORDIC
CORDIC is a simple and efficient algorithm to calculate hyperbolic and trigonometric functions...
algorithm for trigonometric computation in a personal computing device, as well as the first calculator based on reverse Polish notation
Reverse Polish notation
Reverse Polish notation is a mathematical notation wherein every operator follows all of its operands, in contrast to Polish notation, which puts the operator in the prefix position. It is also known as Postfix notation and is parenthesis-free as long as operator arities are fixed...
entry. HP became closely identified with RPN calculators from then on, and even today some of their high-end calculators (particularly the long-lived HP-12C financial calculator and the HP-48 series of graphing calculators) still offer RPN as their default input mode due to having garnered a very large following.
The HP-35
HP-35
The HP-35 was Hewlett-Packard's first pocket calculator and the world's first scientific pocket calculator . Like some of HP's desktop calculators it used reverse Polish notation. Introduced at US$395, the HP-35 was available from 1972 to 1975.Market studies at the time had shown no market for...
, introduced on February 1, 1972, was Hewlett-Packard
Hewlett-Packard
Hewlett-Packard Company or HP is an American multinational information technology corporation headquartered in Palo Alto, California, USA that provides products, technologies, softwares, solutions and services to consumers, small- and medium-sized businesses and large enterprises, including...
's first pocket calculator and the world's first handheld scientific calculator. Like some of HP's desktop calculators it used reverse Polish notation
Reverse Polish notation
Reverse Polish notation is a mathematical notation wherein every operator follows all of its operands, in contrast to Polish notation, which puts the operator in the prefix position. It is also known as Postfix notation and is parenthesis-free as long as operator arities are fixed...
. Introduced at US$395, the HP-35 was available from 1972 to 1975. HP continues to develop and market high-end scientific calculators, like the HP-35s
HP 35s
The HP 35s Scientific Calculator is, as of 2007, the latest in Hewlett-Packard's long line of non-graphing scientific and programmable calculators...
and HP-49 series
HP-49 series
The HP 49G series are Hewlett-Packard manufactured graphing calculators. They are the successors of the popular HP-48 series.There are four calculators in the 49 series of HP graphing calculators...
, which have been favored by scientists and engineers, in labs, offices, as well as in the field.
Texas Instruments
Texas Instruments
Texas Instruments Inc. , widely known as TI, is an American company based in Dallas, Texas, United States, which develops and commercializes semiconductor and computer technology...
, after the introduction of several units with scientific notation, came out with a handheld scientific calculator on January 15, 1974 in the form of the SR-50. TI continues to be a major player in the calculator market, with their long-running TI-30
TI-30
The TI-30 was a scientific calculator manufactured by Texas Instruments, the first model of which was introduced in 1976. While the original TI-30 left production in 1983 after several design revisions, TI maintains the TI-30 designation as a branding for its low and mid-range scientific...
series being one of the most widely used scientific calculators in classrooms.
Casio
Casio
is a multinational electronic devices manufacturing company founded in 1946, with its headquarters in Shibuya, Tokyo, Japan. Casio is best known for its electronic products, such as calculators, audio equipment, PDAs, cameras, musical instruments, and watches...
and Sharp
Sharp Corporation
is a Japanese multinational corporation that designs and manufactures electronic products. Headquartered in Abeno-ku, Osaka, Japan, Sharp employs more than 55,580 people worldwide as of June 2011. The company was founded in September 1912 and takes its name from one of its founder's first...
have also been major players, with Casio's FX series (beginning with the Casio FX-1 in 1972) being a very common brand, used particularly in schools. Casio is also the #3 player in the graphing calculator
Graphing calculator
A graphing calculator typically refers to a class of handheld calculators that are capable of plotting graphs, solving simultaneous equations, and performing numerous other tasks with variables...
market, and was the first company to produce one (Casio fx-7000G
Casio fx-7000G
The Casio fx-7000G is notable for being the world's first graphing calculator.It came with 422 bytes of memory and it was possible to store up to ten programs in 10 program slots. 422 bytes is not much by today's standards, but with its heavily tokenised programming language, programs performing...
).
External links
- The Old Calculator Web Museum
- Programmable calculators – Specifications and descriptions of many programmable and scientific calculators
- The Museum of HP Calculators
- Datamath.org, a Texas Instruments handheld calculator museum
- Online Scientific Calculator
- Javascript calculator program with source code
- Soviet Calculators Collection
- Online Calculators