View source for Graphing calculator

{{Short description|Electronic calculator capable of plotting graphs}}
{{For|the software tool of the same name|NuCalc}}
{{More footnotes needed|date=July 2008}}
{{Use dmy dates|date=August 2020}}
{{original research|date=November 2024}}
[[Image:TI-84 Plus graphing.jpg|thumb|[[TI-84 Plus series|Texas Instruments TI-84 Plus]], the most successful graphing calculator in terms of sales]]
A '''graphing calculator''' (also '''graphics calculator''' or '''graphic display calculator''') is a [[handheld computer]] that is capable of plotting [[Graph of a function|graphs]], solving [[simultaneous equations]], and performing other tasks with [[variable (mathematics)|variables]]. Most popular graphing calculators are [[programmable calculator]]s, allowing the user to create customized programs, typically for scientific, engineering or education applications. They have large screens that display several lines of text and calculations.

== History ==
[[File:Casio fx-7000G Box&Manual.JPG|220px|thumb|[[Casio fx-7000G]]; the world's first graphing calculator]]
An early graphing calculator was designed in 1921 by electrical engineer [[Edith Clarke]].<ref>{{Cite web|url=https://patents.google.com/patent/US1552113A/en|access-date=2021-06-04|title=Patent US1552113A}}</ref><ref name=":10">{{Cite news|url=https://www.ge.com/reports/edith-clarke-mother-of-invention/|title=Mother of Invention: This Barrier-Busting Electrical Engineer Joined Edison, Tesla in National Inventors Hall of Fame - GE Reports|last=Kellner|first=Tomas|date=2017-02-10|work=GE Reports|access-date=2018-11-22|archive-url=https://web.archive.org/web/20180825185215/https://www.ge.com/reports/edith-clarke-mother-of-invention/|archive-date=25 August 2018}}</ref><ref>{{Cite web|url=https://blogs.scientificamerican.com/plugged-in/the-engineer-who-foreshadowed-the-smart-grid-in-1921/|title=The Engineer Who Foreshadowed the Smart Grid--in 1921|date=30 March 2016|access-date=2021-06-04}}</ref> The calculator was used to solve problems with electrical power line transmission.<ref name=":72">{{Cite web|url=https://www.women.cs.cmu.edu/ada/Resources/Women/|title=Pioneering Women in Computer Technology|website=The Ada Project|archive-url=https://web.archive.org/web/20180326031002/https://www.women.cs.cmu.edu/ada/Resources/Women/|archive-date=26 March 2018|access-date=22 November 2018}}</ref>

[[Casio]] produced the first commercially available graphing calculator in 1985. [[Sharp Corporation|Sharp]] produced its first graphing calculator in 1986, with [[Hewlett-Packard|Hewlett Packard]] following in 1988, and [[Texas Instruments]] in 1990.<ref>{{cite web |author1=Tribune Content Agency, LLC. |title=Evolution of the graphing calculator |url=https://www.nydailynews.com/2021/08/10/evolution-of-the-graphing-calculator/ |publisher=NY Daily News |date=August 10, 2021}}</ref>

== Features ==

=== Computer algebra systems ===
[[File:A graph GIF being captured from a TI-89 Titanium.gif|thumb|The Texas Instruments TI-89 Titanium graphing a sine type graph. (Generated from TI ScreenCapture software on TI Connect CE.)]]
Some graphing calculators have a [[computer algebra system]] (CAS), which means that they are capable of producing symbolic results. These calculators can manipulate algebraic expressions, performing operations such as factor, expand, and simplify. In addition, they can give answers in exact form without numerical approximations.<ref>{{cite web|url=https://blogs.uchicago.edu/uei/technology_in_education/the_role_of_computer_algebra_s.shtml|title=The Role of Computer Algebra Systems (CAS) in Math Teaching and the Common Core|website=University of Chicago Blogs|access-date=25 June 2014|archive-url=https://web.archive.org/web/20140810122830/https://blogs.uchicago.edu/uei/technology_in_education/the_role_of_computer_algebra_s.shtml|archive-date=10 August 2014|url-status=dead}}</ref> Calculators that have a computer algebra system are called symbolic or CAS calculators.

=== Laboratory usage ===
Many graphing calculators can be attached to devices like electronic [[thermometer]]s, [[pH]] gauges, weather instruments, [[decibel]] and [[light meter]]s, [[accelerometer]]s, and other sensors and therefore function as [[data logger]]s, as well as WiFi or other communication modules for monitoring, polling and interaction with the teacher. Student laboratory exercises with data from such devices enhances learning of math, especially statistics and mechanics.<ref>{{cite web |title=Texas Instruments Graphing Calculator Data Collection |url=https://education.ti.com/en/products?category=data-collection |website=[[Texas Instruments]] |access-date=29 October 2018}}</ref>

===Games and utilities===
[[File:Game Doom on TI-83 calculator.png|thumb|Graphing calculators are sometimes used for [[Mobile game#Calculator games|gaming]].]]
Since graphing calculators are typically user-programmable, they are also widely used for utilities and [[calculator gaming]], with a sizable body of user-created game software on most popular platforms.<ref name=":0">{{Cite web |last=Connatser |first=Matthew |date=26 May 2024 |title=Bored students can now enjoy Sonic 2 on TI-84 Plus CE calculators, thanks to port |url=https://www.theregister.com/2024/05/26/sonic_texas_instruments_calculator/}}</ref> The ability to create games and utilities has spurred the creation of calculator application sites (e.g., [[Cemetech]]) which, in some cases, may offer programs created using calculators' [[assembly language]]. Even though handheld gaming devices fall in a similar price range, graphing calculators offer superior math programming capability for math based games. However ,due to poor display resolution, slow processor speed and lack of a dedicated keyboard, they are mostly preferred only by high school students.<ref name=":0" />

However, for developers and advanced users like researchers, analysts and gamers, third-party software development involving firmware modifications, whether for powerful gaming or exploiting capabilities beyond the published data sheet and programming language, is a contentious issue with manufacturers and education authorities as it might incite unfair calculator use during standardized high school and college tests where these devices are targeted.

== Software Graphing Calculators ==
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[[File:Desmos グラフ計算機.png|thumb|right|alt=The Desmos graphing calculator in use|The [[Desmos]] graphing calculator in use]]
There are many graphing calculators that do not require dedicated hardware, but run on a device in a web browser or as an app. Notable graphing calculators of this type include [[Desmos]] and [[GeoGebra]].<ref>{{Cite web |title=Desmos {{!}} About Us |url=https://www.desmos.com/about |access-date=2025-02-06 |website=www.desmos.com}}</ref><ref>{{Cite web |title=GeoGebra - the world's favorite, free math tools used by over 100 million students and teachers |url=https://www.geogebra.org |access-date=2025-02-06 |website=GeoGebra |language=en}}</ref>

== Graphing calculators in education ==
{{Update|section|date=September 2018}}
[[File:HP Prime Graphing Calculator.jpg|thumb|upright|[[HP Prime]], a modern graphing calculator capable of doing Symbolic Manipulation, Computer Algebra System (CAS)]]
* '''North America''' – high school mathematics teachers allow and even encourage their students to use graphing calculators in class. In some cases (especially in [[calculus]] courses) they are ''required''.<ref>{{cite journal |last1=A. Banks |first1=Sarah |title=A Historical Analysis Of Attitudes Towards The Use Of Calculators In Junior High And High Schools In The United States Since 1975 |date=28 June 2011 |pages=107 |url=https://files.eric.ed.gov/fulltext/ED525547.pdf |publisher=Cedarville University}}</ref><ref>{{cite web |title=Living in a Mathematical World: The Case for Calculators in the Mathematics Classroom |url=https://elective.collegeboard.org/calculators-classroom-archive-college-board-review |publisher=College Board |date=16 May 2023 |quote=Years ago, we barred calculator use from some classes and from parts of some tests. We no longer do so.}}</ref>
* '''[[College Board]] of the United States''' – permits the use of most graphing or [[Computer algebra system|CAS]] calculators that do not have a [[QWERTY]]-style keyboard for parts of its [[Advanced Placement|AP]] and [[SAT]] exams,<ref>{{Cite web |title=AP Exams Calculator Policy – AP Students {{!}} College Board |url=https://apstudents.collegeboard.org/exam-policies-guidelines/calculator-policies |access-date=2025-02-06 |website=apstudents.collegeboard.org}}</ref> but the [[ACT (test)|ACT]] exam and [[International Baccalaureate|IB]] schools do not permit the use of calculators with computer algebra systems.<ref>{{cite web |title=AP Exams Calculator Policy |url=https://apstudents.collegeboard.org/exam-policies-guidelines/calculator-policies |publisher=College Board}}</ref><ref>{{cite web |title=ACT Calculator Policy |url=https://www.act.org/content/act/en/products-and-services/the-act/test-day/calculator-policy.html |publisher=ACT Education Corp.}}</ref><ref>{{cite web |title=Use of calculators in examinations 2019 – version 1.0 |url=https://www.ibo.org/contentassets/e3e2d5a7b79e48f7a47f8973e7873a10/use-of-calculators-in-examinations-2019_en.pdf |publisher=International Baccalaureate}}</ref>
* '''United Kingdom''' – a graphing calculator is allowed for [[A-level]] maths courses, however they are not required and the exams are designed to be broadly 'calculator neutral'. Similarly, at [[GCSE]], all current courses include one paper where no calculator of any kind can be used, but students are permitted to use graphical calculators for other papers. The use of graphical calculators at [[GCSE]] is not widespread with cost being a likely factor. The use of [[Computer algebra system|CAS]] is not allowed for either [[A-level]] or [[GCSE]]. Similarly, calculators with QWERTY keyboard layout are also not allowed as well.<ref>{{cite web |title=General, Vocational and Diploma Qualifications Instructions for conducting examinations 1 September 2010 to 31 August 2011 |url=http://jcq.org.uk/attachments/published/898/17.%20ICE%2010-11.pdf |access-date=2011-04-07 |url-status=dead |archive-url=https://web.archive.org/web/20110812224928/http://www.jcq.org.uk/attachments/published/898/17.%20ICE%2010-11.pdf |archive-date=12 August 2011}} General, Vocational and Diploma Qualifications Instructions for conducting examinations.</ref><ref>{{cite web |title=Regulations regarding the use of calculators |url=https://www.britishcouncil.jo/sites/default/files/use_of_calculators_0.pdf |publisher=British Council}}</ref> The Scottish SQA allows the use of graphic calculators in maths exams (excluding paper 1, which is exclusively non-calculator), however these should either be checked before exams by invigilators or handed out by the exam centre, as certain functions / information is not allowed to be stored on a calculator in the exam.<ref>{{cite web |title=Exam Handbook |url=https://www.sqa.org.uk/sqa/pdf?full=yes |publisher=SQA}}</ref>
* '''Finland and Slovenia''' – and certain other countries, it is forbidden to use calculators with symbolic calculation ([[Computer algebra system|CAS]]) or 3D graphics features in the [[matriculation|matriculation exam]]. This changed in the case of Finland, however, as symbolic calculators were allowed from spring 2012 onwards.
* '''Norway''' – calculators with [[Wireless|wireless communication]] capabilities, such as [[Infrared|IR]] links, have been banned at some technical universities.
* '''Australia''' – policies vary from state to state.
** '''Victoria''' – the [[Victorian Certificate of Education|VCE]] specifies approved calculators as applicable for its mathematics exams. For [[Further Mathematics]] an approved graphics calculator (for example [[TI-83 series|TI-83]]/[[TI-84 Plus series|84]], [[Casio 9860 series|Casio 9860]], [[HP 39/40 series|HP-39G]]) or CAS (for example [[TI-89 series|TI-89]], [[Casio ClassPad 300|the ClassPad series]], [[HP 39/40 series#HP 40G|HP-40G]]) can be used. Mathematical Methods (CAS) has a technology free examination consisting of short answer and some extended answer questions. It then also has a technology-active examination consisting of extended response and multiple choice questions: a CAS is the assumed technology for Mathematical Methods (CAS). Specialist Mathematics has a technology free examination and a technology-active examination where either an approved graphics calculator or CAS may be used. Calculator memories are not required to be cleared. In subjects like Physics and Chemistry, students are only allowed a standard scientific calculator.
** '''Western Australia''' – all [[tertiary entrance examination]]s in Mathematics involve a calculator section which assume the student has a graphics calculator; CAS enabled calculators are also permitted. In subjects such as Physics, Chemistry and Accounting only non-programmable calculators are permitted.<ref>{{Cite web |year=2011 |title=Calculator use in the 2011 WACE examinations |url=http://www.curriculum.wa.edu.au/internet/_Documents/Policy/Calculators_use_in_the_WACE_examinations_2010_pdf.pdf |url-status=dead |archive-url=https://web.archive.org/web/20120320074615/http://www.curriculum.wa.edu.au/internet/_Documents/Policy/Calculators_use_in_the_WACE_examinations_2010_pdf.pdf |archive-date=2012-03-20 |publisher=[[Curriculum Council of Western Australia|Government of Western Australia Curriculum Council]] and [[Western Australian Certificate of Education|WACE]]}}</ref>{{Update inline|date=March 2022|reason=Cited document is more than 10 years old, and examination requirements may have since been updated}}
** '''New South Wales''' – graphics calculators are allowed for the General Mathematics [[Higher School Certificate (New South Wales)|Higher School Certificate]] exam, but disallowed in the higher level Mathematics courses.
* '''China''' - Only the Shanghai College Entrance Examination allows the use of calculators without graphing and memory. Except for Shanghai, the other provinces and cities do not allow the use of calculators, so calculators in general are banned in primary and secondary education in most parts of China.<ref>{{cite web |title=Similarities and Differences in Teens' Education Between the West and China |url=https://www.echineselearning.com/blog/comparing-teens-education-between-the-west-and-china|date=12 April 2022}}</ref>
* '''India''' - Calculators are prohibited in primary and secondary education. (ICSE allows the Casio fx-82MS, or equivalent scientific calculator in 12th boards). University degree and diploma courses have their own rules on use of permitted models of calculators in exams. Casio's '''fx-991MS, fx-991ES, fx-100MS, and fx-350MS''' scientific calculators are used in many university degree and diploma courses. These calculators are also permitted for university exams as they are non-programmable since programmable calculators are not allowed for university exams. During the online GATE examinations and other competitive examinations, candidates are provided with a virtual scientific calculator as physical calculators of any type are not permitted.
* '''New Zealand''' – Calculators identified as having high-level algebraic manipulation capability are prohibited in [[National Certificate of Educational Achievement|NCEA]] examinations unless specifically allowed by a standard or subject prescription. This includes calculators such as the [[TI-89]] series [https://web.archive.org/web/20070920211508/http://www.nzqa.govt.nz/ncea/acrp/secondary/4/47.html].
* '''Turkey''' – any type of calculator whatsoever is prohibited in all primary and high schools. <ref>{{Cite web |title=Turkish School vs. American School |url=https://www.fivestarjournal.com/news/xq0y4ekyttmbpt9r2sdajw0h4xb6fn |access-date=2024-11-11 |website=Five Star Journal |language=en-US}}</ref>
* '''Singapore''' – graphing calculators are used in junior colleges; it is required in the Mathematics paper of the GCE 'A' Levels, and most schools use the [[TI-84 Plus]] or [[TI-84 Plus Silver Edition]].
* '''Netherlands''' – high school students are obliged to use graphing calculators during tests and exams in their final three years. Most students use the [[TI-83 Plus]] or [[TI-84 Plus]], but other graphing calculators are allowed, including the [[Casio 9860 series|Casio fx-9860G]] and [[HP-39G]]. Graphing calculators are almost always allowed to be used during tests instead of normal calculators, which sometimes results in cheat sheets being made on forehand and exchanged before the test starts using link cables.
* '''Israel''' –  Graphing calculators are forbidden to use in the [[Bagrut]] (equivalent to the British A-Levels) math exam, in addition to programmable calculators.<ref>http://meyda.education.gov.il/sheeloney_bagrut/2012/1/HEB/35807.PDF The instructions for conducting the 5-point exam Bagrut in math, 2012 in Hebrew.</ref> University degree and diploma courses have their own rules on use and permitted models of calculators in exams.

== Programming ==
[[File:TI-84 Plus IO.jpeg|thumb|right|Typical ports on a graphing calculator. These contain a 2.5&nbsp;mm I/O port for connecting to other calculators and a Mini USB port for connecting to a PC.]]
Most graphing calculators, as well as some non-graphing [[scientific calculator]]s and programmer's calculators can be programmed to automate complex and frequently used series of calculations and those inaccessible from the keyboard.

The actual programming can often be done on a computer then later uploaded to the calculators.  The most common tools for this include the PC link cable and software for the given calculator, configurable text editors or hex editors, and specialized programming tools such as the below-mentioned implementation of various languages on the computer side.

Earlier calculators stored programs on magnetic cards and the like; increased memory capacity has made storage on the calculator the most common implementation. Some of the newer machines can also use memory cards.

Many graphing and scientific calculators will tokenize the program text, replacing textual programming elements with short numerical tokens. For example, take this line of TI-BASIC code:
<code>Disp [A]</code>
. In a conventional programming language, this line of code would be nine characters long (eight not including a newline character). For a system as slow as a graphing calculator, this is too inefficient for an [[interpreted language]]. To increase program speed and coding efficiency, the above line of code would be only three characters. "Disp_" as a single character, "[A]" as a single character, and a newline character. This normally means that single byte chars will query the standard [[ASCII]] chart while two byte chars (the Disp_ for example) will build a graphical string of single byte characters but retain the two byte character in the program memory. Many graphical calculators work much like computers and use versions of 7-bit, 8-bit or 9-bit ASCII-derived character sets or even [[UTF-8]] and [[Unicode]]. Many of them have a tool similar to the [[Character Map (Windows)|character map]] on Windows.

They also have [[BASIC]] like functions such as chr$, chr, char, asc, and so on, which sometimes may be more Pascal or C like. One example may be use of ''ord'', as in [[Pascal (programming language)|Pascal]], instead of the ''asc'' of many Basic variants, to return the code of a character, i.e. the position of the character in the collating sequence of the machine.

A cable and/or [[IrDA]] transceiver connecting the calculator to a computer make the process easier and expands other possibilities such as on-board spreadsheet, database, graphics, and word processing programs. The second option is being able to code the programs on board the calculator itself.  This option is facilitated by the inclusion of full-screen text editors and other programming tools in the default feature set of the calculator or as optional items.  Some calculators have [[QWERTY]] keyboards and others can be attached to an external keyboard which can be close to the size of a regular 102-key computer keyboard.  Programming is a major use for the software and cables used to connect calculators to computers.

The most common programming languages used for calculators are similar to keystroke-macro languages and variants of [[BASIC]]. The latter can have a large feature set—approaching that of BASIC as found in computers—including character and string manipulation, advanced conditional and branching statements, sound, graphics, and more including, of course, the huge spectrum of mathematical, string, bit-manipulation, number base, I/O, and graphics functions built into the machine.

Languages for programming calculators fall into all of the main groups, i.e. machine code, low-level, mid-level, high-level languages for systems and application programming, scripting, macro, and glue languages, procedural, functional, imperative &. object-oriented programming can be achieved in some cases.

Most calculators capable to being connected to a computer can be programmed in assembly language and machine code, although on some calculators this is only possible through using exploits. The most common assembly and machine languages are for [[TMS9900]], [[SuperH|SH-3]], [[Zilog Z80]], and various [[Motorola]] chips (e.g. a modified [[68000]]) which serve as the main processors of the machines although many (not all) are modified to some extent from their use elsewhere. Some manufacturers do not document and even mildly discourage the assembly language programming of their machines because they must be programmed in this way by putting together the program on the PC and then forcing it into the calculator by various improvised methods.

Other on-board programming languages include purpose-made languages, variants of [[Eiffel (programming language)|Eiffel]], [[Forth (programming language)|Forth]], and [[Lisp (programming language)|Lisp]], and Command Script facilities which are similar in function to batch/shell programming and other [[Scripting language#Glue languages|glue languages]] on computers but generally not as full featured.  Ports of other languages like [[BBC BASIC]] and development of on-board interpreters for [[Fortran]], [[REXX]], [[AWK]], [[Perl]], [[Unix shell]]s (e.g., [[bash (Unix shell)|bash]], [[Z shell|zsh]]), other shells ([[DOS]]/[[Windows 9x]], [[OS/2]], and [[Windows NT]] family shells as well as the related [[4DOS]], [[Take Command Console|4NT]] and [[4OS2]] as well as [[DIGITAL Command Language|DCL]]), [[COBOL]], [[C (programming language)|C]], [[Python (programming language)|Python]], [[Tcl]], [[Pascal (programming language)|Pascal]], [[Delphi (programming language)|Delphi]], [[ALGOL]], and other languages are at various levels of development.

Some calculators, especially those with other PDA-like functions have actual operating systems including the TI proprietary OS for its more recent machines, [[DOS]], [[Windows CE]], and rarely [[Windows NT 4.0 Embedded]] et seq, and [[Linux]]. Experiments with the [[TI-89]], [[TI-92 series|TI-92]], [[TI-92 Plus]] and [[Voyage 200]] machines show the possibility of installing some variants of other systems such as a chopped-down variant of [[CP/M#The 16-bit world|CP/M-68K]], an operating system which has been used for portable devices in the past.

Tools which allow for programming the calculators in C/C++ and possibly Fortran and assembly language are used on the computer side, such as [[HPGCC]], TIGCC and others. Flash memory is another means of conveyance of information to and from the calculator.

The on-board BASIC variants in TI graphing calculators and the languages available on the [[HP-48 series]] can be used for rapid prototyping by developers, professors, and students, often when a computer is not close at hand.

Most graphing calculators have on-board spreadsheets which usually integrate with Microsoft Excel on the computer side.  At this time, spreadsheets with macro and other automation facilities on the calculator side are not on the market. In some cases, the list, matrix, and data grid facilities can be combined with the native programming language of the calculator to have the effect of a macro and scripting enabled spreadsheet.

== Gallery == 
<gallery widths="200px" heights="140px">
File:Casio fx-7000GA.jpg|Casio fx-7000GA, {{Circa|1987}}, an improved version of the fx-7000G 
File:HP-28S calculator, open, power off (24687429911).jpg|HP28S, c. 1989, the first graphing calculator made by [[Hewlett-Packard]]
File:TI-81 Calculator on Graph Screen.jpg|TI-81, c. 1990, the first graphing calculator made by [[Texas Instruments]]
File:HP 48SX front, power on, displaying square root of 88, on white background (27465191295).jpg|HP48 Series, c. 1992, the first graphing calculator by HP to use Reverse Polish Notation (RPN) and also SD card expansion 
File:TI-92, power on, Calc menu open, on white background (25028570574).jpg|TI-92, c. 1996, the first graphing calculator in a PDA form factor, the first graphing calculator to have Computer Algebra System (CAS) and the first graphing calculator to have 3D graphing capability
File:Texas Instruments TI-83, front, power off, on blue background (35579978055).jpg|TI-83, c. 1996, one of the most commercially successful graphing calculators and a forebearer to the more successful TI-84 and TI-84 Plus
File:CasioClassPad300.JPG|Casio Classpad 300, c. 2003, the first graphing calculator with a touchscreen display 
File:Casio GTR fx-CG 20 — Sven Volkens (cropped).jpg|Casio fx-CG 20, c. 2011, the first graphing calculator with a colour display 
</gallery>

== See also ==
* [[Personal digital assistant]]
* [[:Category:Graphing calculators]]
* [[:Category:Plotting software]]
* [[Scientific calculator]]

== References ==
{{reflist}}

== Further reading ==
{{Commonscat|Graphing calculators}}
* Dick, Thomas P. (1996). Much More than a Toy. Graphing Calculators in Secondary school Calculus. In P. Gómez and B. Waits (Eds.), Roles of Calculators in the Classroom pp 31–46). Una Empresa Docente.
* Ellington, A. J. (2003). A meta-analysis of the effects of calculators on students' achievement and attitude levels in precollege mathematics classes. Journal for Research in Mathematics Education. 34(5), 433–463.
* Heller, J. L., Curtis, D. A., Jaffe, R., & Verboncoeur, C. J. (2005). Impact of handheld graphing calculator use on student achievement in algebra 1: Heller Research Associates.
* Khoju, M., Jaciw, A., & Miller, G. I. (2005). Effectiveness of graphing calculators in K-12 mathematics achievement: A systematic review. Palo Alto, CA: Empirical Education, Inc.
* National Center for Education Statistics. (2001). The nation's report card: Mathematics 2000. (No. NCES 2001-571). Washington DC: U.S. Department of Education.

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[[Category:Graphing calculators| ]]
[[Category:Computer-related introductions in 1985]]
[[Category:Japanese inventions]]
[[Category:Programmable calculators]]
[[Category:20th-century inventions]]