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A typical graphing calculator by Texas Instruments

A graphing calculator (also graphics calculator or graphic display calculator) is a handheld computer that is capable of plotting graphs, solving simultaneous equations, and performing other tasks with variables. Most popular graphing calculators are programmable calculators, 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

Casio fx-7000G; The world's first graphing calculator

An early graphing calculator was designed in 1921 by electrical engineer Edith Clarke.[1][2][3] The calculator was used to solve problems with electrical power line transmission.[4]

Casio produced the first commercially available graphing calculator in 1985. Sharp produced its first graphing calculator in 1986, with Hewlett Packard following in 1988, and Texas Instruments in 1990.[citation needed]

Features

Computer algebra systems

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.[5] 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 thermometers, pH gauges, weather instruments, decibel and light meters, accelerometers, and other sensors and therefore function as data loggers, 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.[6]

Games and utilities

The game Tetris is being played on a TI-83 Plus.
Graphing calculators are sometimes used for 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. 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, 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.

Graphing calculators in education

This section needs to be updated. Please help update this article to reflect recent events or newly available information. (September 2018)
TI-89 Titanium, capable of doing Symbolic Manipulation, Computer Algebra System (CAS)

Programming

Most graphing calculators, as well as some non-graphing scientific calculators 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: Disp [A] . 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 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, 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, 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, Forth, and Lisp, and Command Script facilities which are similar in function to batch/shell programming and other 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 shells (e.g., bash, zsh), other shells (DOS/Windows 9x, OS/2, and Windows NT family shells as well as the related 4DOS, 4NT and 4OS2 as well as DCL), COBOL, C, Python, Tcl, Pascal, 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, 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-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 HP-48 type calculators 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.

See also

References

  1. ^ "Patent US1552113A". Retrieved 4 June 2021.
  2. ^ Kellner, Tomas (10 February 2017). "Mother of Invention: This Barrier-Busting Electrical Engineer Joined Edison, Tesla in National Inventors Hall of Fame - GE Reports". GE Reports. Archived from the original on 25 August 2018. Retrieved 22 November 2018.
  3. ^ "The Engineer Who Foreshadowed the Smart Grid--in 1921". 30 March 2016. Retrieved 4 June 2021.
  4. ^ "Pioneering Women in Computer Technology". The Ada Project. Archived from the original on 26 March 2018. Retrieved 22 November 2018.
  5. ^ "The Role of Computer Algebra Systems (CAS) in Math Teaching and the Common Core". University of Chicago Blogs. Archived from the original on 10 August 2014. Retrieved 25 June 2014.
  6. ^ "Texas Instruments Graphing Calculator Data Collection". Texas Instruments. Retrieved 29 October 2018.
  7. ^ "Periodic table app for the Ti-84". Texas Instruments. Retrieved 25 November 2019.
  8. ^ "General, Vocational and Diploma Qualifications Instructions for conducting examinations 1 September 2010 to 31 August 2011" (PDF). Archived from the original (PDF) on 12 August 2011. Retrieved 7 April 2011. General, Vocational and Diploma Qualifications Instructions for conducting examinations.
  9. ^ "Calculator use in the 2011 WACE examinations" (PDF). Government of Western Australia Curriculum Council and WACE. 2011. Archived from the original (PDF) on 20 March 2012.
  10. ^ 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.

Further reading