Graphing calculator

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A typical graphing calculator by Texas Instruments TI-84 Plus graphing.jpg
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.

Contents

History

Casio fx-7000G; The world's first graphing calculator Casio fx-7000G Box&Manual.JPG
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

Graphing calculators are sometimes used for gaming. TI83tris.JPG
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

TI-89 Titanium, capable of doing Symbolic Manipulation, Computer Algebra System (CAS) TI-biju.jpg
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

Related Research Articles

<span class="mw-page-title-main">TI-89 series</span> Series of graphing calculators

The TI-89 and the TI-89 Titanium are graphing calculators developed by Texas Instruments (TI). They are differentiated from most other TI graphing calculators by their computer algebra system, which allows symbolic manipulation of algebraic expressions—equations can be solved in terms of variables, whereas the TI-83/84 series can only give a numeric result.

A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "computer algebra" or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials.

In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression.

<span class="mw-page-title-main">TI-83 series</span> Series of graphing calculators produced by Texas Instruments

The TI-83 series is a series of graphing calculators manufactured by Texas Instruments.

<span class="mw-page-title-main">Scientific calculator</span> Calculator designed to calculate problems in science, engineering, and mathematics

A scientific calculator is an electronic calculator, either desktop or handheld, designed to perform calculations using basic and complex mathematical operations and functions. They have completely replaced slide rules and are used in both educational and professional settings.

<span class="mw-page-title-main">TI-84 Plus series</span> Series of graphing calculators produced by Texas Instruments

The TI-84 Plus is a graphing calculator made by Texas Instruments which was released in early 2004. There is no original TI-84, only the TI-84 Plus, the TI-84 Plus Silver Edition models, and the TI-84 Plus CE. The TI-84 Plus is an enhanced version of the TI-83 Plus. The key-by-key correspondence is relatively the same, but the TI-84 features improved hardware. The archive (ROM) is about 3 times as large, and the CPU is about 2.5 times as fast. A USB port and built-in clock functionality were also added. The USB port on the TI-84 Plus series is USB On-The-Go compliant, similar to the next generation TI-Nspire calculator, which supports connecting to USB based data collection devices and probes, and supports device to device transfers over USB rather than over the serial link port.

TI-BASIC is the official name of a BASIC-like language built into Texas Instruments (TI)'s graphing calculators. TI-BASIC is a language family of three different and incompatible versions, released on different products:

There are various ways in which calculators interpret keystrokes. These can be categorized into two main types:

<span class="mw-page-title-main">Casio fx-7000G</span> Graphing calculator by Casio

The Casio FX-7000G is a calculator which is widely known as being the world's first graphing calculator available to the public. It was introduced to the public and later manufactured between 1985 and c. 1988. Notable features are its ability to graph functions, and that it is programmable. The calculator offers 82 scientific functions and is capable of manual computation for basic arithmetic problems.

Programmable calculators are calculators that can automatically carry out a sequence of operations under control of a stored program. Most are Turing complete, and, as such, are theoretically general-purpose computers. However, their user interfaces and programming environments are specifically tailored to make performing small-scale numerical computations convenient, rather than general-purpose use.

<span class="mw-page-title-main">Casio ClassPad 300</span> Family of graphing calculators by Casio

The Casio ClassPad 300, ClassPad 330 and fx-CP400 are stylus based touch-screen graphing calculators. It comes with a collection of applications that support self-study, like 3D Graph, Geometry, eActivity, Spreadsheet, etc. A large 160x240 pixel LCD touch screen enables stylus-based operation. It resembles Casio's earlier Pocket Viewer line. HP and Texas Instruments attempted to release similar pen based calculators (the HP Xpander and PET Project, but both were cancelled before release to the market.

<span class="mw-page-title-main">Casio 9850 series</span> Series of graphing calculators by Casio

The Casio CFX-9850G series is a series of graphing calculators manufactured by Casio Computer Co., Ltd. from 1996 to 2008.

<span class="mw-page-title-main">TI-Nspire series</span> Series of graphing calculators

The TI-Nspire is a graphing calculator line made by Texas Instruments, with the first version released on 25 September 2007. The calculators feature a non-QWERTY keyboard and a different key-by-key layout than Texas Instruments's previous flagship calculators such as the TI-89 series.

Casio BASIC is a programming language used in the Casio calculators such as the ClassPad, PRIZM Series, fx-9860G Series, fx-5800P, Algebra FX and CFX graphing calculators. It is also known as "BasicLike" in some models.

<span class="mw-page-title-main">Xcas</span> Computer algebra system

Xcas is a user interface to Giac, which is an open source computer algebra system (CAS) for Windows, macOS and Linux among many other platforms. Xcas is written in C++. Giac can be used directly inside software written in C++.

The Casio fx-9860G is a series of graphing calculators manufactured by Casio, successor of the fx-9750G PLUS/CFX-9850 PLUS/CFX-9950 PLUS/CFX-9970 family of calculators. All of them are capable of being programmed by means of sophisticated languages and tools including assembly language, Basic variants, and ports of programming languages such as C, as well as hosting add-ins which are compiled on a computer and then downloaded to the calculator.

<span class="mw-page-title-main">Casio graphic calculators</span> Overview of the graphic calculators made by Casio

Graphic calculators made by Casio include the touchscreen ClassPad 300 as well as the models with traditional buttons which can be divided into two main generations listed below. Casio produced the world's first graphing calculator, the fx-7000G.

<span class="mw-page-title-main">HP Prime</span> Programmable graphing calculator

The HP Prime Graphing Calculator is a graphing calculator introduced by Hewlett-Packard in 2013 and manufactured by HP Inc. until the licensees Moravia Consulting spol. s r.o. and Royal Consumer Information Products, Inc. took over the continued development, manufacturing, distribution, marketing and support in 2022. It was designed with features resembling those of smartphones, such as a full-color touchscreen display and a user interface centered around different applications. It claims to be the world's smallest and thinnest CAS-enabled calculator currently available.

<span class="mw-page-title-main">Casio Algebra FX Series</span> Series of Casio graphing calculators

The Casio Algebra FX series was a line of graphing calculators manufactured by Casio Computer Co., Ltd from 1999 to 2003. They were the successor models to the CFX-9970G, the first Casio calculator with computer algebra system, or CAS, a program for symbolic manipulation of mathematical expressions. The calculators were discontinued and succeeded by the Casio ClassPad 300 in 2003.

References

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Further reading