Interactive geometry software (IGS) or dynamic geometry environments (DGEs) are
computer programs which allow one to create and then manipulate
geometric constructions, primarily in
plane geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the ''Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms ...
. In most IGS, one starts construction by putting a few points and using them to define new objects such as
lines,
circle
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is con ...
s or other points. After some construction is done, one can move the points one started with and see how the construction changes.
History
The earliest IGS was the Geometric Supposer, which was developed in the early 1980s. This was soon followed by Cabri in 1986 and The Geometer's Sketchpad.
Comparison
There are three main types of computer environments for studying school geometry: supposers, dynamic geometry environments (DGEs) and
Logo-based programs. Most are DGEs: software that allows the user to manipulate ("drag") the geometric object into different shapes or positions. The main example of a supposer is the Geometric Supposer, which does not have draggable objects, but allows students to study pre-defined shapes. Nearly all of the following programs are DGEs. For a related, comparative physical example of these algorithms, see
Lenart Sphere Lenart may refer to:
* Municipality of Lenart, Slovenia
* Lenart v Slovenskih Goricah, the seat of the Municipality of Lenart, Slovenia
* Lenart Regional Gifted Center, United States, school
* Lénárt sphere, an educational model for spherical ...
.
License and platform
The following table provides a first comparison of the different software according to their license and platform.
3D Software
General features
The following table provides a more detailed comparison :
Macros
Features related to macro constructions: (TODO)
Loci
Loci features related to IGS: (TODO)
Proof
We detail here the proof related features. (TODO)
Measurements and calculation
Measurement and calculation features related to IGS: (TODO)
Graphics export formats
Object attributes
2D programs
C.a.R.
C.a.R.
C.a.R.– Compass and Ruler (also known as Z.u.L., which stands for the German "Zirkel und Lineal") — is a free and open source interactive geometry app that can do geometrical constructions in Euclidean and non-Euclidean geometry.
The softwar ...
is a free
GPL analog of The Geometer's Sketchpad (GSP), written in
Java.
Cabri
Cabri
Cabri was developed by the French school of mathematics education in Grenoble (Laborde, 1993)
CaRMetal
CaRMetal
CaRMetal is an interactive geometry program which inherited the C.a.R. engine. The software has been created by Eric Hakenholz, in Java. CaRMetal is free, under GNU GPL license. It keeps an amount of functionality of C.a.R. but uses a different g ...
is a free
GPL software written in
Java. Derived from C.a.R., it provides a different user interface.
Cinderella
Cinderella
"Cinderella",; french: link=no, Cendrillon; german: link=no, Aschenputtel) or "The Little Glass Slipper", is a folk tale with thousands of variants throughout the world.Dundes, Alan. Cinderella, a Casebook. Madison, Wis: University of Wisconsi ...
, written in
Java, is very different from The Geometer's Sketchpad. The later version Cinderella.2 also includes a physics simulation engine and a scripting language. Also, it now supports macros, line segments, calculations, arbitrary functions, plots, etc. Full documentation is available online.
Dr Genius
Dr Genius was an attempt to merge
Dr. Geo and the
Genius calculator.
Dr. Geo
Dr. Geo is a GPL interactive software intended for younger students (7-15). The later version, Dr. Geo II, is a complete rewrite of Dr. Geo, for the
Squeak/
Smalltalk
Smalltalk is an object-oriented, dynamically typed reflective programming language. It was designed and created in part for educational use, specifically for constructionist learning, at the Learning Research Group (LRG) of Xerox PARC by Alan K ...
environment.
GCLC
GCLC is a dynamic geometry tool for visualizing and teaching geometry, and for producing mathematical illustrations. In GCLC, figures are described rather than drawn. This approach stresses the fact that geometrical constructions are abstract, formal procedures and not figures. A concrete figure can be generated on the basis of the abstract description. There are several output formats, including
LaTeX, LaTeX/PStricks, LaTeX/Tikz,
SVG
Scalable Vector Graphics (SVG) is an XML-based vector image format for defining two-dimensional graphics, having support for interactivity and animation. The SVG specification is an open standard developed by the World Wide Web Consortium s ...
and
PostScript
PostScript (PS) is a page description language in the electronic publishing and desktop publishing realm. It is a dynamically typed, concatenative programming language. It was created at Adobe Systems by John Warnock, Charles Geschke, Doug B ...
. There is a built-in geometry theorem prover (based on the area method). GCLC is available for
Windows and
Linux. WinGCLC is a Windows version of GCLC with a graphical interface that provides a range of additional functionalities. GCLC is open source software (licence CC BY-ND).
GeoGebra
GeoGebra
GeoGebra (a portmanteau of ''geometry'' and ''algebra'') is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level. GeoGebra is ...
is software that combines geometry, algebra and calculus for mathematics education in schools and universities. It is available free of charge for non-commercial users.
* License: open source under
GPL license
The GNU General Public License (GNU GPL or simply GPL) is a series of widely used free software licenses that guarantee end users the four freedoms to run, study, share, and modify the software. The license was the first copyleft for general us ...
(free of charge)
* Languages: 55
* Geometry: points, lines, all conic sections, vectors, parametric curves, locus lines
* Algebra: direct input of inequalities, implicit polynomials, linear and quadratic equations; calculations with numbers, points and vectors
* Calculus: direct input of functions (including piecewise-defined); intersections and roots of functions; symbolic derivatives and integrals (built-in CAS); sliders as parameters
* Parametric Graphs: Yes
* Implicit Polynomials: Yes
* Web Export: all constructions exportable as web pages as a
Java applet
Java applets were small applications written in the Java programming language, or another programming language that compiles to Java bytecode, and delivered to users in the form of Java bytecode. The user launched the Java applet from a ...
* Macros: usable both as tools with the mouse and as commands in the input field
* Animation: Yes
* Spreadsheet: Yes, the cells can contain any GeoGebra object (numbers, points, functions etc.)
* Dynamic text: Yes (including LaTeX)
* Platforms: Mac OS, Unix/Linux, Windows (any platform that supports Java 1.5 or later)
* Continuity: uses a heuristic 'near-to-approach' to avoid jumping objects
GeoKone.NET
GeoKone.NET is an interactive recursive natural geometry (or "sacred geometry") generator that runs in a web browser. GeoKone allows the user to create geometric figures using naturalistic rules of recursive copying, such as the
Golden ratio.
Geolog
Geolog is a logic programming language for finitary geometric logic.
Geometry Expressions
Geometry Expressions Does symbolic geometry. It uses real symbolic inputs and returns real and symbolic outputs. It emphasises use with a
Computer Algebra System
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 d ...
(CAS), as well as exporting and sharing via interactive
HTML5,
Lua, and
OS X
macOS (; previously OS X and originally Mac OS X) is a Unix operating system developed and marketed by Apple Inc. since 2001. It is the primary operating system for Apple's Mac computers. Within the market of desktop and lap ...
dashboard widget apps.
The Geometer's Sketchpad
The Geometer's Sketchpad
The Geometer's Sketchpad is a commercial interactive geometry software program for exploring Euclidean geometry, algebra, calculus, and other areas of mathematics. It was created as part of the NSF-funded Visual Geometry Project led by Eugene Kl ...
(GSP)
* Deterministic
* Languages: English, Spanish, Danish, Russian, Korean, Thai, Traditional and Simplified Chinese, French, Lithuanian (current version); others (older versions)
* Macros: Yes ("custom tools" and "scripts")
* Java-applet: Yes
* Animation: Yes
* Locus: Yes, including point on locus
* Assignments: No
* Measurement/Calculations: Yes
* Platform: Windows, Mac OS, TI-92+, works under
Wine
* Proofs: No
The Geometric Supposer
The Geometric Supposer
Géoplan-Géospace
Geonext
Geonext was developed by the
University of Bayreuth
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the ...
until 2007 and is completely implemented in Java. Its final version was 1.74.
GeoProof
GeoProof is a free
GPL dynamic geometry software, written in
OCaml
OCaml ( , formerly Objective Caml) is a general-purpose, multi-paradigm programming language which extends the Caml dialect of ML with object-oriented features. OCaml was created in 1996 by Xavier Leroy, Jérôme Vouillon, Damien Doligez, Di ...
.
GEUP
GEUP
GEUP is a commercial interactive geometry software program, similar to Cabri Geometry. Originally using the Spanish language, it was programmed by Ramón
Alvarez Galván. Recent versions include support for three-dimensional geometry
In mat ...
is a more calculus-oriented analog of The Geometer's Sketchpad.
*Deterministic
*Languages: English, French, German, Italian, Portuguese, Spanish
*Macros: Yes
*Java-applet: No
* Animation: Yes
* Locus: Yes, including point on locus
* Assignments: No
* Measurement/Calculations: Yes
* Platform: Windows
* Proofs: No
GRACE
GRACE (The Graphical Ruler And Compass Editor) is an analog of The Geometer's Sketchpad (GSP), written in
Java.
Jeometry
Jeometry is a dynamic geometry applet.
Kig
Kig is a free (
GPL) analog of The Geometer's Sketchpad (GSP) for
KDE
KDE is an international free software community that develops free and open-source software. As a central development hub, it provides tools and resources that allow collaborative work on this kind of software. Well-known products include the ...
, but more calculus-oriented. It is a part of the
KDE Edutainment Project.
KmPlot
KmPlot
KmPlot is a mathematical function plotter for the KDE Desktop. It has a powerful built-in parser. The graphs can be colorized and the view is scalable, so that you are able to zoom to the level you need. Users can plot different functions simult ...
is a mathematical function plotter released under the free
GPL license
The GNU General Public License (GNU GPL or simply GPL) is a series of widely used free software licenses that guarantee end users the four freedoms to run, study, share, and modify the software. The license was the first copyleft for general us ...
. Includes a powerful parser and precision printing in correct scale. Simultaneously plot multiple functions and combine function terms to build new functions. Supports functions with parameters and functions in polar coordinates. Several grid modes are available. Features include:
* powerful mathematical parser
* precise metric printing
* different plot types (functions, parametric, polar)
* highly configurable visual settings (plot line, axes, grid)
* export to bitmap format (
BMP and
PNG) and to
Scalable Vector Graphics (SVG)
* save/load complete session in readable
XML
Extensible Markup Language (XML) is a markup language and file format for storing, transmitting, and reconstructing arbitrary data. It defines a set of rules for encoding documents in a format that is both human-readable and machine-readable. T ...
format
* trace mode: cross-hair following plot, coordinates shown in the status bar
* zooming support
* ability to draw the 1st and 2nd derivative and the integral of a plot function
* support user-defined constants and parameter values
* various tools for plot functions: find minimum/maximum point, get y-value and draw the area between the function and the y-axis
KSEG
KSEG is a free (
GPL) analog of The Geometer's Sketchpad (GSP) with some unique features. This software can handle heavy, complex constructions in Euclidean geometry.
*Deterministic
*Languages: Dutch, English, French, Chinese, German, Hungarian, Italian, Japanese, Norwegian Bokmål, Portuguese, Russian, Spanish, Turkish, Welsh
*Macros: Yes. Editable and with support for recursion
*Java-applet: No
* Animation: No
* Locus: Yes, but no direct way to place a point on a locus.
* Assignments: No
* Measurement/Calculations: Yes (the calculator is a bit strange)
* Platform: Unix/Linux, Windows, Mac OS (any platform that supports
Qt)
* Proofs: No
* Extra: Editable
Live Geometry
Live Geometry is a free
CodePlex
CodePlex was a forge website by Microsoft. While it was active, it allowed shared development of open-source software.
Its features included wiki pages, source control based on Mercurial, TFVC, Subversion or Git, discussion forums, issue tra ...
project that lets you create interactive ruler and compass constructions and experiment with them. It is written in
Silverlight
Microsoft Silverlight is a discontinued application framework designed for writing and running rich web applications, similar to Adobe's runtime, Adobe Flash. A plugin for Silverlight is still available for a very small number of browsers. Whi ...
4 and C# 4.0 (Visual Studio 2010). The core engine is a flexible and extensible framework that allows easy addition of new figure types and features. The project has two front-ends: WPF and Silverlight, which both share the common ''DynamicGeometry'' library.
TracenPoche
TracenPoche
''TracenPoche'' (TeP) is a free interactive geometry software, written in Adobe Flash language. It is very light weight.
Features
It is widely used in French secondary schools in the framework of the :fr:MathenPoche exerciser suite developed b ...
is a completely
Adobe Flash
Adobe Flash (formerly Macromedia Flash and FutureSplash) is a multimedia Computing platform, software platform used for production of Flash animation, animations, rich web applications, application software, desktop applications, mobile apps, mo ...
program. It is available in English, Spanish, and French.
3D programs
Cabri 3D
Cabri Geometry
Cabri Geometry is a commercial interactive geometry software produced by the French company Cabrilog for teaching and learning geometry and trigonometry.. It was designed with ease-of-use in mind. The program allows the user to animate geometric ...
Archimedes Geo3D
Archimedes Geo3D
Euler 3D
Euler (software)
Euler 3D is a program that allows you to create and manipulate your own polyhedrons. It has a number of facilities: transformations, animations, creating duals, import/export VRML, etc.
Free registration required.
GeoGebra
GeoGebra
GeoGebra (a portmanteau of ''geometry'' and ''algebra'') is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level. GeoGebra is ...
, includes a 3D mode since version 5.0
Geomview
Geomview
The Geometry Center was a mathematics research and education center at the University of Minnesota. It was established by the National Science Foundation in the late 1980s and closed in 1998. The focus of the center's work was the use of comp ...
Continuity versus determinism
All these programs can be divided into two category: deterministic and continuous.
GeoGebra can be deterministic or continuous (one can change it in preferences).
All constructions in the deterministic programs (GSP, Cabri, Kseg and most of others) are completely determined by the given points but the result of some constructions can jump or behave unexpectedly when a given point is moved.
On the contrary, some constructions in continuous programs (so far only Cinderella and GeoGebra), depend on the number of hidden parameters and in such a way that moving a given point produces a continuous motion of the construction, as a result, if the point is moved back to the original position the result of construction might be different.
Here is a test to check whether a particular program is continuous:
Construct the
orthocenter of triangle and three midpoints (say ''A', B' C' '' ) between vertices and orthocenter.
Construct a
circumcircle
In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius.
Not every polyg ...
of ''A'B'C' ''.
This is the
nine-point circle, it intersects each side of the original triangle at two points: the base of altitude and midpoint. Construct an intersection of one side with the circle at midpoint now move opposite vertex of the original triangle, if the constructed point does not move when base of altitude moves through it that probably means that your program is continuous.
Although it is possible to make a deterministic program which behaves continuously in this and similar simple examples, in general it can be proved that no program can be continuous and deterministic at the same time.
[Kortenkamp, Ulrich (1999): Foundations of Dynamic Geometry, Dissertation, ETH Zurich 1999. Available online at http://kortenkamps.net/papers/1999/diss.pdf]
See also
*
Mathematical software Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data.
Evolution of mathematical software
Numerical analysis and symbolic computation had been in most important place of the subject, but other ...
*
Constructive solid geometry
Constructive solid geometry (CSG; formerly called computational binary solid geometry) is a technique used in solid modeling. Constructive solid geometry allows a modeler to create a complex surface or object by using Boolean operators to combin ...
*
Lénárt sphere
A Lénárt sphere is a educational manipulative and writing surface for exploring spherical geometry, invented by Hungarian István Lénárt as a modern replacement for a spherical blackboard. It can be used for visualizing the geometry of poi ...
References
External links
A Comparison of Geometry Software for the Classroom
{{DEFAULTSORT:Interactive Geometry Software
*
Lists of software
Geometry education