List of interactive geometry software

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. In most IGS, one starts construction by putting a few points and using them to define new objects such as lines, circles 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.^{[1]} 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 Logobased programs.^{[2]} 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 predefined shapes. Nearly all of the following programs are DGEs.
License and platform
The following table provides a first comparison of the different software according to their licence and platform.
2D Software
Software Cost (USD) Licence Platforms Apollonius 3.99 US$ Proprietary iPhone/iPod Touch Baghera ? ? Windows/? Cabri Geometry ? Proprietary Windows, Mac OS X CabriEuclide ? ? Windows/? C.a.R. Free GPL Windows, GNU/Linux, Mac OS X CaRMetal Free GPL Windows, GNU Linux, Mac OS X Cinderella 1.4 Free Proprietary Windows, GNU/Linux, Mac OS X (Java) Cinderella 2.0 69 US$ Proprietary Windows, GNU/Linux, Mac OS X (Java) Defi ? ? ? DrGeo Free GPL Windows, GNU/Linux, Mac OS X Euklid DynaGeo Shareware Proprietary Windows Euklides Shareware Proprietary Windows Eukleides Free GPL Windows, GNU/Linux, Mac OS X Gambol ? ? Windows, GNU/Linux, Mac OS X GCLC Free Proprietary Windows, GNU/Linux GeoGebra Free GPL Windows, GNU/Linux, Mac OS X Geolog ? ? Windows/? The Geometer's Sketchpad ? Proprietary GNU/Linux, Windows, Mac OS X (Java) Geometric Supposer ? ? ? Geometrix Free Proprietary Linux, Windows Geometry Expert (GEX) ? ? Windows, GNU/Linux, Mac OS X Geometry Explorer Free ? Windows, GNU/Linux, Mac OS X Geometry Expressions ? Proprietary Windows, GNU/Linux, Mac Geometry Tutor ? ? Windows/? GeoNext Free GPL Windows, GNU/Linux, Mac OS X Géoplan Free CeCILL Windows GeoProof Free GPL Windows, GNU/Linux, Mac OS X GeoView Free GPL Windows, GNU/Linux, Mac OS X GEUP ? Proprietary Windows GRACE ? ? Windows, GNU/Linux, Mac OS X iGeom Free Proprietary GNU/Linux, Windows, Mac OS X Isard ? ? Windows Jeometry ? ? Windows, GNU/Linux, Mac OS X JSXGraph Free GNU LGPL Windows, GNU/Linux, Mac OS X Kig Free GPL GNU/Linux Kgeo Free GPL GNU/Linux KmPlot Free GPL GNU/Linux, Mac OS X KSEG Free GPL Windows, GNU/Linux, Mac OS X Live Geometry Free Free Windows, Mac OS X (Silverlight & WPF) MathKit ? Proprietary GNU/Linux, Windows, Mac OS X (Java) Mentoniezh ? ? ? OpenEuclide Free GPL Windows, GNU/Linux Tabula 19.95 US$ Proprietary Windows, Mac OS X (Silverlight) Tabulae Free Proprietary GNU/Linux, Windows, Mac OS X (Java) WinGeom ? ? Windows WIRIS ? Proprietary GNU/Linux, Windows, Mac OS X (Java) 3D Software
Software Cost (USD) Licence Platforms Archimedes Geo3D Shareware Proprietary Windows/Mac OS X/Linux Cabri 3D Shareware Proprietary Windows/Mac OS X GeoGebra (from version 5.0) Free GPL Windows, GNU/Linux, Mac OS X Geometria Free GPL Windows, GNU/Linux, Mac OS X GeomSpace Free GPL Windows, GNU/Linux, OpenSolaris, BSD GeomView Free GNU LGPL Unix Géospace Free CeCILL Windows GEUP 3D Shareware Proprietary Windows Yenka 3D Shapes Free for noncommercial use Proprietary Windows WIRIS ? Proprietary Windows, GNU/Linux, Mac OS X Anydimensional Software
Software Cost (USD) License Platforms Brief Info SpaceFuncs Free BSD Windows, GNU/Linux,
Mac OS X (Python)Uses FuncDesigner for parametrization and automatic differentiation,
OpenOpt for solving systems of geometric equations and numerical optimizationGeneral features
The following table provides a more detailed comparison :
Software Calculations Macros Loci Animations Scripting Assignments LaTeX export Web export Multilingual Proofs Extra Cabri II Plus Yes Yes Yes Yes Yes Yes (with plugin) No Yes Yes Yes (on relations) Available on TI Calculator CaR Yes Yes Yes Yes Yes Yes Yes Yes Yes No ? CaRMetal Yes (recursive) Yes Yes Yes (multiple) Yes (JavaScript) Yes Yes Yes Yes Yes (probabilistic) Amodality, folder system, the Monkey Cinderella Yes Yes Yes Yes Yes Yes Yes (PDF) Yes Yes Probabilistic Several geometries, Physics simulations GCLC Yes Yes Yes Yes Yes Yes Yes No No Yes Readable proofs, support for 3D GeoGebra Yes Yes Yes Yes Yes (JavaScript) Yes (JavaScript) Yes (PSTricks & PGF/TikZ) Yes Yes (55 languages) No CAS, HTML5 Export (from version 4.2)
3D (from version 5.0)Geometria Yes No Yes Yes No Yes No Yes Yes No Tworole (teacher, student) model Geometrix Yes No Yes Yes No Yes No No No Yes Interactive proof, diagram checking, teacher/student models, labels with dynamic placeholders GeoNext Yes No No Yes ? ? No ? Yes No Available as a web app GéoplanGéospace Yes Yes Yes Yes Yes No No Yes (activeX) Yes Yes Sequences, 2D & 3D, human readable file format GeoProof Yes No No No No No Yes No No Yes Automatic formal proofs GEUP Yes Yes Yes Yes ? No ? No Yes No ? iGeom Yes Yes Yes No Yes Yes No Yes Yes Probabilist Recurrent scripts Kig Yes Yes Yes No Yes (Python) No Yes (PSTricks) No Yes No Labels with dynamic placeholders Live Geometry Yes Yes Yes Yes No No No No No No Includes player. Sketchpad Yes Yes Yes Yes Yes No ? Yes (limited) Yes No Functions & function plots, symbolic differentiation, mathematical notation Tabula Yes Yes Yes Yes No No No No No No Folding, cutting, taping, marker, and working instrument models. Tabulae Yes Yes Yes No No No No Yes Yes No Collaborative sessions over the internet. Cabri 3D Yes No No Yes No No No Yes (limited) Yes No ? Archimedes Geo3D Yes Yes Yes Yes No No No No No (Eng De Fr) No Intersection of Loci GEUP 3D Yes No Yes No No No No No Yes No ? Software Calculations Macros Loci Animations Scripting Assignments LaTeX export Web export Multilingual Proofs Extra Macros
We detail here the features related to macro constructions. (TODO)
Software Allows recursity Allows saving Cabri II Plus Yes Yes GCLC No No GeoGebra Yes Yes GéoplanGéospace Yes Yes iGeom Yes Yes Kig ? Yes KSEG Yes Yes Sketchpad (GSP) Yes (via Iteration) Yes Loci
We detail here the loci features. (TODO)
Software Take a point of a locus Intersection of two loci Cabri II Plus Yes Yes CaR Yes Yes GeoGebra Yes No GéoplanGéospace Yes No iGeom Yes No Kig Yes No Sketchpad (GSP) Yes No Proof
We detail here the proof related features. (TODO)
Software Interactive Proofs Automatic Proofs Probabilist Proofs Cabri II Plus Feedback for No Yes in Cabri I Cinderella No Using external CAS Yes GCLC No Yes No Geometrix Yes Yes No GéoplanGéospace No No Yes GeoProof Yes Yes No iGeom No No Yes Jeometry No Yes No Measurements and calculation
We detail here the measurements and calculation features. (TODO)
Software Arbitrary Precision Arithmetic expressions Trigonometric functions If Object existence test Cabri Yes Yes Yes Yes No C.a.R. No Yes Yes Yes Yes GCLC No Yes Yes Yes Yes GeoGebra No Yes Yes Yes Yes (JavaScript) Geometria No Yes Yes No No GéoplanGéospace No Yes Yes Yes (µ fonction) No GeoProof Yes Yes Yes Yes No Geometrix No Yes Yes Yes No iGeom No Yes Yes No No Graphics Export Formats
Software PNG BMP TIFF GIF SWF SVG EMF Fig Postscript Pdf LaTeX/Eukleides LaTeX/Pstricks LaTeX/PGF/TikZ Asymptote C.a.R. Yes No ? ? ? Yes No Yes Yes No No Yes ? ? Cinderella Yes Yes ? ? ? ? ? ? No Yes ? ? ? ? GCLC No Yes ? ? ? Yes No No Yes No No Yes ? ? GeoGebra Yes No No Yes (animated) No Yes Yes No Yes Yes No Yes Yes Yes GeoProof Yes No ? ? ? Yes No No No No Yes No ? ? Kig Yes Yes ? ? ? Yes No Yes Yes Yes No Yes ? ? KmPlot Yes Yes ? ? ? Yes ? ? ? ? ? ? ? ? KSEG Yes Yes ? ? ? α No No ? No No No ? ? Geometrix No Yes Yes Yes Yes Yes No No No No No No ? ? iGeom No No No Yes No No No No Yes No No No ? ? Object attributes
Software Color Filled/Not filled Width Transparency Shown/Hidden Layer Shape of points Type of line Cabri Yes Yes Yes Yes Yes No Yes Yes C.a.R. Yes Yes Yes Yes Yes Yes Yes Yes GCLC Yes Yes Yes No Yes No Yes Yes GeoGebra Yes Yes Yes Yes Yes Yes Yes Yes Geometria Yes Yes No Yes Yes Yes No Yes GéoplanGéospace Yes Yes Yes Yes Yes No Yes Yes Kig Yes Yes Yes No Yes No Yes Yes GeoProof Yes No Yes No Yes Yes Yes Yes Geometrix Yes Yes Yes No Yes No Yes Yes iGeom Yes Yes Yes No Yes No No Yes 2D programs
C.a.R.
C.a.R. a free GPL analog of GSP, written in Java.
CaRMetal
CaRMetal a free GPL software written in Java. It is derived from C.a.R and provides another user interface.
Cabri II Plus
Cabri II Plus an extended analog of GSP and actually the ancestor of all DGSs.
Cinderella
Cinderella  very different from GSP, written in Java.
The new 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.Euklid DynaGeo
Euklid DynaGeo[1] is a shareware analog of GSP for windows.
Eukleides
Eukleides[2], GPL, is a geometry drawing language.
Dr Genius
Dr Genius was an attempt to merge Dr. Geo and the Genius calculator
Dr. Geo
Dr. Geo[3] is a GPL interactive software especially valuable for younger students (715). Now Dr. Geo II^{[3]} complete rewrite of Dr. Geo for the Squeak/Smalltalk environment is available.
Gambol
Gambol[4] is a Euclidean, constructionbased, drawing system
GCLC
GCLC^{[4]} 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 abstract description. There are several output formats, including LaTeX, LaTeX/PStricks, LaTeX/Tikz, SVG, PostScript. There is a builtin geometry theorem prover (based on the area method). GCLC is available for Windows and Linux. WinGCLC is a Windows version of GCLC with graphical interface and provides a range of additional functionalities.
GeoGebra
GeoGebra is free software that joins geometry, algebra and calculus for mathematics education in schools and universities.
 License: open source under GNU General Public License (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 piecewisedefined); 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; JavaScript interface for interactive exercises
 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 (anything which supports Java 1.5 or later)
 Continuity: uses a heuristic 'neartoapproach' to avoid jumping objects
Geolog
Geolog^{[5]} is a logic programming language for finitary geometric logic.
Geometry Expressions
Geometry Expressions Does symbolic geometry. It uses symbolic inputs and returns symbolic outputs.
The Geometer's Sketchpad
The Geometer's Sketchpad (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")
 Javaapplet: Yes
 Animation: Yes
 Locus: Yes, including point on locus
 Assignments: No
 Measurement/Calculations: Yes
 Platform: Windows, Mac OS, TI92+, works under wine
 Proofs: No
Geometrix
Geometrix[5] a free interactive geometry software, written in Prolog and Free Pascal (Lazarus).
Geonext
Geonext [6] free (GPL) analog of GSP written in Java and offers a view calculus features (parametric curves, functions) as well.
The Geometric Supposer
The Geometric Supposer^{[6]}
GéoplanGéospace
GeoProof
GeoProof^{[7]} a free GPL dynamic geometry software, written in Objective Caml.
GEUP
GEUP bit more calculusoriented analog of GSP.
 Deterministic
 Languages: English, French, German, Italian, Portuguese, Spanish.
 Macros: Yes
 Javaapplet: No
 Animation: Yes
 Locus: Yes / point on locus
 Assignments: No
 Measurement/Calculations: Yes
 Platform: Windows
 Proofs: No
GRACE
GRACE The Graphical Ruler And Compass Editor, an analog of GSP, written in Java.
iGeom
iGeom[7]  Interactive Geometry on Internet is a freeware software for learning and teaching Geometry (analog of GSP and Cabri), written in Java.
Jeometry
Jeometry is a dynamic geometry applet
Isard
Isard^{[8]} is an interactive geometry software originally written in Smalltalk. The latest version only works under VisualWorks 7.
Kig
Kig a free (GPL) analog of GSP for KDE, bit more to calculusoriented, part of KDE Edutainment Project.
Kgeo
Kgeo[8] a free (GPL) analog of GSP for KDE, bit more too calculusoriented, its interface is similar to Kig.
It is no more developed, replaced and improved by Kig.
KmPlot
KmPlot[9] is a mathematical function plotter released under the free (GPL). 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.
 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 scalable vector graphics (SVG)
 save/load complete session in readable xml 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 minium/maximum point, get yvalue and draw the area between the function and the yaxis
KSEG
KSEG free (GPL) analog of GSP which has a few important unique features. If you plan to do some heavy, complicated constructions in Euclidean geometry this is for you.
 Deterministic
 Languages: Dutch, English, French, Chinese, German, Hungarian, Italian, Japanese, Norwegian Bokmal, Portuguese, Russian, Spanish, Turkish, Welsh.
 Macros: Yes. Editable and with support for recursion
 Javaapplet: No
 Animation: No
 Locus: Yes, No direct way to put point on locus.
 Assignments: No
 Measurement/Calculations: Yes (calculator is bit strange)
 Platform: Unix/Linux, Windows, Mac OS (anything which supports Qt)
 Proofs: No
 Extra: Editable
NonEuclid
NonEuclid^{[9]} is a very basic JavaIGS only for hyperbolic geometry in the Poincaré disk and the upper halfplane models.
OpenEuclide
OpenEuclide^{[10]} is a GPL 2D geometry software.
Sphaerica
Sphaerica^{[11]} is an open source geometry software for spherical geometry.
Live Geometry
Live Geometry [10] is a free codeplex project that lets you create interactive ruler and compass constructions and experiment with them. It is written with Silverlight 4 and C# 4.0 (Visual Studio 2010). The core engine is a flexible and extensible framework that allows you to easily add new figure types and features. The project has two frontends: WPF and Silverlight; they both share the common DynamicGeometry library.
TracenPoche
TracenPoche[11] completely Adobe Flash program. Available in French,English and Spanish.
Tabula
Tabula is a commercial dynamic geometry program created by Numeracy Works. Tabula supports handson learning and can be used to construct, cut, tape, fold, measure, and transform geometric figures. Built using Silverlight, it is both MacOS and Windows compatible.
Tabulae
Tabulae [12] is a dynamic geometry software written in Java. Under development from Federal University of Rio de Janeiro. Available in Brazilian Portuguese.
Wingeom
Wingeom^{[12]} for highprecision geometric constructions in both two and three dimensions
3D programs
Archimedes Geo3D
Cabri 3D
Euler 3D
Euler 3D
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.
Geometria
Geometria is free (GPL) crossplatform software based on a tworole (teacher, student) model. The teacher creates a problem, provides it with an answer and saves the problem in a file. The student opens the file and solves the problem. The student's actions are recorded. The teacher plays back the solution and grades it. The figures are limited to convex polyhedra, which can be measured, drawn upon, transformed, cut and joined.
Geomview
Geomview
GEUP 3D
PyGeo
PyGeo
JavaView
JavaView
JavaView is a 3D geometry viewer and a mathematical visualization software. You can explore miscellaneous 3D models with it.
SingSurf
SingSurf
Based on JavaView, this program can calculate and draw singular algebraic curves and surfaces.
Doorzien 4
A very simple, online applet that allows one to view and bisect a cube in 3D space.
Anydimensional programs
SpaceFuncs
a crossplatform (Linux, Windows, Mac etc) completely free (license: BSD) Python language module for 2D, 3D, Ndimensional space calculations with abilities of
 parametrized modeling (using FuncDesigner)
 performing numerical optimization and solving geometrical systems of equations (possibly parametrized) by OpenOpt, using FuncDesigner automatic differentiation, that yields more precise (and very often faster) results than finitedifferences derivatives approximation
 some graphic output using Matplotlib (any other Python graphic visualization library from the variety can be easily connected).
Continuity vs. 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 mid points (say A', B' C' ) between vertices and orthocenter.
Construct a circumcircle of A'B'C' .
This is the ninepoint 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 mid point 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.^{[13]}
References
 ^ Schwartz; Yerushalmy and Wilson (1993). The Geometric Supposer: What is it a Case of?. Hillsdale, NJ: Lawrence Erlbaum Associates.
 ^ Battista, M.T. (2007). "The Development of Geometric and Spatial Thinking". In Lester, Jr., F.K.. Second Handbook of Research on Mathematics Teaching and Learning. Charlotte, NC: Information Age and the National Council of Teachers of Mathematics. pp. 843–903.
 ^ http://wiki.laptop.org/go/DrGeo
 ^ http://www.matf.bg.ac.rs/~janicic/gclc/
 ^ http://www.csupomona.edu/~jrfisher/www/geolog/
 ^ http://www.cet.ac.il/mathinternational/software5.htm
 ^ http://home.gna.org/geoproof/
 ^ http://www.jeannot.org/~js/isard/
 ^ http://www.cs.unm.edu/~joel/NonEuclid/NonEuclid.html
 ^ http://coulon.publi.free.fr/openeuclide/
 ^ http://sourceforge.net/projects/sphaerica/
 ^ http://math.exeter.edu/rparris/wingeom.html
 ^ 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
 Constructive solid geometry (There's also a list of software.)
External links
 Links to other lists
 Links to the other programs
 Geometry Software Stepbystep problem solver, download available
 Geops Free perl script for performing compass and straightedge constructions in the manner of the Ancient Greeks.
 Geometria An online tool to compute lines, surfaces and volumes of the main plane and solid figures, through direct and indirect formulas.
 Interactive geometry on web:
 Cabri software editor website Available resources for teaching
 Geometry at cuttheknot
 Sketchpad Resource Center Including classroom activities, research bibliography, demo version, etc.
 The Math Open Reference Project Collection of applets
 Math tools Catalog of applets
 Yenka 3D Shapes Free 3D geometry software available to download
 Interactive geometry examples in Mathematica The Wolfram Demonstrations Project
 Dynamic Geometry Sketches Includes student explorations and classroom demonstrations.
 Interactive Math And Geometry Applets Collection of java and Cabri 3D applets
Categories: Interactive geometry software
 Lists of software
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