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.
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.
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.
License and platform
The following table provides a first comparison of the different software according to their licence and platform.
Software Cost (USD) Licence Platforms Apollonius 3.99 US$ Proprietary iPhone/iPod Touch Baghera ? ? Windows/? Cabri Geometry ? Proprietary Windows, Mac OS X Cabri-Euclide ? ? 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)
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 non-commercial use Proprietary Windows WIRIS ? Proprietary Windows, GNU/Linux, Mac OS X
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 optimization
The following table provides a more detailed comparison :
3D (from version 5.0)
Geometria Yes No Yes Yes No Yes No Yes Yes No Two-role (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 Géoplan-Géospace 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
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 Géoplan-Géospace Yes Yes iGeom Yes Yes Kig ? Yes KSEG Yes Yes Sketchpad (GSP) Yes (via Iteration) Yes
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 Géoplan-Géospace Yes No iGeom Yes No Kig Yes No Sketchpad (GSP) Yes No
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 Géoplan-Géospace 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)
Graphics Export Formats
Software PNG BMP TIFF GIF SWF SVG EMF Fig Postscript 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 ? ?
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 Géoplan-Géospace 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
Cabri II Plus
Cabri II Plus an extended analog of GSP and actually the ancestor of all DGSs.
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.
Dr Genius was an attempt to merge Dr. Geo and the Genius calculator
Gambol is a Euclidean, construction-based, drawing system
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 abstract description. There are several output formats, including LaTeX, LaTeX/PStricks, LaTeX/Tikz, SVG, PostScript. 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 graphical interface and provides a range of additional functionalities.
- 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 piecewise-defined); intersections and roots of functions; symbolic derivatives and integrals (built in CAS); sliders as parameters
- Parametric Graphs: Yes
- Implicit Polynomials: Yes
- 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 'near-to-approach' to avoid jumping objects
Geolog is a logic programming language for finitary geometric logic.
Geometry Expressions Does symbolic geometry. It uses symbolic inputs and returns symbolic outputs.
The Geometer's Sketchpad
The Geometer's Sketchpad (GSP)
- 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
GEUP bit more calculus-oriented analog of GSP.
- Languages: English, French, German, Italian, Portuguese, Spanish.
- Macros: Yes
- Java-applet: No
- Animation: Yes
- Locus: Yes / point on locus
- Assignments: No
- Measurement/Calculations: Yes
- Platform: Windows
- Proofs: No
GRACE The Graphical Ruler And Compass Editor, an analog of GSP, written in Java.
Jeometry is a dynamic geometry applet
Isard is an interactive geometry software originally written in Smalltalk. The latest version only works under VisualWorks 7.
It is no more developed, replaced and improved by Kig.
KmPlot 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 y-value and draw the area between the function and the y-axis
- Languages: Dutch, English, French, Chinese, German, Hungarian, Italian, Japanese, Norwegian Bokmal, Portuguese, Russian, Spanish, Turkish, Welsh.
- Macros: Yes. Editable and with support for recursion
- Java-applet: 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
OpenEuclide is a GPL 2D geometry software.
Sphaerica is an open source geometry software for spherical geometry.
Live Geometry  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 front-ends: WPF and Silverlight; they both share the common DynamicGeometry library.
Tabula is a commercial dynamic geometry program created by Numeracy Works. Tabula supports hands-on 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  is a dynamic geometry software written in Java. Under development from Federal University of Rio de Janeiro. Available in Brazilian Portuguese.
Wingeom for high-precision geometric constructions in both two and three dimensions
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 is free (GPL) cross-platform software based on a two-role (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.
JavaView is a 3D geometry viewer and a mathematical visualization software. You can explore miscellaneous 3D models with it.
Based on JavaView, this program can calculate and draw singular algebraic curves and surfaces.
A very simple, online applet that allows one to view and bisect a cube in 3D space.
- 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 finite-differences 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 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 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.
- ^ 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/math-international/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
- Links to other lists
- Links to the other programs
- Geometry Software Step-by-step 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 cut-the-knot
- 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
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