List of interactive geometry software


Interactive geometry software or dynamic geometry environments 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. 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 and Logo-based programs. Most are DGEs: software that allows the user to manipulate 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.

License and platform

The following table provides a first comparison of the different software according to their licence and platform.
SoftwareCost LicencePlatforms
Cabri GeometryWindows, Mac OS X
C.a.R.Windows, Linux, Mac OS X
CaRMetalWindows, GNU Linux, Mac OS X
Cinderella 1.4Windows, Linux, Mac OS X
Cinderella 2.069 US$Windows, Linux, Mac OS X
DrGeoWindows, Linux, Mac OS X
GeoGebraWindows, Linux, Mac OS X
Windows, MacOS, Linux
The Geometer's Sketchpad70.02 US$Windows, Mac OS X
Geometry Expert Windows, Linux, Mac OS X
GEUPWindows
KigLinux
KSEGWindows, Linux, Mac OS X
WIRISLinux, Windows, Mac OS X

3D Software

SoftwareCost LicencePlatforms
Archimedes Geo3DWindows/Mac OS X/Linux
GeoGebra Windows, Linux, Mac OS X, Android, iOS, Windows RT
Yenka 3D ShapesWindows
WIRISWindows, Linux, Mac OS X

General features

The following table provides a more detailed comparison :
SoftwareCalculationsMacrosLociAnimationsScriptingAssignmentsLaTeX exportWeb exportMultilingualProofsExtra
Cabri II Plus Available on TI Calculator
Calques 3D Experimental connection with some CAS
CaR
CaRMetal Amodality, folder system, the Monkey
Cinderella ProbabilisticSeveral geometries, Physics simulations
Ganja.js2D and 3D, projective and conformal, Geometric Algebra.
GCLCReadable proofs, support for 3D
GeoGebra CAS, HTML5 Export
3D & Automatic Proof
GeometriaTwo-role model
GeometrixInteractive proof, diagram checking, teacher/student models, labels with dynamic placeholders
Geometry Expressions Symbolic calculations, which can be copied as input for CAS, TeX, and source code in 21 formats/languages. Functions. Arcs on any function or curve. Website for exported HTML5 Canvas and JavaScript Interactive Apps.
GeoNextAvailable as a web app
Géoplan-Géospace Sequences, 2D & 3D, human readable file format
GeoProofAutomatic formal proofs
GEUP
iGeomProbabilistRecurrent scripts
Kig Labels with dynamic placeholders
Live GeometryIncludes player.
Sarit2dAvailable on web
Sketchpad Functions & function plots, symbolic differentiation, mathematical notation
TabulaFolding, cutting, taping, marker, and working instrument models.
TabulaeCollaborative sessions over the internet.
Cabri 3D
Archimedes Geo3D Intersection of Loci
GEUP 3D
NetpadBase on Web
SoftwareCalculationsMacrosLociAnimationsScriptingAssignmentsLaTeX exportWeb exportMultilingualProofsExtra

Macros

Features related to macro constructions:
SoftwareAllows recursityAllows saving
Cabri II Plus
Calques 3D
GCLC
GeoGebra
Géoplan-Géospace
GEUP
iGeom
Kig
KSEG
Sketchpad

Loci

Loci features related to IGS:
SoftwareTake a point of a locusIntersection of two loci
Cabri II Plus
Calques 3D
CaR
GeoGebra
Géoplan-Géospace
GEUP
iGeom
Kig
Sketchpad
NetPad

Proof

We detail here the proof related features.
SoftwareInteractive ProofsAutomatic ProofsProbabilist Proofs
Cabri II PlusFeedback for in Cabri I
CinderellaUsing external CAS
GCLC
GeoGebra
Geometrix
Géoplan-Géospace
GeoProof
iGeom
Jeometry
NetPad

Measurements and calculation

Measurement and calculation features related to IGS:
SoftwareArbitrary PrecisionArithmetic expressionsTrigonometric functionsIfObject existence test
Cabri
Calques 3D
C.a.R.
GCLC
GeoGebra
Geometria
Géoplan-Géospace
GeoProof
Geometrix
iGeom
NetPad

Graphics export formats

SoftwarePNGBMPTIFFGIFSWFSVGEMFFigPostscriptPdfLaTeX/EukleidesLaTeX/PstricksLaTeX/PGF/TikZAsymptote
Calques 3D
C.a.R.
Cinderella
GCLC
GeoGebra
Geometry Expressions
GeoProof
Kig
KmPlot
KSEG
Geometrix
iGeom

Object attributes

SoftwareColorFilled/Not filledWidthTransparencyShown/HiddenLayerShape of pointsType of line
Cabri
Calques 3D
C.a.R.
GCLC
GeoGebra
Geometria
Geometry Expressions
Géoplan-Géospace
Kig
GeoProof
Geometrix
GEUP
iGeom
Sketchpad
NetPad

2D programs

C.a.R.

is a free GPL analog of The Geometer's Sketchpad, written in Java.

CaRMetal

is a free GPL software written in Java. Derived from C.a.R., it provides a different user interface.

Cinderella

, 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

is a GPL interactive software intended for younger students. The later version, Dr. Geo II, is a complete rewrite of Dr. Geo, for the Squeak/Smalltalk 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 and PostScript. There is a built-in geometry theorem prover. 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.

GeoGebra

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.
GeoKone.NET is an interactive recursive natural 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, as well as exporting and sharing via interactive HTML5, Lua, and OS X dashboard widget apps.

The Geometer's Sketchpad

The Geometric Supposer

Géoplan-Géospace

GeoProof

GeoProof is a free GPL dynamic geometry software, written in OCaml.

GEUP

is a more calculus-oriented analog of The Geometer's Sketchpad.
GRACE is an analog of The Geometer's Sketchpad, written in Java.

Jeometry

Jeometry is a dynamic geometry applet.

Kig

is a free analog of The Geometer's Sketchpad for KDE, but more calculus-oriented. It is a part of the KDE Edutainment Project.

KmPlot

is a mathematical function plotter released under the free GPL license. 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:
is a free analog of The Geometer's Sketchpad with some unique features. This software can handle heavy, complex constructions in Euclidean geometry.
Live Geometry is a free CodePlex project that lets you create interactive ruler and compass constructions and experiment with them. It is written in Silverlight 4 and C# 4.0. 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

is a completely Adobe Flash program. It is available in English, Spanish, and French.

3D programs

Archimedes Geo3D

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.

Geomview

Continuity versus determinism

All these programs can be divided into two category: deterministic and continuous.
GeoGebra can be deterministic or continuous.
All constructions in the deterministic programs 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, 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 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 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.