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 license and platform.

Software	Cost	Licence	Platforms
Cabri Geometry			Windows, macOS
C.a.R.			Windows, Linux, macOS
CaRMetal			Windows, Linux, macOS
Cinderella 1.4			Windows, Linux, Mac OS X
Cinderella 2.0			Windows, Linux, Mac OS X
DrGeo			Windows, Linux, Mac OS X
GeoGebra	Free/Paid	GeoGebra License	Windows, Linux, Mac OS X
			Windows, MacOS, Linux
The Geometer's Sketchpad	70.02 US$		Windows, Mac OS X
Geometry Expert			Windows, Linux, Mac OS X
GEUP			Windows
Kig			Linux
KSEG			Windows, Linux, Mac OS X
WIRIS			Linux, Windows, Mac OS X

3D software

Software	Cost	Licence	Platforms
Archimedes Geo3D			Windows/Mac OS X/Linux
GeoGebra	Free/Paid	GeoGebra License	Windows, Linux, Mac OS X, Android, iOS, Windows RT
GEUP 3D			Windows
Yenka 3D Shapes			Windows
WIRIS			Windows, Linux, Mac OS X

General 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											Available on TI Calculator
Calques 3D											Experimental connection with some CAS
CaR
CaRMetal											Amodality, folder system, the Monkey
Cinderella										Probabilistic	Several geometries, Physics simulations
Ganja.js											2D and 3D, projective and conformal, Geometric Algebra.
GCLC											Readable proofs, support for 3D
GeoGebra											CAS, HTML5 Export 3D & Automatic Proof
Geometria											Two-role model
Geometrix											Interactive 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.
GeoNext											Available as a web app
Géoplan-Géospace											Sequences, 2D & 3D, human readable file format
GeoProof											Automatic formal proofs
GEUP											CAD functionality through CADGEUP
iGeom										Probabilist	Recurrent scripts
Kig											Labels with dynamic placeholders
Live Geometry											Includes player.
Sarit2d											Available on web
Sketchpad											Functions & function plots, symbolic differentiation, mathematical notation
Tabula											Folding, cutting, taping, marker, and working instrument models.
Tabulae											Collaborative sessions over the internet.
Cabri 3D
Archimedes Geo3D											Intersection of Loci
GEUP 3D											CAD functionality through CADGEUP
Netpad											Base on Web
Software	Calculations	Macros	Loci	Animations	Scripting	Assignments	LaTeX export	Web export	Multilingual	Proofs	Extra

Macros

Features related to macro constructions:

Software	Allows recursity	Allows saving
Cabri II Plus
Calques 3D
GCLC
GeoGebra
Géoplan-Géospace
GEUP
iGeom
Kig
KSEG
Sketchpad

Loci

Loci features related to IGS:

Software	Take a point of a locus	Intersection 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.

Software	Interactive proofs	Automatic proofs	Probabilistic proofs
Cabri II Plus	Feedback for		in Cabri I
Cinderella		Using external CAS
GCLC
GeoGebra
Geometrix
Géoplan-Géospace
GeoProof
iGeom
Jeometry
NetPad

Measurements and calculation

Measurement and calculation features related to IGS:

Software	Arbitrary precision	Arithmetic expressions	Trigonometric functions	If	Object existence test
Cabri
Calques 3D
C.a.R.
GCLC
GeoGebra
Geometria
Géoplan-Géospace
GeoProof
Geometrix
iGeom
NetPad

Graphics export formats

Software

PNG

BMP

TIFF

GIF

SWF

SVG

EMF

Fig

Postscript

Pdf

LaTeX/Eukleides

LaTeX/Pstricks

LaTeX/PGF/TikZ

Asymptote

Calques 3D

C.a.R.

Cinderella

GCLC

GeoGebra

Geometry Expressions

GeoProof

Kig

KmPlot

KSEG

Geometrix

iGeom

Object attributes

Software	Color	Filled/not filled	Width	Transparency	Shown/hidden	Layer	Shape of points	Type 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.

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

Cabri

Cabri
Cabri was developed by the French school of mathematics education in Grenoble

CaRMetal

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

Cinderella

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

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. GCLC is open source software.

GeoGebra

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.License: open source under GPL license Languages: 55Geometry: points, lines, all conic sections, vectors, parametric curves, locus linesAlgebra: direct input of inequalities, implicit polynomials, linear and quadratic equations; calculations with numbers, points and vectorsCalculus: direct input of functions ; intersections and roots of functions; symbolic derivatives and integrals ; sliders as parametersParametric graphs: YesImplicit polynomials: YesWeb export: all constructions exportable as web pages as a Java appletMacros: usable both as tools with the mouse and as commands in the input fieldAnimation: YesSpreadsheet: Yes, the cells can contain any GeoGebra object Dynamic text: Yes Platforms: Mac OS, Unix/Linux, Windows Continuity: uses a heuristic 'near-to-approach' to avoid jumping objects

GeoKone.NET

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 Geometer's Sketchpad DeterministicLanguages: English, Spanish, Danish, Russian, Korean, Thai, Traditional and Simplified Chinese, French, Lithuanian ; others Macros: Yes Java-applet: YesAnimation: YesLocus: Yes, including point on locusAssignments: NoMeasurement/calculations: YesPlatform: Windows, Mac OS, TI-92+, works under WineProofs: No

The Geometric Supposer

'''The Geometric Supposer'''

Geonext

Geonext was developed by the University of Bayreuth 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.

GEUP

GEUP is a more calculus-oriented analog of The Geometer's Sketchpad.

Deterministic
Languages: English, French, German, Italian, Portuguese, Spanish
Macros: Yes
Java-applet: NoAnimation: YesLocus: Yes, including point on locusAssignments: NoMeasurement/calculations: YesPlatform: WindowsProofs: No

GRACE

GRACE is an analog of The Geometer's Sketchpad, written in Java.

Jeometry

Jeometry is a dynamic geometry applet.

Kig

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

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:

powerful mathematical parser
precise metric printing
different plot types
highly configurable visual settings
export to bitmap format and to Scalable Vector Graphics
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 minimum/maximum point, get y-value and draw the area between the function and the y-axis

KSEG

KSEG is a free analog of The Geometer's Sketchpad 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: NoAnimation: NoLocus: Yes, but no direct way to place a point on a locus.Assignments: NoMeasurement/calculations: Yes Platform: Unix/Linux, Windows, Mac OS Proofs: NoExtra: Editable

Live 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

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

3D programs

Cabri 3D

Cabri Geometry

Archimedes Geo3D

Archimedes Geo3D is a shareware program designed for 3D geometric constructions. It extends traditional ruler and compass constructions into 3D space, allowing users to work with elements such as points, lines, circles, planes, spheres, vectors, and loci. This software is compatible with Windows, macOS, and Linux platforms.

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, includes a 3D mode since version 5.0

Geomview

GEUP 3D

GEUP

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.