# 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[vague], dynamic geometry environments (DGEs) and Logo-based 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 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.

Software Cost (USD) Licence Platforms
Cabri Geometry ? Proprietary Windows, Mac OS X
C.a.R. Free GPL Windows, Linux, Mac OS X
CaRMetal Free GPL Windows, GNU Linux, Mac OS X
Cinderella 1.4 Free Proprietary Windows, Linux, Mac OS X (Java)
Cinderella 2.0 69 US$Proprietary Windows, Linux, Mac OS X (Java) DrGeo Free GPL Windows, Linux, Mac OS X GeoGebra Free GPL Windows, Linux, Mac OS X The Geometer's Sketchpad 70.02 US$ Proprietary Windows, Mac OS X (Java)
Geometry Expert (GEX) ? ? Windows, Linux, Mac OS X
GEUP ? Proprietary Windows
Kig Free GPL Linux
KSEG Free GPL Windows, Linux, Mac OS X
WIRIS ? Proprietary Linux, Windows, Mac OS X (Java)

#### 3D Software

Software Cost (USD) Licence Platforms
Archimedes Geo3D Shareware Proprietary Windows/Mac OS X/Linux
GeoGebra (from version 5.0 Beta) Free GPL Windows, Linux, Mac OS X, Android, iOS, Windows RT
Yenka 3D Shapes Free for non-commercial use Proprietary Windows
WIRIS ? Proprietary 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 Yes Yes Yes Yes Yes Yes (with plug-in) No Yes Yes Yes (on relations) Available on TI Calculator
Calques 3D Yes Yes Yes Yes No No No No Yes (FRA ENG DEU ESP PTG) Yes (on relations) Experimental connection with some CAS
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
Ganja.js Yes Yes Yes Yes Yes Yes No Yes No No 2D and 3D, projective and conformal, Geometric Algebra.
GCLC Yes Yes Yes Yes Yes Yes Yes No No Yes Readable proofs, support for 3D
GeoGebra Yes Yes Yes Yes Yes (JavaScript) No Yes (PSTricks & PGF/TikZ) Yes Yes (55 languages) Yes CAS, HTML5 Export (from version 4.2)
3D & Automatic Proof (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 Yes Yes Interactive proof, diagram checking, teacher/student models, labels with dynamic placeholders
Geometry Expressions Yes No Yes Yes No No Yes Yes (Interactive HTML5/JS Apps) Yes No 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 (Euclid's Muse).
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.
Sarit2d Yes Yes Yes Yes Yes Yes Yes Yes No Yes Avalaible on web
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 Yes Yes Yes No No No No Yes No ?
Netpad Yes Yes Yes Yes No No No Yes No Yes Base on Web
Software Calculations Macros Loci Animations Scripting Assignments LaTeX export Web export Multilingual Proofs Extra

### Macros

Features related to macro constructions: (TODO)

Software Allows recursity Allows saving
Cabri II Plus Yes Yes
Calques 3D No Yes
GCLC No No
GeoGebra Yes Yes
Géoplan-Géospace Yes Yes
GEUP Yes Yes
iGeom Yes Yes
Kig ? Yes
KSEG Yes Yes
Sketchpad (GSP) Yes (via Iteration) Yes

### Loci

Loci features related to IGS: (TODO)

Software Take a point of a locus Intersection of two loci
Cabri II Plus Yes Yes
Calques 3D No No
CaR Yes Yes
GeoGebra Yes No
Géoplan-Géospace Yes No
GEUP Yes Yes
iGeom Yes No
Kig Yes No
Sketchpad (GSP) Yes No
NetPad Yes Yes

### 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
GeoGebra Yes Yes No
Geometrix Yes Yes No
Géoplan-Géospace No No Yes
GeoProof Yes Yes No
iGeom No No Yes
Jeometry No Yes No
NetPad Yes Yes ?

### Measurements and calculation

Measurement and calculation features related to IGS: (TODO)

Software Arbitrary Precision Arithmetic expressions Trigonometric functions If Object existence test
Cabri Yes Yes Yes Yes No
Calques 3D No Yes Yes No 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
Géoplan-Géospace No Yes Yes Yes (µ function) No
GeoProof Yes Yes Yes Yes No
Geometrix No Yes Yes Yes No
iGeom No Yes Yes No No
NetPad Yes Yes Yes Yes No

### Graphics export formats

Software PNG BMP TIFF GIF SWF SVG EMF Fig Postscript Pdf LaTeX/Eukleides LaTeX/Pstricks LaTeX/PGF/TikZ Asymptote
Calques 3D No No No No No No No Yes No No No No No No
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
Geometry Expressions Yes Yes Yes Yes (animated) No No Yes No Yes No ? ? ? ?
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 ? ? ? ${\displaystyle \alpha }$  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
Calques 3D Yes Yes Yes No Yes Yes 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
Geometry Expressions Yes Yes Yes Yes Yes Yes No (but size) 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
Sketchpad Yes Yes Yes Yes Yes ? Yes Yes
NetPad Yes Yes Yes Yes Yes Yes No (but size) Yes

## 2D programs

### C.a.R.

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

### 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[when?] 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 [1] is a GPL interactive software intended for younger students (7-15). The later version, Dr. Geo II,[3] is a complete rewrite of Dr. Geo, for the Squeak/Smalltalk environment.

### 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 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 (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.

### 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. [5]

• License: open source under GPL 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
• Web Export: all constructions exportable as web pages as a Java applet
• 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[6] 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[7] is a logic programming language for finitary geometric logic.

### Geometry Expressions

Geometry Expressions[8] Does symbolic geometry. It uses real symbolic inputs and returns real and symbolic outputs. It emphasises use with a Computer Algebra System (CAS), as well as exporting and sharing via interactive HTML5, Lua, and OS X dashboard widget apps.

### The Geometer's Sketchpad

• 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[9]

### GeoProof

GeoProof[10] 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: 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.

### iGeom

iGeom [2] is freeware interactive geometry software hosted on the Internet for learning and teaching geometry (an analog of GSP and Cabri), written in Java.

### Isard

Isard[11] is an interactive geometry software originally written in Smalltalk. The latest version only works under VisualWorks 7.

### Jeometry

Jeometry is a dynamic geometry applet.

### Kig

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

### Kgeo

Kgeo [3] was a free (GPL) analog of The Geometer's Sketchpad (GSP) for KDE, but more calculus-oriented, with an interface similar to Kig's. Development has stopped, and the project was replaced and superseded by Kig.

### KmPlot

KmPlot [4] 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 (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 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 [5] 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 (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.

### Non-Euclid

Non-Euclid[12] is a very basic Java-IGS used only for hyperbolic geometry in the Poincaré disk and the upper half-plane models.

### OpenEuclide

OpenEuclide[13] is a GPL 2D geometry software.

### Sarit2d

Sarit2d[14] is a library for Javascript created for drawing and solving 2d-geometric problems. The library contains many functions for drawing the main geometric shapes: segments, arcs, points, texts, etc. But the very core of the library are the functions for solving the most common geometry problems: intersections between shapes, areas calculation, geometric formulas, etc.With Sarit2d library it's possible solving hard problems through few code rows.

### Sphaerica

Sphaerica[15] is an open source geometry software for spherical geometry. It supports orthographic, stereographic and gnomonic projections and various tools for constructions on the sphere.

### Tabula

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 Mac OS and Windows compatible.

### Tabulae

Tabulae [6] is a dynamic geometry software written in Java. It is under development by the Federal University of Rio de Janeiro. It is available in Brazilian and Portuguese.

### TracenPoche

TracenPoche [7] is a completely Adobe Flash program. It is available in English, Spanish, and French.

### Wingeom

Wingeom[16] is a program for high-precision geometric constructions in both two and three dimensions.

## 3D programs

### Ganja.js

Ganja.js implements 2D and 3D projective and conformal Geometric Algebra. It features animation, interactivity and live editing without registration or download.

### 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.

## 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 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.[17]

## References

1. ^ Schwartz; Yerushalmy and Wilson (1993). The Geometric Supposer: What is it a Case of?. Hillsdale, NJ: Lawrence Erlbaum Associates.
2. ^ 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.
3. ^ http://wiki.laptop.org/go/DrGeo
4. ^ http://www.matf.bg.ac.rs/~janicic/gclc/
5. ^ http://www.geogebra.org/license#FAQ
6. ^ http://GeoKone.NET
7. ^ "Archived copy". Archived from the original on 2008-04-09. Retrieved 2008-03-01.CS1 maint: Archived copy as title (link)
8. ^ http://geometryexpressions.com
9. ^ http://www.cet.ac.il/math-international/software5.htm
10. ^ "Archived copy". Archived from the original on 2006-04-21. Retrieved 2006-04-21.CS1 maint: Archived copy as title (link)
11. ^ http://www.jeannot.org/~js/isard/
12. ^ http://www.cs.unm.edu/~joel/NonEuclid/NonEuclid.html
13. ^ http://coulon.publi.free.fr/openeuclide/
14. ^ https://sourceforge.net/projects/sarit2d/
15. ^ http://sourceforge.net/projects/sphaerica/
16. ^ "Archived copy". Archived from the original on 2008-02-19. Retrieved 2008-03-01.CS1 maint: Archived copy as title (link)
17. ^ Kortenkamp, Ulrich (1999): Foundations of Dynamic Geometry, Dissertation, ETH Zurich 1999. Available online at http://kortenkamps.net/papers/1999/diss.pdf