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. 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 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. For a related, comparative physical example of these algorithms, see Lenart Sphere.

License and platform

The table below provides a first comparison of the different software according to license and platform.

Software Cost (USD) License Platforms Cabri Geometry Windows, macOS C.a.R. Windows, Linux, macOS CaRMetal Windows, Linux, macOS Cinderella 1.4 Windows, Linux, macOS (Java) Cinderella 2.0 Windows, Linux, macOS (Java) DrGeo Windows, Linux, macOS GeoGebra Free/Paid GeoGebra License Windows, Linux, macOS Geom Windows, macOS, LinuxiGeom*Linux, macOS, Windows (Java*/JavaScript) The Geometer's Sketchpad 70.02 Windows, macOS (Java) Geometry Expert (GEX) Windows, Linux, macOS GEUP Windows Kig Linux KSEG Windows, Linux, macOS WIRIS Linux, Windows, macOS (Java)

3D software

Software Cost (USD) License Platforms Archimedes Geo3D Windows, macOS, Linux GeoGebra (from version 5.0 beta) Free or paid GeoGebra License Windows, Linux, macOS, Android, iOS/iPadOS, Windows RT GEUP 3D Windows Yenka 3D Shapes Windows WIRIS Windows, Linux, macOS

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 (with plug-in) (on relations) Available on TI Calculator Calques 3D (FRA ENG DEU ESP PTG) (on relations) Experimental connection with some CAS CaR CaRMetal (recursive) (multiple) (JavaScript) (probabilistic) Amodality, folder system, the Monkey Cinderella (PDF) Probabilistic Several geometries, Physics simulations Ganja.js 2D and 3D, projective and conformal, Geometric Algebra. GCLC Readable proofs, support for 3D GeoGebra (JavaScript) (PSTricks & PGF/TikZ) (55 languages) CAS, HTML5 Export (from version 4.2) 3D & Automatic Proof (from version 5.0) Geometria Two-role (teacher, student) model Geometrix Interactive proof, diagram checking, teacher/student models, labels with dynamic placeholders Geometry Expressions (Interactive HTML5/JS Apps) 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 Available as a web app Géoplan-Géospace (activeX) Sequences, 2D & 3D, human readable file format GeoProof Automatic formal proofs GEUP CAD functionality through CADGEUP iGeom Probabilist Recurrent scripts Kig (Python) (PSTricks) Labels with dynamic placeholders Live Geometry Includes player. Sarit2d Available on web Sketchpad (limited) Functions & function plots, symbolic differentiation, mathematical notation Tabula Folding, cutting, taping, marker, and working instrument models. Tabulae Collaborative sessions over the internet. Cabri 3D (limited) Archimedes Geo3D (Eng De Fr) 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: (TODO) Software Allows recursity Allows saving Cabri II Plus Calques 3D GCLC GeoGebra Géoplan-Géospace GEUP iGeom Kig KSEG Sketchpad (GSP) (via Iteration)

Loci

Loci features related to IGS: (TODO)

Software Take a point of a locus Intersection of two loci Cabri II Plus Calques 3D CaR GeoGebra Géoplan-Géospace GEUP iGeom Kig Sketchpad (GSP) NetPad

Proof

We detail here the proof related features. (TODO)

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: (TODO)

Software Arbitrary precision Arithmetic expressions Trigonometric functions If Object existence test Cabri Calques 3D C.a.R. GCLC GeoGebra (JavaScript) Geometria Géoplan-Géospace (μ function) 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 (animated) Geometry Expressions (animated) 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 (but size) Géoplan-Géospace Kig GeoProof Geometrix GEUP iGeom Sketchpad NetPad (but size)

2D programs

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

Cabri Cabri Cabri was developed by the French school of mathematics education in Grenoble (Laborde, 1993)

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 (7-15). 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 (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. GCLC is open source software (licence CC BY-ND).

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 (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 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 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 (CAS), and exporting and sharing via interactive HTML5, Lua, and macOS dashboard widget apps.

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") 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

Géoplan-Géospace

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: 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.

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.

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 (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