List of interactive geometry software

From Wikipedia, the free encyclopedia

Interactive geometry software (IGS, also called "dynamic geometry environments", DGEs) are computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry. 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.

Contents

[edit] History

The two historic software are Cabri and Sketchpad.

[edit] Comparison

[edit] Licence and platform

The following table provides a first comparison of the different software according to their licence and platform.

[edit] 2D Software

Software Licence Platforms
Baghera  ? Windows/?
Cabri Commercial Windows/Mac OS X
Cabri-Euclide  ? Windows/?
C.a.R. GPL Windows/Mac OS X/Linux
CaRMetal GPL Windows/Mac OS X/Linux
Chypre  ?  ?
Cinderella Commercial Windows/Mac OS X/Linux/Java
Defi  ?  ?
DrGeo GPL Linux/Mac OS X
Euklid DynaGeo Shareware Windows
Euklides Shareware Windows
Eukleides GPL Windows/Mac OS X/Linux
Gambol  ? Windows/Mac OS X/Linux
GCLC Freeware Windows/Linux
GeoGebra GPL Windows/Mac OS X/Linux
Geolog  ? Windows/?
Geometer Sketchpad Commercial Windows/Mac OS X
Geometric Supposer  ?  ?
Geometrix Freeware Windows
Geometry Expert (GEX)  ? Windows/Mac OS X/Linux
Geometry Explorer  ? Windows/Mac OS X/Linux
Geometry Expressions Commercial Windows/Mac/Linux
Geometry Tutor  ? Windows/?
GeoNext  ? Windows/Mac OS X/Linux
GeoPlan  ? Windows
GeoProof GPL Windows/Mac OS X/Linux
GeoView GPL Windows/Mac OS X/Linux
GEUP Commercial Windows
GRACE  ? Windows/Mac OS X/Linux
iGeom Freeware Linux/Windows/Mac OS X
Isard  ? Windows
Jeometry  ? Windows/Linux/Mac OS X
Kig GPL Linux
Kgeo GPL Linux
KSEG GPL Windows/Mac OS X/Linux
Mentoniezh  ?  ?
OpenEuclide GPL Windows/Linux
XCas GPL Windows/Mac OS X/Linux
WinGeom  ? Windows

[edit] 3D Software

Software Licence Platforms
Archimedes Geo3D Shareware Windows/Mac OS X/Linux
Cabri 3D Commercial Windows/Mac OS X
GeomSpace  ? Windows
GeomView LGPL Unix
Xcas GPL Windows/Mac OS X/Linux
Yenka 3D Shapes Commercial Windows

[edit] 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
CaR Yes Yes Yes Yes Yes Yes Yes Yes Yes No
Cinderella Yes Yes Yes Yes Yes Yes Yes (PDF) Yes Yes Probabilistic Several geometries, Physics simulations
GCLC Yes Yes Yes Yes Yes Yes Yes No No Yes Readable proofs, support for 3D
GeoGebra Yes Yes Yes No Yes (JavaScript) Yes (JavaScript) Yes (pstricks) Yes 35 languages No Algebraic manipulations
Geometrix Yes No Yes yes No Yes No No No Yes Interactive proof, diagram checking, labels with dynamic placeholders
GeoNext Yes No No Yes  ?  ? No  ? Yes No Available as a web app
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
Sketchpad Yes Yes Yes Yes Yes No  ? Yes (limited) Yes No Functions & function plots, symbolic differentiation, mathematical notation
Cabri 3D Yes No No Yes No No No Yes (limited) Yes No
Archimedes Geo3D Yes Yes Yes Yes No No No No No (2 Languages) No Intersection of Loci
Xcas Yes No (programs) 2-d Yes Yes No Yes No Yes No Algebraic manipulations
Software Calculations Macros Loci Animations Scripting Assignments Latex export Web export Multilingual Proofs Extra

[edit] Macros

We detail here the features related to macro constructions. (TODO)

Software Allows recursity Allows saving
GCLC Yes Yes
GeoGebra Yes Yes
iGeom Yes Yes
Kig  ? Yes
KSEG Yes Yes
Sketchpad (GSP) Yes (via Iteration) Yes
XCas Yes (programs) Yes (programs)

[edit] Loci

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
iGeom Yes No
Kig Yes No
Sketchpad (GSP) Yes No
Xcas Yes Like other parametric curves

[edit] Proof

We detail here the proof related features. (TODO)

Software Interactive Proofs Automatic Proofs Probabilist Proofs
Cinderella No Using external CAS Yes
GCLC Yes Yes No
Geometrix Yes Yes No
GeoProof Yes Yes No
iGeom No No Yes
Jeometry No Yes No
Xcas No Using built-in CAS No

[edit] Measurements and calculation

We detail here the measurements and calculation features. (TODO)

Software Arbitrary Precision Arithmetic expressions Trigonometric functions If Object existence test
Cabri Yes Yes Yes Yes No
C.a.R. No Yes Yes Yes Yes
GCLC No Yes Yes Yes Yes
GeoGebra No Yes Yes Yes Yes (JavaScript)
GeoProof Yes Yes Yes Yes No
Geometrix No Yes Yes Yes No
iGeom No Yes Yes No No
Xcas Yes Yes Yes Yes Yes

[edit] Graphics Export Formats

Software PNG BMP TIFF GIFF SWF SVG EMF Fig Postscript Pdf Latex/Eukleides Latex/Pstricks
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 Yes Yes No Yes Yes No Yes
GeoProof Yes No Yes No No No No Yes No
Kig Yes Yes Yes No Yes Yes Yes No 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

[edit] 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
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 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

[edit] 2D programs

[edit] C.a.R.

C.a.R. a free GPL analog of GSP, written in Java.

Plus:

  • Multi-platform,
  • Multi-lingual,
  • Macro-constructions,
  • Assignments (good for teachers).

Minus

  • Unfriendly measurements,
  • Unfriendly loci (trajectories).

[edit] CaRMetal

CaRMetal a free GPL software written in Java. It is derived from C.a.R and provides another user interface.

[edit] Cabri II Plus

Cabri II Plus an extended analog of GSP.

  • the more complete locus support, includes intersection of two loci.
  • compatible with TI calculators
  • based on research on education

[edit] Cinderella

Cinderella - very different from GSP, written in Java.

Plus:

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.

[edit] Euklid DynaGeo

Euklid DynaGeo[1] is a shareware analog of GSP for windows.

Minus: There is no function to create a java applet for publishing on web.

[edit] Eukleides

Eukleides[2], GPL, is a geometry drawing language.

Plus:

  • Macros
  • Layers

Minus: There is no function to create a java applet for publishing on web.

[edit] Dr Genius

Dr Genius was an attempt to merge Dr. Geo and the Genius calculator

[edit] Dr. Geo

Dr. Geo[3] is a GPL interactive software especially valuable for younger students (7-15). Now Dr. Geo II[4] complete rewrite of Dr. Geo for the Squeak/Smalltalk environment is available.

Plus:

  • Macro-constructions
  • Embedded scripting
  • Programmatically defined interactive drawing
  • Customizable interface
  • Multilingual

Minus:

  • No way to publish objects on the web

[edit] Gambol

Gambol[5] is a Euclidean, construction-based, drawing system

[edit] GCLC

GCLC[6] 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, 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.

[edit] GeoGebra

GeoGebra is free software that joins geometry, algebra and calculus for mathematics education in schools.

  • License: open source under GNU General Public License (free of charge)
  • Languages: 35
  • Geometry: points, lines, all conic sections, vectors, parametric curves, locus lines
  • Algebra: direct input of cartesian or polar coordinates, linear and quadratic equations; calculations with numbers, points and vectors
  • Calculus: direct input of functions; intersections and roots of functions; symbolic derivatives and integrals (built in CAS); sliders as parameters
  • Web Export: all constructions exportable as web pages; JavaScript interface for interactive exercises
  • Macros: usable both as tools with the mouse and as commands in the input field
  • Platforms: Mac OS, Unix/Linux, Windows (anything which supports Java 1.4.2 or later)
  • Continuity: uses a heuristic 'near-to-approach' to avoid jumping objects

[edit] Geolog

Geolog[7] is a logic programming language for finitary geometric logic.

[edit] Geometry Expressions

Geometry Expressions Does symbolic geometry.

Plus:

  • Allows algebraic input
  • Gives algebraic formulas for measurements
  • Constraints supported
  • Parametric & implicit equations of loci
  • Envelopes of lines & circles
  • Supports MathML
  • Works with computer algebra systems like Mathematica

Minus:

  • No macros

[edit] 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

[edit] Geometrix

Geometrix[8] an interactive geometry software, written in Prolog, Free Pascal (Lazarus) and Python. The new french version (3.5) is now free and is being translated into English.

Plus:

  • Allows a teacher to propose to a student a specific geometry construction exercise and then the software will check the student's diagram for accuracy.
  • Allows the teacher to program specific suggestions in written form, orally and visually via diagrams and short animations of all sort that the teacher can store and have appear at the appropriate times.
  • Can automatically generate proof exercises.
  • Allows students to do proofs and gives automatic feedback at every step along the way.
  • Dynamic labels : Yes
  • Animations : Yes
  • Loci : Yes
  • Proofs : yes
  • Assignements : Yes
  • Measurement/Calculations : Yes
  • Diagram-checking : Yes
  • No-cost software

Minus:

  • No macros
  • There is no function to create a java applet for publishing on web.

[edit] Geonext

Geonext[9] free (GPL) analog of GSP written in Java and offers a view calculus features (parametric curves, functions) as well.

[edit] The Geometric Supposer

The Geometric Supposer[10]

[edit] GeoProof

GeoProof[11] a free GPL dynamic geometry software, written in Ocaml.

Plus:

  • Can import XML files containing a description of a theorem
  • Can check if a theorem is true using automated theorem proving methods
  • Can help doing proof interactively using the Coq proof assistant
  • Can be used to produce high quality figures for latex using Eukleides export
  • Dynamic labels
  • Computation are done using arbitrary precision
  • Layers are available

Minus:

  • No locus
  • No macros
  • There is no function to create a java applet for publishing on web.

[edit] GEUP

GEUP bit more calculus-oriented analog of GSP.

  • Deterministic
  • 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

[edit] GRACE

GRACE The Graphical Ruler And Compass Editor, an analog of GSP, written in Java.

Plus: includes proof capabilities

[edit] iGeom

iGeom[12] - Interactive Geometry on Internet is a freeware software for learning and teaching Geometry (analog of GSP and Cabri), written in Java.

Plus:

  • Multi-platform,
  • Multi-lingual,
  • Macro-constructions, including recurrence (good for fractals constructions),
  • Assignments (good for teachers).

[edit] Jeometry

Jeometry is a dynamic geometry applet

[edit] Isard

Isard[13] is an interactive geometry software originally written in Smalltalk. The latest version only works under VisualWorks 7.

[edit] Kig

Kig a free (GPL) analog of GSP for KDE, bit more to calculus-oriented, part of KDE Edutainment Project.

Plus:

  • can read simple files from KGeo, KSeg, Dr. Geo and Cabri Geometry (but not very good at this so far).
  • builtin support for various types of conics, and for cubics
  • basics of differential geometry: tangent line, center of curvature, osculating circle, evolute
  • transformations include projective transformations
  • poligonal objects (including star polygons like the pentagram) with some operations such as intersection between polygons or line/polygon, convex hull, center of mass

Minus:

  • It takes more time to create the same construction than in GSP
  • application with "mode": you have to know in which mode you are (normal, constructing, moving, etc)
  • there is no function to create a java applet for publishing on web
  • no calculations

[edit] Kgeo

Kgeo[14] a free (GPL) analog of GSP for KDE, bit more too calculus-oriented, its interface is similar to Kig.

It is no more developed, replaced and improved by Kig.

[edit] KSEG

KSEG free (GPL) analog of GSP which has a few important unique features. If you plan to do some heavy, complicated constructions in Euclidean geometry this is for you.

  • Deterministic
  • 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

[edit] Non-Euclid

Non-Euclid[15] is a very basic Java-IGS only for hyperbolic geometry in the Poincaré disk and the upper half-plane models.

[edit] OpenEuclide

OpenEuclide[16] is a GPL 2D geometry software.

[edit] TracenPoche

TracenPoche[17] completely Adobe Flash program. Available only on France language

[edit] Wingeom

Wingeom[18] for high-precision geometric constructions in both two and three dimensions

[edit] 3D programs

[edit] Archimedes Geo3D

Archimedes Geo3D

[edit] Cabri 3D

Cabri 3D

[edit] Euler 3D

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.

[edit] Geomview

Geomview

[edit] PyGeo

PyGeo

[edit] JavaView

JavaView

JavaView is a 3D geometry viewer and a mathematical visualization software. You can explore miscellaneous 3D models with it.

[edit] SingSurf

SingSurf

Based on JavaView, this program can calculate and draw singular algebraic curves and surfaces.

[edit] Doorzien 4

Doorzien 4

A very simple, online applet that allows one to view and bisect a cube in 3D space.

[edit] Continuity vs. determinism

All these programs can be divided into two category: deterministic and continuous.

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 the a given point is moved.

On the contrary, some constructions in continuous programs (so far only Cinderella), 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.

[edit] Related programs

  • Cabri II Plus Plug-in
  • Cabri 3D Plug-in
  • Cabri Java
  • The Geometry Applet
  • JavaSketchpad

[edit] External links

  • 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.
    • Geometry programs list