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.
History
The two historic software are Cabri and Sketchpad.
Comparison
Licence and platform
The following table provides a first comparison of the different software according to their licence and platform.
| Software | Dimensions | Licence | Platforms |
|---|---|---|---|
| Baghera | ? | ? | Windows/? |
| Cabri | 2D | Commercial | Windows/MacOSX |
| Cabri-Euclide | 2D | ? | Windows/? |
| Cabri 3D | 3D | Commercial | Windows/MacOSX |
| CaR | 2D | GPL | Windows/MacOSX/Linux |
| CaRMetal | 2D | GPL | Windows/MacOSX/Linux |
| Chypre | 2D | ? | ? |
| Defi | 2D | ? | ? |
| Cinderella | 2D | Commercial | Windows/? |
| DrGeo | 2D | GPL | Linux/MacOSX |
| Euklides | 2D | Shareware | Windows |
| Eukleides | 2D | GPL | Windows/MacOSX/Linux |
| GCLC | 2D | ? | Windows/Linux |
| Geogebra | 2D | GPL | Windows/MacOSX/Linux |
| Geolog | 2D | ? | Windows/? |
| Geometer Sketchpad | 2D | Commercial | Windows/MacOSX |
| Geometrix | 2D | Freeware | Windows |
| Geometry Expert | 2D | ? | Windows |
| Geometry Explorer | 2D | ? | Windows/MacOSX/Linux |
| Geometry Expressions | 2D | Commercial | Linux |
| Geometry Tutor | 2D | ? | Windows/? |
| GeomView | 3D | ? | Windows/MacOSX |
| GeoNext | 2D | ? | Windows/MacOSX/Linux |
| GeoProof | 2D | GPL | Windows/MacOSX/Linux |
| GeoView | 2D | GPL | Windows/MacOSX/Linux |
| GEUP | 2D | Commercial | Windows |
| Kig | 2D | GPL | Linux |
| Kgeo | 2D | GPL | Linux |
| KSEG | 2D | GPL | Windows/MacOSX/Linux |
| Mentoniezh | 2D | ? | ? |
General features
The following table provides a more detailed comparison :
| Software | Calculations | Macros | Locus | Animations | Scripting | Assignments | Latex export | Web export | Multilingual | Proofs | Extra |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Cabri | Yes | Yes | Yes | Yes | ? | No | ? | Yes | Yes | No | Available on TI Calculator |
| CaR | Yes | Yes | Yes | Yes | Yes | Yes | Yes | Yes | Yes | No | |
| Cinderella | Yes | Yes | Yes | ? | ? | No | ? | ? | Yes | Probabilist | Several geometries |
| GeoGebra | Yes | No | Yes | No | No | No | ? | Yes | Yes | No | Algebric manipulations |
| Geometrix | Yes | No | Yes | yes | ? | Yes | ? | ? | ? | Yes | Interactive proof |
| 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 |
| Kig | Yes | Yes | Yes | Yes | Yes | No | ? | ? | Yes | No | |
| Sketchpad | Yes | Yes | Yes | Yes | Yes | No | ? | Yes | Yes | No |
Macros
We detail here the features related to macro constructions. (TODO)
| Software | Allows recursity | Allows saving |
|---|---|---|
| Kig | ? | Yes |
| KSEG | Yes | Yes |
Loci
We detail here the loci features. (TODO)
| Software | Take a point of a locus | Intersection of two loci |
|---|---|---|
| Cabri | Yes | Yes |
Proof
We detail here the proof related features. (TODO)
| Software | Interactive Proofs | Automatic Proofs | Probabilist Proofs |
|---|---|---|---|
| Cinderella | No | Using external CAS | Yes |
| Geometrix | Yes | No | No |
| GeoProof | Yes | Yes | No |
Measurements and calculation
We detail here the measurements and calculation features. (TODO)
2D programs
C.a.R.
C.a.R. a free GPL analog of GSP, written in Java.
Plus:
- Multi-platform,
- Multi-lingual,
- Assignments (good for teachers).
Minus
- Unfriendly measurements,
- Unfriendly loci (trajectories), no way to put a point on a locus.
CaRMetal
CaRMetal a free GPL software written in Java. It is derived from C.a.R and provides another user interface.
Cabri Geometry
Cabri Geometry an extended analog of GSP. Plus:
- the more complete better locus support, includes intersection of two loci.
- compatible with TI calculators
- based on research on education
Minus: the general look is a bit oldy.
Cinderella
Cinderella - very different from GSP, written in Java.
Plus:
- The continuity problem is solved here,
- Switch between elliptic, hyperbolic and Euclidean geometry by one click.
- Two clicks gives projective dual diagram.
- Minor pluses:
- continuous angle function (can take arbitrary big values).
- multi-platform.
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.
Euklid DynaGeo
Euklid DynaGeo is a shareware analog of GSP for windows.
Minus: There is no function to create a java applet for publishing on web.
Eukleides
Eukleides, GPL, is a bit more calculus-oriented analog of GSP.
Plus:
- Macros
- Layers
Minus: There is no function to create a java applet for publishing on web.
Dr Genius
Dr Genius was an attempt to merge Dr. Geo and the Genius calculator
Dr. Geo
Dr. Geo is a GPL interactive software especially valuable for younger students (7-15)
Plus:
- Macro-constructions
- Embedded scripting
- Programmaticaly defined interactive drawing
- Customizable interface
- Multilingual
Minus:
- No way to publish objects on the web
Gambol
Gambol ???
GeoGebra
- Continuous
- Languages: Catalan, Chinese, Danish, Dutch, English, French, German, Italian, Norwegian, Portuguese, Slovenian, Spanish
- Macros: No
- Java-applet: Yes
- Animation: No?
- Locus: Yes, No direct way to put point on locus.
- Assignments: No
- Measurement/Calculations: Yes
- Platform: MacOS, Unix/Linux, Windows (anythig which supports Java)
- Proofs: No
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 and Maple
Minus:
- No macros
The Geometer's Sketchpad
The Geometer's Sketchpad (GSP)
- Deterministic
- Languages: English, Spanish.
- Macros: Yes
- Java-applet: Yes
- Animation: Yes
- Locus: Yes, direct way to put point on locus?
- Assignments: No
- Measurement/Calculations: Yes
- Platform: Windows, MacOS, works under wine
- Proofs: No
Geometrix
Geometrix an interactive geometry software, written in Prolog, Python and VB. The new french version (3.0) 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.
- Layers : 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.
Geonext
Geonext free (GPL) analog of GSP written in Java and offers a view calculus features (parametric curves, functions) as well.
The Geometric Supposer
The Geometric Supposer.
GeoProof
GeoProof 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.
GEUP
GEUP bit more calculus-oriented analog of GSP.
- Deterministic
- Languages: English, Spanish.
- Macros: Yes
- Java-applet: No
- Animation: Yes
- Locus: Yes / point on locus
- Assignments: No
- Measurement/Calculations: Yes
- Platform: Windows
- Proofs: No
GRACE
GRACE The Graphical Ruler And Compass Editor, an analog of GSP, written in Java.
Plus: includes proof capabilities
Isard
Isard ???
Kig
Kig a free (GPL) analog of GSP for KDE, bit more to calculus-oriented, part of KDE Edutainment Project, its interface is similar to Kgeo.
Plus:
- can read simple files from KGeo, KSeg, Dr. Geo and Cabri Geometry (but not very good at this so far).
Minus:
- It takes more time to create the same construction than in GSP,
- there is no function to create a java applet for publishing on web,
- no measurements,
- no calculations.
Kgeo
Kgeo a free (GPL) analog of GSP for KDE, bit more too calculus-oriented, its interface is similar to Kig.
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, MacOS (anything which supports Qt)
- Proofs: No
- Extra: Editable
Non-Euclid
Non-Euclid is a very basic Java-IGS only for hyperbolic geometry in the Poincaré disk and the upper half-plane models.
OpenEuclide
OpenEuclide is a GPL 2D geometry software.
Wingeom
3D programs
Cabri 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.
Geomview
PyGeo
JavaView
JavaView is a 3D geometry viewer and a mathematical visualization software. You can explore miscellaneous 3D models with it.
SingSurf
Based on JavaView, this programm can calculate and draw singular algebraic curves and surfaces.
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 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 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.
Related programs
External links
- Interactive geometry on web: