Interactive geometry software

Interactive geometry software (IGS) are computer programs which allow one to create and then manipulate geometry constructions, primary in plane geometry. One starts construction by putting a few points and using them to define new objects (line (mathematics), circles, other points, etc). After some construction is done, one can move the points one starts with and see how the construction changes.

This article compares various IGS programs. It uses The Geometer s Sketchpad (GSP) as a comparison basis, and it describes only how each of the other programs differ from GSP. It should be mentioned that if one needs only basic ruler-and-compass construction, then there is no real difference between these programs.

=2D programs=

==C.a.R.==

.

Plus: *Multi-platform, *Multi-lingual, *Assignments (good for teachers).

Minus *No calculations (in particular you will not be able to trisect an angle), *Unfriendly measurements, *Unfriendly loci (trajectories), no way to put a point on a locus.

==Cabri Geometry==

Cabri Geometry [http://www.cabri.com/] an extended analog of GSP. The standard for Education.

Plus:

the more complete

better locus support, includes intersection of two loci.

compatible with Graphing calculator

based on research on education

Minus: the general look is a bit oldy.

==Cinderella==

.

Plus: *The #Principle_of_continuity is solved here, *Switch between elliptic geometry, hyperbolic geometry and Euclidean geometry by one click. *Two clicks gives Duality (projective geometry) diagram. *Minor pluses: **continuous angle function (can take arbitrary big values).

multi-platform.

Minus:

There is no way to do calculations (in particular you will not be able to trisect an angle).

No macro constructions,

Bit too algebraic: one can not construct a segment or arc, only lines and circles,

There is no way to hide objects,

It takes longer time to make the same construction on Cinderella than on GSP

No direct way to put a point on locus.

If you want to do non-Euclidean geometry as well then this is definitely for you.

==Drgeocaml==

.

Plus:

Can import XML files containing a description of a theorem

Can check if a theorem is true using automated theorem proving methods

Layers

Minus:

No locus

No macros

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

==Euklid DynaGeo==

Euklid DynaGeo [http://www.dynageo.com/] very reasonable analog of GSP.

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

==Euklides==

Euklides [http://www.euklides.hu/] 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

==Dr Geo==

Dr Geo [http://www.ofset.org/drgeo] very basic compass and ruler construction program GPL.

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

==Gambol==

Gambol [http://gambol.sourceforge.net/]

==GeoGebra==

GeoGebra [http://www.geogebra.at/] free analog of GSP.

==The Geometer s Sketchpad==

The Geometer s Sketchpad [http://www.keypress.com/sketchpad/] (GSP) The most popular program right now.

==The Geometric Supposer==

The Geometric Supposer. [http://cet.ac.il/math-international/software5.htm]

==GEUP==

GEUP [http://www.geup.net] bit more calculus-oriented analog of GSP.

Plus: drawing part is bit better.

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

==GRACE==

.

Plus: includes proof capabilities

==Isard==

Isard (software) [http://www.jeannot.org/~js/isard/]

==Kig==

.

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==

, bit more too calculus-oriented.

==KSEG==

) analog of GSP which has a few important unique features.

Plus: *very comfortable interface, *very fast, *support large constructions, *makes better loci. *easy to use editable macro with support for recursion, *multilingual,

Minus: *there is no direct way to put a point on locus, *there is no function to create a java applet for publishing on web.

If you plan to do some heavy, complicated constructions in Euclidean geometry this is for you.

==Geonext==

) analog of GSP written in Java and offers a view calculus features (parametric curves, functions) as well.

==Non-Euclid==

.

=3D programs=

==Cabri 3D==

Cabri 3D [http://www.cabri.com/]

==Geomview==

Geomview [http://www.geom.uiuc.edu/software/download/geomview.html]

=Principle of continuity=

Right now all IGS except Cinderella suffer from continuity problem: when you move a point in a construction points might jump or behave unexpectedly. Here is a test to check whether a particular program has such a problem:

Construct the orthocenter of triangle and three mid points (say A , B C ) between vertexes and orthocenter.

Construct a circumcircle of A B C .

This is the nine-point circle, it intersect 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 movies trough it that probably means that your program does not have Continuity problem.

=Related programs=

*The Geometry Applet [http://aleph0.clarku.edu/~djoyce/java/Geometry/Geometry.html]

*JavaSketchpad [http://www.keypress.com/sketchpad/javasketchpad/index.php]

=External links=

*Interactive geometry on web: **[http://www.cut-the-knot.org/geometry.shtml Geometry] at cut-the-knot.org. **[http://agutie.homestead.com/ Geometry from the Land of the Incas].