Interactive geometry software

Encyclopedia : I : IN : INT : Interactive geometry software

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 (lines, 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 compass and straightedge construction, then there is no real difference between these programs.

Contents

2D programs

C.a.R.

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

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 [link] an extended analog of GSP. The standard for Education.

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 [link] - 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.

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.

Euklid DynaGeo

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

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

Euklides

Euklides [link] 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 [link] is a GPL interactive software especially valuable for younger students (7-15)

Plus:

Macro-construction

Embedded scripting

Programmaticaly defined interactive drawing

Customizable interface

Multilingual

Minus:

Less advanced geometry, compared to Kig or GeoGebra

No way to publish objects on the web

Gambol

Gambol [link] ???

GeoGebra

GeoGebra [link] А free software analog of GSP.

Plus:

Continuity problem solved
Multi-platform
Multi-lingual
Free tutorials
Teacher sharing resources

Minus:

No macros

Geometry Expressions

Geometry Expressions [link] Does symbolic geometry.

Plus:

Allows algebraic input
Gives algebraic formulas for measurements
Constraints supported
Parametric & implicit equations of loci
Envelopes of lines & circles

Minus:

No macros

The Geometer's Sketchpad

The Geometer's Sketchpad [link] (GSP) The most popular program right now (in USA).

Geometrix

Geometrix [link] a free interactive geometry software, written in Prolog, Python and VB.

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
Can build Flash animations

Minus:

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

Geonext

Geonext [link] 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. [link]

GeoProof

GeoProof [link] 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
Layers are available

Minus:

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

GEUP

GEUP [link] bit more calculus-oriented analog of GSP.

Plus:

very comfortable interface.
very fast.
makes better loci.
drawing part is bit better.
Multilingual.

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

GRACE

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

Plus: includes proof capabilities

Isard

Isard [link] ???

Kig

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

KSEG

KSEG [link] free (GPL) 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,
functions cannot be plotted,
texts cannot be put in.

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

Non-Euclid

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

3D programs

Cabri 3D

Cabri 3D [link]

Euler 3D

Euler 3D [link]

Allows you to make and manipulate your own polyhedrons.

Geomview

Geomview [link]

PyGeo

PyGeo [link]

JavaView

JavaView [link]

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 hiden 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 continuousely 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

Cabri Java [link]

The Geometry Applet [link]

JavaSketchpad [link]

External links

Interactive geometry on web:
* [Geometry] at cut-the-knot
* [Geometry from the Land of the Incas].

From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating.
All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.