Interactive geometry software
Interactive geometry software (IGS) allows you to create and then manipulate geometric constructions, primary in plane geometry. You start construction by putting few points and use them to define new objects (lines, circles, other points and so no). Then you can move points you start with and see how your construction changes.
We use The Geometer's Sketchpad (GSP) as basis and describe only how each program differ from GSP. If you will need only basic ruler-and-compass construction, then there is no real difference between these programs for you.
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Programs
C.a.R.
C.a.R. [1] 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 [2]
- Geometry and Mathematics teaching software based upon Cabri technology. - Software products derived from Cabri technology designed for public use.
Cinderella
Cinderella [3] - 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.
Drgeocaml
Drgeocaml [4] a free GPL analog of GSP, written in Ocaml.
Plus:
- Can import xml files containing a description of a theorem
Minus:
- No locus
- No macros
- There is no function to create a java applet for publishing on web.
Euklid DynaGeo
Euklid DynaGeo [5] very reasonable analog of GSP.
Euklides
Euklides very basic, bit more calculus-oriented analog of GSP.
Minus: very slow and lot more.
Dr genius
Dr genius ???
Dr Geo
Dr Geo [6] very basic compass and ruler construction program GPL.
Gambol
Gambol [7] ???
The Geometer's Sketchpad
The Geometer's Sketchpad [8] (GSP) The most popular program right now.
The Geometric Supposer
The Geometric Supposer. [9]
GEUP
GEUP [10] very basic, bit more calculus-oriented analog of GSP.
Plus: drawing part is bit better.
Minus: a lot.
Isard
Isard [11] ???
Kig
Kig [12] 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).
Minus:
- It takes more time to create the same construction than in GSP,
- there is no function to create a java applet for publishig on web,
- no measurements,
- no calculations.
Kgeo
Kgeo [13] a free (GPL) analog of GSP for KDE, bit more too calculus-oriented. ???
KSEG
KSEG [14] free (GPL) analog of GSP which has 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
Geonext [15] free (GPL) analog of GSP written in Java and offers a view claculus features (paramteric curves, functions) as well.
Non-Euclid
Non-Euclid [16] is a very basic Java-IGS only for Hyperbolic Geometry in the Poincaré disk and the upper half-plane models.
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 [17]
- JavaSketchpad [18]
External links
- Interactive geometry on web:
- Geometry at cut-the-knot.org.
- Geometry from the Land of the Incas.