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.

Contents

1 Programs 1.1 C.a.R. 1.2 Cabri Geometry 1.3 Cinderella 1.4 Euklid DynaGeo 1.5 Euklides 1.6 Dr genius 1.7 Dr Geo 1.8 Gambol 1.9 The Geometer's Sketchpad 1.10 The Geometric Supposer 1.11 GEUP 1.12 Isard 1.13 Kig 1.14 Kgeo 1.15 KSEG 1.16 Non-Euclid 2 Principle of continuity 3 Related programs 4 External links

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] an extended analog of GSP.

Plus: better locus support, includes intersection of two loci.

Minus: interface is a bit unfriendly.

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.

Euklid DynaGeo

Euklid DynaGeo [4] 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 [5] very basic compass and ruler construction program GPL.

Gambol

Gambol [6] ???

The Geometer's Sketchpad

The Geometer's Sketchpad [7] (GSP) The most popular program right now.

The Geometric Supposer

The Geometric Supposer [8] ???

GEUP

GEUP [9] very basic, bit more calculus-oriented analog of GSP.

Plus: drawing part is bit better.

Minus: a lot.

Isard

Isard [10] ???

Kig

Kig [11] 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 [12] a free (GPL) analog of GSP for KDE, bit more too calculus-oriented. ???

KSEG

KSEG [13] 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.

Non-Euclid

Non-Euclid [14] 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 [15]

• JavaSketchpad [16]

External links

• Interactive geometry on web:
  • Geometry at cut-the-knot.org.
  • Geometry from the Land of the Incas.