Daftar/Tabel -- interactive geometry software

Interactive geometry software (IGS, or dynamic geometry environments, DGEs) are computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry. In most IGS, 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 earliest IGS was the Geometric Supposer, which was developed in the early 1980s.^[1] This was soon followed by Cabri in 1986 and The Geometer's Sketchpad.

Comparison

There are three main types of computer environments for studying school geometry: supposers, dynamic geometry environments (DGEs) and Logo-based programs.^[2] Most are DGEs: software that allows the user to manipulate ("drag") the geometric object into different shapes or positions. The main example of a supposer is the Geometric Supposer, which does not have draggable objects, but allows students to study pre-defined shapes. Nearly all of the following programs are DGEs. For a related, comparative physical example of these algorithms, see Lenart Sphere.

License and platform

The following table provides a first comparison of the different software according to their licence and platform.

2D Software

3D Software

Any-dimensional Software

General features

The following table provides a more detailed comparison :

Macros

We detail here the features related to macro constructions. (TODO)

Loci

We detail here the loci features. (TODO)

Proof

We detail here the proof related features. (TODO)

Measurements and calculation

We detail here the measurements and calculation features. (TODO)

Graphics Export Formats

Software	PNG	BMP	TIFF	GIF	SWF	SVG	EMF	Fig	Postscript	Pdf	LaTeX/Eukleides	LaTeX/Pstricks	LaTeX/PGF/TikZ	Asymptote
C.a.R.	Yes	No	?	?	?	Yes	No	Yes	Yes	No	No	Yes	?	?
Cinderella	Yes	Yes	?	?	?	?	?	?	No	Yes	?	?	?	?
GCLC	No	Yes	?	?	?	Yes	No	No	Yes	No	No	Yes	?	?
GeoGebra	Yes	No	No	Yes (animated)	No	Yes	Yes	No	Yes	Yes	No	Yes	Yes	Yes
Geometry Expressions	Yes	Yes	Yes	Yes (animated)	No	No	Yes	No	Yes	No	?	?	?	?
GeoProof	Yes	No	?	?	?	Yes	No	No	No	No	Yes	No	?	?
Kig	Yes	Yes	?	?	?	Yes	No	Yes	Yes	Yes	No	Yes	?	?
KmPlot	Yes	Yes	?	?	?	Yes	?	?	?	?	?	?	?	?
KSEG	Yes	Yes	?	?	?		No	No	?	No	No	No	?	?
Geometrix	No	Yes	Yes	Yes	Yes	Yes	No	No	No	No	No	No	?	?
iGeom	No	No	No	Yes	No	No	No	No	Yes	No	No	No	?	?

Object attributes

2D programs

C.a.R.

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

CaRMetal

CaRMetal a free GPL software written in Java. It is derived from C.a.R and provides another user interface.

Cabri II Plus

Cabri II Plus an extended analog of GSP and actually the ancestor of all DGSs.

Cinderella

Cinderella - very different from GSP, written in Java.

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[1] is a shareware analog of GSP for windows.

Eukleides

Eukleides[2], GPL, is a geometry drawing language.

Dr Genius

Dr Genius was an attempt to merge Dr. Geo and the Genius calculator

Dr. Geo

Dr. Geo[3] is a GPL interactive software especially valuable for younger students (7-15). Now Dr. Geo II^[3] complete rewrite of Dr. Geo for the Squeak/Smalltalk environment is available.

Gambol

Gambol[4] is a Euclidean, construction-based, drawing system

GCLC

GCLC^[4] is a dynamic geometry tool for visualizing and teaching geometry, and for producing mathematical illustrations. In GCLC figures are described rather than drawn. This approach stresses the fact that geometrical constructions are abstract, formal procedures and not figures. A concrete figure can be generated on the basis of abstract description. There are several output formats, including LaTeX, LaTeX/PStricks, LaTeX/Tikz, SVG, PostScript. There is a built-in geometry theorem prover (based on the area method). GCLC is available for Windows and Linux. WinGCLC is a Windows version of GCLC with graphical interface and provides a range of additional functionalities.

GeoGebra

GeoGebra is free software that joins geometry, algebra and calculus for mathematics education in schools and universities.

• License: open source under GNU General Public License (free of charge)
• Languages: 55
• Geometry: points, lines, all conic sections, vectors, parametric curves, locus lines
• Algebra: direct input of inequalities, implicit polynomials, linear and quadratic equations; calculations with numbers, points and vectors
• Calculus: direct input of functions (including piecewise-defined); intersections and roots of functions; symbolic derivatives and integrals (built in CAS); sliders as parameters
• Parametric Graphs: Yes
• Implicit Polynomials: Yes
• Web Export: all constructions exportable as web pages; JavaScript interface for interactive exercises
• Macros: usable both as tools with the mouse and as commands in the input field
• Animation: Yes
• Spreadsheet: Yes, the cells can contain any GeoGebra object (Numbers, Points, Functions etc.)
• Dynamic text: Yes (including LaTeX)
• Platforms: Mac OS, Unix/Linux, Windows (anything which supports Java 1.5 or later)
• Continuity: uses a heuristic 'near-to-approach' to avoid jumping objects

Geolog

Geolog^[5] is a logic programming language for finitary geometric logic.

Geometry Expressions

Geometry Expressions ^[6] Does symbolic geometry. It uses real symbolic inputs and returns real and symbolic outputs. An emphasis is placed on use with CAS, as well as export and sharing via interactive HTML5, Lua, and OSX dashboard widget apps.

The Geometer's Sketchpad

The Geometer's Sketchpad (GSP)

• Deterministic
• Languages: English, Spanish, Danish, Russian, Korean, Thai, Traditional and Simplified Chinese, French, Lithuanian (current version); others (older versions).
• Macros: Yes ("custom tools" and "scripts")
• Java-applet: Yes
• Animation: Yes
• Locus: Yes, including point on locus
• Assignments: No
• Measurement/Calculations: Yes
• Platform: Windows, Mac OS, TI-92+, works under wine
• Proofs: No

Geometrix

Geometrix[5] a free interactive geometry software, written in Prolog and Free Pascal (Lazarus).

• In December 2011, a new inference engine is implemented, it allows Geometrix to reason while the student is constructing the figure so that he can be aware of all the demonstrable proposals. This feature is also available while he is doing exercises even though the software is checking the construction of the student.
• 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.
• Automatic coding of the figure. Can produce conjectures.
• Dynamic labels.
• Animations.
• Loci.
• Proofs.
• Assignments.
• Measurement/Calculations.
• Diagram-checking.
• No-cost software

Geonext

Geonext [6] 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^[7]

Géoplan-Géospace

GeoProof

GeoProof^[8] a free GPL dynamic geometry software, written in OCaml.

GEUP

GEUP bit more calculus-oriented analog of GSP.

• Deterministic
• Languages: English, French, German, Italian, Portuguese, 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.

iGeom

iGeom[7] - Interactive Geometry on Internet is a freeware software for learning and teaching Geometry (analog of GSP and Cabri), written in Java.

Jeometry

Jeometry is a dynamic geometry applet

Isard

Isard^[9] is an interactive geometry software originally written in Smalltalk. The latest version only works under VisualWorks 7.

Kig

Kig a free (GPL) analog of GSP for KDE, bit more to calculus-oriented, part of KDE Edutainment Project.

Kgeo

Kgeo[8] a free (GPL) analog of GSP for KDE, bit more too calculus-oriented, its interface is similar to Kig.

It is no more developed, replaced and improved by Kig.

KmPlot

KmPlot[9] is a mathematical function plotter released under the free (GPL). Includes a powerful parser and precision printing in correct scale. Simultaneously plot multiple functions and combine function terms to build new functions. Supports functions with parameters and functions in polar coordinates. Several grid modes are available.

• powerful mathematical parser
• precise metric printing
• different plot types (functions, parametric, polar)
• highly configurable visual settings (plot line, axes, grid)
• export to bitmap format (BMP and PNG) and scalable vector graphics (SVG)
• save/load complete session in readable xml format
• trace mode: cross hair following plot, coordinates shown in the status bar
• zooming support
• ability to draw the 1st and 2nd derivative and the integral of a plot function
• support user defined constants and parameter values
• various tools for plot functions: find minium/maximum point, get y-value and draw the area between the function and the y-axis

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, Mac OS (anything which supports Qt)
• Proofs: No
• Extra: Editable

Non-Euclid

Non-Euclid^[10] is a very basic Java-IGS only for hyperbolic geometry in the Poincaré disk and the upper half-plane models.

OpenEuclide

OpenEuclide^[11] is a GPL 2D geometry software.

Sphaerica

Sphaerica^[12] is an open source geometry software for spherical geometry.

Live Geometry

Live Geometry [10] is a free codeplex project that lets you create interactive ruler and compass constructions and experiment with them. It is written with Silverlight 4 and C# 4.0 (Visual Studio 2010). The core engine is a flexible and extensible framework that allows you to easily add new figure types and features. The project has two front-ends: WPF and Silverlight; they both share the common DynamicGeometry library.

TracenPoche

TracenPoche[11] completely Adobe Flash program. Available in French,English and Spanish.

Tabula

Tabula is a commercial dynamic geometry program created by Numeracy Works. Tabula supports hands-on learning and can be used to construct, cut, tape, fold, measure, and transform geometric figures. Built using Silverlight, it is both MacOS and Windows compatible.

Tabulae

Tabulae [12] is a dynamic geometry software written in Java. Under development from Federal University of Rio de Janeiro. Available in Brazilian Portuguese.

Wingeom

Wingeom^[13] for high-precision geometric constructions in both two and three dimensions

3D programs

Archimedes Geo3D

Archimedes Geo3D

Cabri 3D

Cabri 3D v2

Euler 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.

Geometria

Geometria is free (GPL) cross-platform software based on a two-role (teacher, student) model. The teacher creates a problem, provides it with an answer and saves the problem in a file. The student opens the file and solves the problem. The student's actions are recorded. The teacher plays back the solution and grades it. The figures are limited to convex polyhedra, which can be measured, drawn upon, transformed, cut and joined.

Geomview

Geomview

GEUP 3D

GEUP 3D

PyGeo

PyGeo

JavaView

JavaView

JavaView is a 3D geometry viewer and a mathematical visualization software. You can explore miscellaneous 3D models with it.

SingSurf

SingSurf

Based on JavaView, this program can calculate and draw singular algebraic curves and surfaces.

Any-dimensional programs

SpaceFuncs

a cross-platform (Linux, Windows, Mac etc.) completely free (license: BSD) Python language module for 2D, 3D, N-dimensional space calculations with abilities of

• parametrized modeling (using FuncDesigner)
• performing numerical optimization and solving geometrical systems of equations (possibly parametrized) by OpenOpt, using FuncDesigner automatic differentiation, that yields more precise (and very often faster) results than finite-differences derivatives approximation
• some graphic output using Matplotlib (any other Python graphic visualization library from the variety can be easily connected).

Continuity vs. determinism

All these programs can be divided into two category: deterministic and continuous. GeoGebra can be deterministic or continuous (one can change it in preferences).

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 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 midpoints (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 midpoint 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.^[14]

See also

• Mathematical software
• Constructive solid geometry

References

External links

• A Perbandingan -- Geometry Software for the Classroom