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词条 List of interactive geometry software
释义

  1. History

  2. Comparison

      License and platform    3D Software    General features    Macros    Loci    Proof    Measurements and calculation    Graphics export formats    Object attributes  

  3. 2D programs

      C.a.R.    CaRMetal    Cinderella    Dr Genius    Dr. Geo    GCLC    GeoGebra    GeoKone.NET    Geolog    Geometry Expressions    The Geometer's Sketchpad    The Geometric Supposer    Géoplan-Géospace    GeoProof    GEUP    GRACE    iGeom    Isard    Jeometry    Kig    Kgeo    KmPlot    KSEG   Live Geometry    Non-Euclid    OpenEuclide    Sarit2d    Sphaerica    Tabula    Tabulae    TracenPoche    Wingeom  

  4. 3D programs

     Archimedes Geo3D  Ganja.js  Euler 3D  Geomview 

  5. Continuity versus determinism

  6. See also

  7. References

  8. External links

{{lead too short|date=September 2009}}

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{{vague|date=July 2018}}, 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.

Software Cost (USD) Licence Platforms
Cabri Geometry {{dunno}} {{Proprietary}} Windows, Mac OS X
C.a.R. {{Free}}GPL}} Windows, Linux, Mac OS X
CaRMetal {{Free}}GPL}} Windows, GNU Linux, Mac OS X
Cinderella 1.4 {{Free}} {{Proprietary}} Windows, Linux, Mac OS X (Java)
Cinderella 2.0 69 US$ {{Proprietary}} Windows, Linux, Mac OS X (Java)
DrGeo {{Free}}GPL}} Windows, Linux, Mac OS X
GeoGebra {{Free}}GPL}} Windows, Linux, Mac OS X
The Geometer's Sketchpad 70.02 US$ {{Proprietary}} Windows, Mac OS X (Java)
Geometry Expert (GEX) {{dunno}} {{dunno}} Windows, Linux, Mac OS X
GEUP {{dunno}} {{Proprietary}} Windows
Kig {{Free}}GPL}} Linux
KSEG {{Free}}GPL}} Windows, Linux, Mac OS X
WIRIS {{dunno}} {{Proprietary}} Linux, Windows, Mac OS X (Java)

3D Software

Software Cost (USD) Licence Platforms
Archimedes Geo3DShareware}} {{Proprietary}} Windows/Mac OS X/Linux
GeoGebra (from version 5.0 Beta) {{Free}}GPL}} Windows, Linux, Mac OS X, Android, iOS, Windows RT
Yenka 3D ShapesFree for non-commercial use}} {{Proprietary}} Windows
WIRIS {{dunno}} {{Proprietary}} Windows, Linux, Mac OS X

General features

The following table provides a more detailed comparison :

Software Calculations Macros Loci Animations Scripting Assignments LaTeX export Web export Multilingual Proofs Extra
Cabri II Plus {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} (with plug-in) {{No}} {{Yes}} {{Yes}} {{Yes}} (on relations) Available on TI Calculator
Calques 3D {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}} {{No}} {{No}} {{No}} {{Yes}} (FRA ENG DEU ESP PTG) {{Yes}} (on relations) Experimental connection with some CAS
CaR {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}} {{dunno}}
CaRMetal {{Yes}} (recursive) {{Yes}} {{Yes}} {{Yes}} (multiple) {{Yes}} (JavaScript) {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} (probabilistic) Amodality, folder system, the Monkey
Cinderella {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} (PDF) {{Yes}} {{Yes}} Probabilistic Several geometries, Physics simulations
Ganja.js {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{no}} {{Yes}} {{no}} {{no}} 2D and 3D, projective and conformal, Geometric Algebra.
GCLC {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}} {{No}} {{Yes}} Readable proofs, support for 3D
GeoGebra {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} (JavaScript) {{No}} {{Yes}} (PSTricks & PGF/TikZ) {{Yes}} {{Yes}} (55 languages) {{Yes}} CAS, HTML5 Export (from version 4.2)
3D & Automatic Proof (from version 5.0)
Geometria {{Yes}} {{No}} {{Yes}} {{Yes}} {{No}} {{Yes}} {{No}} {{Yes}} {{Yes}} {{No}} Two-role (teacher, student) model
Geometrix {{Yes}} {{No}} {{Yes}} {{Yes}} {{No}} {{Yes}} {{No}} {{No}} {{Yes}} {{Yes}} Interactive proof, diagram checking, teacher/student models, labels with dynamic placeholders
Geometry Expressions {{Yes}} {{No}} {{Yes}} {{Yes}} {{No}} {{No}} {{Yes}} {{Yes}} (Interactive HTML5/JS Apps) {{Yes}} {{No}} Symbolic calculations, which can be copied as input for CAS, TeX, and source code in 21 formats/languages. Functions. Arcs on any function or curve. Website for exported HTML5 Canvas and JavaScript Interactive Apps (Euclid's Muse).
GeoNext {{Yes}} {{No}} {{No}} {{Yes}} {{dunno}} {{dunno}} {{No}} {{dunno}} {{Yes}} {{No}} Available as a web app
Géoplan-Géospace {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}} {{No}} {{Yes}} (activeX) {{Yes}} {{Yes}} Sequences, 2D & 3D, human readable file format
GeoProof {{Yes}} {{No}} {{No}} {{No}} {{No}} {{No}} {{Yes}} {{No}} {{No}} {{Yes}} Automatic formal proofs
GEUP {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{dunno}} {{No}} {{dunno}} {{No}} {{Yes}} {{No}} {{dunno}}
iGeom {{Yes}} {{Yes}} {{Yes}} {{No}} {{Yes}} {{Yes}} {{No}} {{Yes}} {{Yes}} Probabilist Recurrent scripts
Kig {{Yes}} {{Yes}} {{Yes}} {{No}} {{Yes}} (Python) {{No}} {{Yes}} (PSTricks) {{No}} {{Yes}} {{No}} Labels with dynamic placeholders
Live Geometry {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}} {{No}} {{No}} {{No}} {{No}} {{No}} Includes player.
Sarit2d {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}} {{Yes}}Avalaible on web
Sketchpad {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}} {{dunno}} {{Yes}} (limited) {{Yes}} {{No}}Functions & function plots, symbolic differentiation, mathematical notation
Tabula {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}} {{No}} {{No}} {{No}} {{No}} {{No}} Folding, cutting, taping, marker, and working instrument models.
Tabulae {{Yes}} {{Yes}} {{Yes}} {{No}} {{No}} {{No}} {{No}} {{Yes}} {{Yes}} {{No}} Collaborative sessions over the internet.
Cabri 3D {{Yes}} {{No}} {{No}} {{Yes}} {{No}} {{No}} {{No}} {{Yes}} (limited) {{Yes}} {{No}} {{dunno}}
Archimedes Geo3D {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}} {{No}} {{No}} {{No}} {{No}} (Eng De Fr) {{No}} Intersection of Loci
GEUP 3D {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}} {{No}} {{No}} {{No}} {{Yes}} {{No}} {{dunno}}
Netpad {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}} {{No}} {{No}} {{Yes}} {{No}} {{Yes}} Base on Web
Software Calculations Macros Loci Animations Scripting Assignments LaTeX export Web export Multilingual Proofs Extra

Macros

Features related to macro constructions: (TODO)

Software Allows recursity Allows saving
Cabri II Plus {{Yes}} {{Yes}}
Calques 3D {{No}} {{Yes}}
GCLC {{No}} {{No}}
GeoGebra {{Yes}} {{Yes}}
Géoplan-Géospace {{Yes}} {{Yes}}
GEUP {{Yes}} {{Yes}}
iGeom {{Yes}} {{Yes}}
Kig {{dunno}} {{Yes}}
KSEG {{Yes}} {{Yes}}
Sketchpad (GSP) {{Yes}} (via Iteration) {{Yes}}

Loci

Loci features related to IGS: (TODO)

Software Take a point of a locus Intersection of two loci
Cabri II Plus {{Yes}} {{Yes}}
Calques 3D {{No}} {{No}}
CaR {{Yes}} {{Yes}}
GeoGebra {{Yes}} {{No}}
Géoplan-Géospace {{Yes}} {{No}}
GEUP {{Yes}} {{Yes}}
iGeom {{Yes}} {{No}}
Kig {{Yes}} {{No}}
Sketchpad (GSP) {{Yes}} {{No}}
NetPad {{Yes}} {{Yes}}

Proof

We detail here the proof related features. (TODO)

Software Interactive Proofs Automatic Proofs Probabilist Proofs
Cabri II Plus Feedback for {{No}} {{Yes}} in Cabri I
Cinderella {{No}} Using external CAS {{Yes}}
GCLC {{No}} {{Yes}} {{No}}
GeoGebra {{Yes}} {{Yes}} {{No}}
Geometrix {{Yes}} {{Yes}} {{No}}
Géoplan-Géospace {{No}} {{No}} {{Yes}}
GeoProof {{Yes}} {{Yes}} {{No}}
iGeom {{No}} {{No}} {{Yes}}
Jeometry {{No}} {{Yes}} {{No}}
NetPad {{Yes}} {{Yes}} {{dunno}}

Measurements and calculation

Measurement and calculation features related to IGS: (TODO)

Software Arbitrary Precision Arithmetic expressions Trigonometric functions If Object existence test
Cabri {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}}
Calques 3D {{No}} {{Yes}} {{Yes}} {{No}} {{No}}
C.a.R. {{No}} {{Yes}} {{Yes}} {{Yes}} {{Yes}}
GCLC {{No}} {{Yes}} {{Yes}} {{Yes}} {{Yes}}
GeoGebra {{No}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} (JavaScript)
Geometria {{No}} {{Yes}} {{Yes}} {{No}} {{No}}
Géoplan-Géospace {{No}} {{Yes}} {{Yes}} {{Yes}} (µ function) {{No}}
GeoProof {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}}
Geometrix {{No}} {{Yes}} {{Yes}} {{Yes}} {{No}}
iGeom {{No}} {{Yes}} {{Yes}} {{No}} {{No}}
NetPad {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}}

Graphics export formats

Software PNG BMP TIFF GIF SWF SVG EMF Fig Postscript Pdf LaTeX/Eukleides LaTeX/Pstricks LaTeX/PGF/TikZ Asymptote
Calques 3D {{No}} {{No}} {{No}} {{No}} {{No}} {{No}} {{No}} {{Yes}} {{No}} {{No}} {{No}} {{No}} {{No}} {{No}}
C.a.R. {{Yes}} {{No}} {{dunno}} {{dunno}} {{dunno}} {{Yes}} {{No}} {{Yes}} {{Yes}} {{No}} {{No}} {{Yes}} {{dunno}} {{dunno}}
Cinderella {{Yes}} {{Yes}} {{dunno}} {{dunno}} {{dunno}} {{dunno}} {{dunno}} {{dunno}} {{No}} {{Yes}} {{dunno}} {{dunno}} {{dunno}} {{dunno}}
GCLC {{No}} {{Yes}} {{dunno}} {{dunno}} {{dunno}} {{Yes}} {{No}} {{No}} {{Yes}} {{No}} {{No}} {{Yes}} {{dunno}} {{dunno}}
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}} {{dunno}} {{dunno}} {{dunno}} {{dunno}}
GeoProof {{Yes}} {{No}} {{dunno}} {{dunno}} {{dunno}} {{Yes}} {{No}} {{No}} {{No}} {{No}} {{Yes}} {{No}} {{dunno}} {{dunno}}
Kig {{Yes}} {{Yes}} {{dunno}} {{dunno}} {{dunno}} {{Yes}} {{No}} {{Yes}} {{Yes}} {{Yes}} {{No}} {{Yes}} {{dunno}} {{dunno}}
KmPlot {{Yes}} {{Yes}} {{dunno}} {{dunno}} {{dunno}} {{Yes}} {{dunno}} {{dunno}} {{dunno}} {{dunno}} {{dunno}} {{dunno}} {{dunno}} {{dunno}}
KSEG {{Yes}} {{Yes}} {{dunno}} {{dunno}} {{dunno}} {{No}} {{No}} {{dunno}} {{No}} {{No}} {{No}} {{dunno}} {{dunno}}
Geometrix {{No}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}} {{No}} {{No}} {{No}} {{No}} {{No}} {{dunno}} {{dunno}}
iGeom {{No}} {{No}} {{No}} {{Yes}} {{No}} {{No}} {{No}} {{No}} {{Yes}} {{No}} {{No}} {{No}} {{dunno}} {{dunno}}

Object attributes

Software Color Filled/Not filled Width Transparency Shown/Hidden Layer Shape of points Type of line
Cabri {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}} {{Yes}} {{Yes}}
Calques 3D {{Yes}} {{Yes}} {{Yes}} {{No}} {{Yes}} {{Yes}} {{Yes}} {{Yes}}
C.a.R. {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}}
GCLC {{Yes}} {{Yes}} {{Yes}} {{No}} {{Yes}} {{No}} {{Yes}} {{Yes}}
GeoGebra {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}}
Geometria {{Yes}} {{Yes}} {{No}} {{Yes}} {{Yes}} {{Yes}} {{No}} {{Yes}}
Geometry Expressions {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}} (but size) {{Yes}}
Géoplan-Géospace {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}} {{Yes}} {{Yes}}
Kig {{Yes}} {{Yes}} {{Yes}} {{No}} {{Yes}} {{No}} {{Yes}} {{Yes}}
GeoProof {{Yes}} {{No}} {{Yes}} {{No}} {{Yes}} {{Yes}} {{Yes}} {{Yes}}
Geometrix {{Yes}} {{Yes}} {{Yes}} {{No}} {{Yes}} {{No}} {{Yes}} {{Yes}}
iGeom {{Yes}} {{Yes}} {{Yes}} {{No}} {{Yes}} {{No}} {{No}} {{Yes}}
Sketchpad {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{dunno}} {{Yes}} {{Yes}}
NetPad {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{Yes}} {{No}} (but size) {{Yes}}

2D programs

C.a.R.

C.a.R. is a free GPL analog of The Geometer's Sketchpad (GSP), written in Java.

CaRMetal

CaRMetal is a free GPL software written in Java. Derived from C.a.R., it provides a different user interface.

Cinderella

Cinderella, written in Java, is very different from The Geometer's Sketchpad. The later version Cinderella.2 also includes a physics simulation engine and a scripting language. Also, it now{{when?|date=July 2018}} supports macros, line segments, calculations, arbitrary functions, plots, etc. Full documentation is available online.

Dr Genius

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

Dr. Geo

Dr. Geo [https://web.archive.org/web/20080303211301/http://www.ofset.org/drgeo] is a GPL interactive software intended for younger students (7-15). The later version, Dr. Geo II,[3] is a complete rewrite of Dr. Geo, for the Squeak/Smalltalk environment.

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 the abstract description. There are several output formats, including LaTeX, LaTeX/PStricks, LaTeX/Tikz, SVG and 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 a graphical interface that provides a range of additional functionalities.

GeoGebra

GeoGebra is software that combines geometry, algebra and calculus for mathematics education in schools and universities. It is available free of charge for non-commercial users. [5]
  • License: open source under GPL 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 as a Java applet
  • 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 (any platform that supports Java 1.5 or later)
  • Continuity: uses a heuristic 'near-to-approach' to avoid jumping objects

GeoKone.NET

GeoKone.NET[6] is an interactive recursive natural geometry (or "sacred geometry") generator that runs in a web browser. GeoKone allows the user to create geometric figures using naturalistic rules of recursive copying, such as the Golden ratio.

Geolog

Geolog[7] is a logic programming language for finitary geometric logic.

Geometry Expressions

Geometry Expressions[8] Does symbolic geometry. It uses real symbolic inputs and returns real and symbolic outputs. It emphasises use with a Computer Algebra System (CAS), as well as exporting and sharing via interactive HTML5, Lua, and OS X 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

The Geometric Supposer

{{Expand section|date=November 2013}}The Geometric Supposer[9]

Géoplan-Géospace

{{Expand section|date=July 2018}}

GeoProof

GeoProof[10] is a free GPL dynamic geometry software, written in OCaml.

GEUP

GEUP is a more calculus-oriented analog of The Geometer's Sketchpad.

  • Deterministic
  • Languages: English, French, German, Italian, Portuguese, Spanish
  • Macros: Yes
  • Java-applet: No
  • Animation: Yes
  • Locus: Yes, including point on locus
  • Assignments: No
  • Measurement/Calculations: Yes
  • Platform: Windows
  • Proofs: No

GRACE

GRACE (The Graphical Ruler And Compass Editor) is an analog of The Geometer's Sketchpad (GSP), written in Java.

iGeom

iGeom   is freeware interactive geometry software hosted on the Internet for learning and teaching geometry (an analog of GSP and Cabri), written in Java.

Isard

Isard[11] is an interactive geometry software originally written in Smalltalk. The latest version only works under VisualWorks 7.

Jeometry

Jeometry is a dynamic geometry applet.

Kig

Kig is a free (GPL) analog of The Geometer's Sketchpad (GSP) for KDE, but more calculus-oriented. It is a part of the KDE Edutainment Project.

Kgeo

Kgeo   was a free (GPL) analog of The Geometer's Sketchpad (GSP) for KDE, but more calculus-oriented, with an interface similar to Kig's. Development has stopped, and the project was replaced and superseded by Kig.

KmPlot

KmPlot   is a mathematical function plotter released under the free GPL license. 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. Features include:

  • 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 to 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 minimum/maximum point, get y-value and draw the area between the function and the y-axis

KSEG

KSEG is a free (GPL) analog of The Geometer's Sketchpad (GSP) with some unique features. This software can handle heavy, complex constructions in Euclidean geometry.

  • Deterministic
  • Languages: Dutch, English, French, Chinese, German, Hungarian, Italian, Japanese, Norwegian Bokmål, Portuguese, Russian, Spanish, Turkish, Welsh
  • Macros: Yes. Editable and with support for recursion
  • Java-applet: No
  • Animation: No
  • Locus: Yes, but no direct way to place a point on a locus.
  • Assignments: No
  • Measurement/Calculations: Yes (the calculator is a bit strange)
  • Platform: Unix/Linux, Windows, Mac OS (any platform that supports Qt)
  • Proofs: No
  • Extra: Editable

Live Geometry

Live Geometry   is a free CodePlex project that lets you create interactive ruler and compass constructions and experiment with them. It is written in Silverlight 4 and C# 4.0 (Visual Studio 2010). The core engine is a flexible and extensible framework that allows easy addition of new figure types and features. The project has two front-ends: WPF and Silverlight, which both share the common DynamicGeometry library.

Non-Euclid

Non-Euclid[12] is a very basic Java-IGS used only for hyperbolic geometry in the Poincaré disk and the upper half-plane models.

OpenEuclide

OpenEuclide[13] is a GPL 2D geometry software.

Sarit2d

Sarit2d[14] is a library for Javascript created for drawing and solving 2d-geometric problems. The library contains many functions for drawing the main geometric shapes: segments, arcs, points, texts, etc. But the very core of the library are the functions for solving the most common geometry problems: intersections between shapes, areas calculation, geometric formulas, etc. With Sarit2d library it's possible solving hard problems through few code rows.

Sphaerica

Sphaerica[15] is an open source geometry software for spherical geometry. It supports orthographic, stereographic and gnomonic projections and various tools for constructions on the sphere.

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 Mac OS and Windows compatible.

Tabulae

Tabulae [https://web.archive.org/web/20050615030051/http://tabulae.net/] is a dynamic geometry software written in Java. It is under development by the Federal University of Rio de Janeiro. It is available in Brazilian and Portuguese.

TracenPoche

TracenPoche   is a completely Adobe Flash program. It is available in English, Spanish, and French.

Wingeom

Wingeom[16] is a program for high-precision geometric constructions in both two and three dimensions.

3D programs

{{Expand section|date=November 2013}}

Archimedes Geo3D

Archimedes Geo3D

Ganja.js

[https://enkimute.github.io/ganja.js/examples/coffeeshop.html Ganja.js] implements 2D and 3D projective and conformal Geometric Algebra. It features animation, interactivity and live

editing without registration or download.

Euler 3D

Euler (software)

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.

Geomview

Geomview

Continuity versus 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.[17]

See also

  • Mathematical software
  • Constructive solid geometry
  • Lénárt sphere

References

1. ^{{cite book | last = Schwartz |author2=Yerushalmy and Wilson | title = The Geometric Supposer: What is it a Case of? | publisher = Lawrence Erlbaum Associates | year = 1993 | location = Hillsdale, NJ}}
2. ^{{Cite book | last = Battista | first = M.T. | contribution = The Development of Geometric and Spatial Thinking | editor-last = Lester, Jr. | editor-first = F.K. | title = Second Handbook of Research on Mathematics Teaching and Learning | pages = 843–903 | publisher = Information Age and the National Council of Teachers of Mathematics | place = Charlotte, NC | year = 2007 | postscript = .}}
3. ^http://wiki.laptop.org/go/DrGeo
4. ^http://www.matf.bg.ac.rs/~janicic/gclc/
5. ^http://www.geogebra.org/license#FAQ
6. ^http://GeoKone.NET
7. ^{{cite web|url=http://www.csupomona.edu/~jrfisher/www/geolog/ |title=Archived copy |accessdate=2008-03-01 |deadurl=yes |archiveurl=https://web.archive.org/web/20080409014328/http://www.csupomona.edu/~jrfisher/www/geolog/ |archivedate=2008-04-09 |df= }}
8. ^http://geometryexpressions.com
9. ^http://www.cet.ac.il/math-international/software5.htm
10. ^{{cite web |url=http://home.gna.org/geoproof/ |title=Archived copy |accessdate=2006-04-21 |deadurl=yes |archiveurl=https://web.archive.org/web/20060421112504/http://home.gna.org/geoproof/ |archivedate=2006-04-21 |df= }}
11. ^http://www.jeannot.org/~js/isard/
12. ^http://www.cs.unm.edu/~joel/NonEuclid/NonEuclid.html
13. ^http://coulon.publi.free.fr/openeuclide/
14. ^https://sourceforge.net/projects/sarit2d/
15. ^http://sourceforge.net/projects/sphaerica/
16. ^{{cite web |url=http://math.exeter.edu/rparris/wingeom.html |title=Archived copy |accessdate=2008-03-01 |deadurl=yes |archiveurl=https://web.archive.org/web/20080219061420/http://math.exeter.edu/rparris/wingeom.html |archivedate=2008-02-19 |df= }}
17. ^Kortenkamp, Ulrich (1999): Foundations of Dynamic Geometry, Dissertation, ETH Zurich 1999. Available online at http://kortenkamps.net/papers/1999/diss.pdf

External links

  • [https://web.archive.org/web/20110717134621/http://geometryclass.info/software.htm A Comparison of Geometry Software for the Classroom]
{{DEFAULTSORT:Interactive Geometry Software}}

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