List of 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.
Software | Cost (USD) | Licence | Platforms |
---|---|---|---|
Apollonius | 0.00 US$ | Proprietary | iPhone/iPod Touch |
Baghera | ? | ? | Windows/? |
Cabri Geometry | ? | Proprietary | Windows, Mac OS X |
Cabri-Euclide | ? | ? | Windows/? |
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) |
Defi | ? | ? | ? |
DrGeo | Free | GPL | Windows, Linux, Mac OS X |
Euklid DynaGeo | Shareware | Proprietary | Windows |
Euklides | Shareware | Proprietary | Windows |
Eukleides | Free | GPL | Windows, Linux, Mac OS X |
Gambol | ? | ? | Windows, Linux, Mac OS X |
GCLC | Free | Proprietary | Windows, Linux |
GeoGebra | Free | Proprietary | Windows, Linux, Mac OS X |
GeoKone.NET | Free | GPL | Web Browser (HTML5 & js) |
Geolog | ? | ? | Windows/? |
The Geometer's Sketchpad | 70.02 US$ | Proprietary | Windows, Mac OS X (Java) |
Geometric Supposer | ? | ? | ? |
Geometrix | Free | Proprietary | Linux, Windows |
Geometry Expert (GEX) | ? | ? | Windows, Linux, Mac OS X |
Geometry Explorer | Free | ? | Windows, Linux, Mac OS X |
Geometry Expressions | $99 USD | Proprietary | Windows, Linux, Mac |
Geometry Tutor | ? | ? | Windows/? |
GeoNext | Free | GPL | Windows, Linux, Mac OS X |
Géoplan | Free | CeCILL | Windows |
GeoProof | Free | GPL | Windows, Linux, Mac OS X |
GeoView | Free | GPL | Windows, Linux, Mac OS X |
GEUP | ? | Proprietary | Windows |
GRACE | ? | ? | Windows, Linux, Mac OS X |
iGeom | Free | Proprietary | Linux, Windows, Mac OS X |
Isard | ? | ? | Windows |
Jeometry | ? | ? | Windows, Linux, Mac OS X |
JSXGraph | Free | GNU LGPL | Windows, Linux, Mac OS X |
Kig | Free | GPL | Linux |
Kgeo | Free | GPL | Linux |
KmPlot | Free | GPL | Linux, Mac OS X |
KSEG | Free | GPL | Windows, Linux, Mac OS X |
Live Geometry | Free | Free | Windows, Mac OS X (Silverlight & WPF) |
MathKit | ? | Proprietary | Linux, Windows, Mac OS X (Java) |
Mentoniezh | ? | ? | ? |
OpenEuclide | Free | GPL | Windows, Linux |
Tabula | 19.95 US$ | Proprietary | Windows, Mac OS X (Silverlight) |
Tabulae | Free | Proprietary | Linux, Windows, Mac OS X (Java) |
WinGeom | ? | ? | Windows |
WIRIS | ? | Proprietary | Linux, Windows, Mac OS X (Java) |
3D Software
Software | Cost (USD) | Licence | Platforms |
---|---|---|---|
Archimedes Geo3D | Shareware | Proprietary | Windows/Mac OS X/Linux |
Cabri 3D | Shareware | Proprietary | Windows/Mac OS X |
GBgeom | Free | Proprietary | Windows |
GeoGebra (from version 5.0 Beta) | Free | Proprietary | Windows, Linux, Mac OS X, Android, iOS, Windows RT |
Geometria | Free | MIT | Windows, Linux, Mac OS X |
GeomSpace | Free | GPL | Windows, Linux, OpenSolaris, BSD |
GeomView | Free | GNU LGPL | Unix |
Géospace | Free | CeCILL | Windows |
GEUP 3D | Shareware | Proprietary | Windows |
Sterizium | Free for non-commercial use | Proprietary | Windows |
Yenka 3D Shapes | Free for non-commercial use | Proprietary | Windows |
WIRIS | ? | Proprietary | Windows, Linux, Mac OS X |
Any-dimensional software
Software | Cost (USD) | License | Platforms | Brief Info |
---|---|---|---|---|
SpaceFuncs | Free | BSD | Windows, Linux, Mac OS X (Python) |
Uses FuncDesigner for parametrization and automatic differentiation, OpenOpt for solving systems of geometric equations and numerical optimization |
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 |
CaR | Yes | Yes | Yes | Yes | Yes | Yes | Yes | Yes | Yes | No | ? |
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 |
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) | No | 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 | ? | ? | No | ? | 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 | ? | No | ? | No | Yes | No | ? |
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. |
Sketchpad | Yes | Yes | Yes | Yes | Yes | No | ? | 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 | ? |
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 | ? |
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 |
GCLC | No | No |
GeoGebra | Yes | Yes |
Géoplan-Géospace | Yes | Yes |
GEUP | Yes | Yes |
iGeom | Yes | Yes |
Kig | ? | 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 |
CaR | Yes | Yes |
GeoGebra | Yes | No |
Géoplan-Géospace | Yes | No |
GEUP | Yes | Yes |
iGeom | Yes | No |
Kig | Yes | No |
Sketchpad (GSP) | Yes | No |
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 |
Geometrix | Yes | Yes | No |
Géoplan-Géospace | No | No | Yes |
GeoProof | Yes | Yes | No |
iGeom | No | No | Yes |
Jeometry | No | Yes | No |
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 |
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 fonction) | No |
GeoProof | Yes | Yes | Yes | Yes | No |
Geometrix | No | Yes | Yes | Yes | No |
iGeom | No | Yes | Yes | No | No |
Graphics export formats
Software | PNG | BMP | TIFF | GIF | SWF | SVG | EMF | Fig | Postscript | 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
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 |
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 | ? | Yes | Yes |
2D programs
C.a.R.
C.a.R. is a free GPL analog of GSP, written in Java.
CaRMetal
CaRMetal is 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 is an extended analog of GSP and actually the ancestor of all DGSs.
Cinderella
Cinderella is 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 is a shareware analog of GSP for windows.
Eukleides
Eukleides , part of 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 is a GPL interactive software especially valuable for younger students (7-15). Now Dr. Geo II,^{[3]} a complete rewrite of Dr. Geo for the Squeak/Smalltalk environment, is available.
Gambol
Gambol 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 software that joins 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 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
GeoKone.NET
GeoKone.NET^{[6]} is an Interactive Recursive Natural Geometry (or Sacred Geometry) Generator that runs in your browser. GeoKone allows you the user to create Geometry Based on the same rules of recursive copying that can be found in Nature, like 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. 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 is a free interactive geometry software, written in Prolog and Free Pascal (Lazarus).
- Geometrix can directly guide the student in his demonstration of any property of the figure. It calculates all the proofs while the student is constructing the figure. Three types of reasoning are allowed (and can be intermixed): deduction, induction, abduction. Geometrix, which generates a large number of different solutions, offers the student, when he has finished his demonstration, a canonical form of the demonstration and displays some suggestions on possible alternatives.
- 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 is a 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^{[9]}
GeoProof
GeoProof^{[10]} is a free GPL dynamic geometry software, written in OCaml.
GEUP
GEUP is a 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) is an analog of GSP, written in Java.
iGeom
iGeom is freeware interactive geometry software hosted on the Internet for learning and teaching geometry (analog of GSP and Cabri), written in Java.
Jeometry
Jeometry is a dynamic geometry applet.
Isard
Isard^{[11]} is an interactive geometry software originally written in Smalltalk. The latest version only works under VisualWorks 7.
Kig
Kig is a free (GPL) analog of GSP for KDE, but a bit more to calculus-oriented, and part of KDE Edutainment Project.
Kgeo
Kgeo is a free (GPL) analog of GSP for KDE, but a bit more too calculus-oriented, and its interface is similar to Kig.
Development has stopped, and the project was replaced and improved by Kig.
KmPlot
KmPlot 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 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 GSP which has a few features unique to it. This software can handle heavy, complicated 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, 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^{[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.
Sphaerica
Sphaerica^{[14]} is an open source geometry software for spherical geometry. It supports orthographic, stereographic and gnomonic projections and various tools for constructions on the sphere.
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 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 is a completely Adobe Flash program. It is available in English, Spanish, and French.
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 is a dynamic geometry software written in Java. It is under development from the Federal University of Rio de Janeiro. It is available in Brazilian and Portuguese.
Wingeom
Wingeom^{[15]} is a program for high-precision geometric constructions in both two and three dimensions.
3D programs
Archimedes Geo3D
Cabri 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.
GeoGebra 5
Since version 5.0 (and beta release 4.9) GeoGebra comprises a full 3D mode as well and plane section of it can also be viewed and manipulated in the traditional 2D interface.
Geometria
Geometria is free (MIT License) 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
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.
Sterizium
Sterizium is freeware stereometry viewer application for the development of spatial thinking.
- Kinect sensor support.
Vectory
Vectory is a freeware specifically developed for school students. This program visualizes primitive geometry, like points, lines, planes and spheres. Further features like intersections, distance calculation and parametrizing the inputs are available.
Any-dimensional programs
SpaceFuncs
SpaceFuncs is 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 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.^{[16]}
See also
References
- ↑ Schwartz; Yerushalmy and Wilson (1993). The Geometric Supposer: What is it a Case of?. Hillsdale, NJ: Lawrence Erlbaum Associates.
- ↑ Battista, M.T. (2007). "The Development of Geometric and Spatial Thinking". In Lester, Jr., F.K. Second Handbook of Research on Mathematics Teaching and Learning. Charlotte, NC: Information Age and the National Council of Teachers of Mathematics. pp. 843–903.
- ↑ http://wiki.laptop.org/go/DrGeo
- ↑ http://www.matf.bg.ac.rs/~janicic/gclc/
- ↑ http://www.geogebra.org/license#FAQ
- ↑ http://GeoKone.NET
- ↑ http://www.csupomona.edu/~jrfisher/www/geolog/
- ↑ http://geometryexpressions.com
- ↑ http://www.cet.ac.il/math-international/software5.htm
- ↑ http://home.gna.org/geoproof/
- ↑ http://www.jeannot.org/~js/isard/
- ↑ http://www.cs.unm.edu/~joel/NonEuclid/NonEuclid.html
- ↑ http://coulon.publi.free.fr/openeuclide/
- ↑ http://sourceforge.net/projects/sphaerica/
- ↑ http://math.exeter.edu/rparris/wingeom.html
- ↑ Kortenkamp, Ulrich (1999): Foundations of Dynamic Geometry, Dissertation, ETH Zurich 1999. Available online at http://kortenkamps.net/papers/1999/diss.pdf