Interactive geometry software
Encyclopedia
Interactive geometry software (IGS, or dynamic geometry environments, DGEs) are computer program
s 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
, circle
s or other points. After some construction is done, one can move the points one started with and see how the construction changes.
-based programs. 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.
a free GPL
analog of GSP, written in Java
.
a free GPL
software written in Java
.
It is derived from C.a.R and provides another user interface.
- 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.
analog of GSP for windows
.
, is a geometry drawing language.
Now Dr. Geo II complete rewrite of Dr. Geo for the Squeak/Smalltalk environment is available.
is free software
that joins geometry, algebra and calculus for mathematics education in schools and universities.
Does symbolic geometry. It uses symbolic inputs and returns symbolic outputs.
(GSP)
and Free Pascal
(Lazarus).
) analog of GSP written in Java and offers a view calculus features (parametric curves, functions) as well.
dynamic geometry software, written in Objective Caml
.
bit more calculus-oriented analog of GSP.
.
.
a free (GPL
) analog of GSP for KDE
, bit more to calculus-oriented, part of KDE Edutainment Project.
http://kgeo.sourceforge.net/ 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
.
). 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.
) 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.
-IGS only for hyperbolic geometry
in the Poincaré disk
and the upper half-plane models
.
http://tracenpoche.sesamath.net completely Adobe Flash
program. Available in French,English and Spanish.
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.
JavaView is a 3D geometry viewer and a mathematical visualization software. You can explore miscellaneous 3D models with it.
Based on JavaView, this program can calculate and draw singular algebraic curves and surfaces.
A very simple, online applet that allows one to view and bisect a cube in 3D space.
) Python
language module for 2D, 3D, N-dimensional space calculations with abilities of
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 mid points (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 mid point 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.
Computer program
A computer program is a sequence of instructions written to perform a specified task with a computer. A computer requires programs to function, typically executing the program's instructions in a central processor. The program has an executable form that the computer can use directly to execute...
s which allow one to create and then manipulate geometric
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
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
Line (mathematics)
The notion of line or straight line was introduced by the ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects...
, circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
s 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. 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 LogoLogo (programming language)
Logo is a multi-paradigm computer programming language used in education. It is an adaptation and dialect of the Lisp language; some have called it Lisp without the parentheses. It was originally conceived and written as functional programming language, and drove a mechanical turtle as an output...
-based programs. 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.
License and platform
The following table provides a first comparison of the different software according to their licence and platform.2D Software
| Software | Cost (USD United States dollar The United States dollar , also referred to as the American dollar, is the official currency of the United States of America. It is divided into 100 smaller units called cents or pennies.... ) |
Licence | Platforms |
|---|---|---|---|
| Apollonius | 3.99 US$ | iPhone/iPod Touch | |
| Baghera | Windows/? | ||
| Cabri Geometry Cabri Geometry Cabri Geometry is a commercial interactive geometry software produced by the French company Cabrilog for teaching and learning geometry and trigonometry. It was designed with ease-of-use in mind. The program allows the user to animate geometric figures, proving a significant advantage over those... |
Windows, Mac OS X | ||
| Cabri-Euclide | Windows/? | ||
| C.a.R. C.a.R. C.a.R.– Compass and Ruler – is a free and open source interactive geometry software that can do geometrical constructions in Euclidean and non-Euclidean geometry. The software is Java based. The author is R... |
Windows, GNU/Linux, Mac OS X | ||
| CaRMetal CaRMetal CaRMetal is an interactive geometry program which inherited the C.a.R. engine. The software has been created by Eric Hakenholz, in the Java . CaRMetal is free, under GNU GPL license. It keeps an amount of functionality of C.a.R. but uses a different graphical interface which purportedly eliminates... |
Windows, GNU Linux, Mac OS X | ||
| Cinderella 1.4 Cinderella (software) Cinderella is a proprietary interactive geometry software, written in Java programming language.- History :Cinderella was initially developed by Jürgen Richter-Gebert and Henry Crapo and was used to input incidence theorems and conjectures for automatic theorem proving using the binomial proving... |
Windows, GNU/Linux, Mac OS X (Java) | ||
| Cinderella 2.0 Cinderella (software) Cinderella is a proprietary interactive geometry software, written in Java programming language.- History :Cinderella was initially developed by Jürgen Richter-Gebert and Henry Crapo and was used to input incidence theorems and conjectures for automatic theorem proving using the binomial proving... |
69 US$ | Windows, GNU/Linux, Mac OS X (Java) | |
| Defi | |||
| DrGeo DrGeo DrGeo is a free software, created by Hilaire Fernandes for the Ofset. As its names suggests, it is a geometry software... |
Windows, GNU/Linux, Mac OS X | ||
| Euklid DynaGeo | Windows | ||
| Euklides | Windows | ||
| Eukleides | Windows, GNU/Linux, Mac OS X | ||
| Gambol | Windows, GNU/Linux, Mac OS X | ||
| GCLC | Windows, GNU/Linux | ||
| GeoGebra GeoGebra GeoGebra is an interactive geometry software for education in schools. Most parts of GeoGebra are free software. GeoGebra is written in Java and thus available for multiple platforms.... |
Windows, GNU/Linux, Mac OS X | ||
| Geolog | Windows/? | ||
| The Geometer's Sketchpad The Geometer's Sketchpad Arsh is a popular commercial interactive geometry software program for exploring Euclidean geometry, algebra, calculus, and other areas of mathematics. It was created by Nicholas Jackiw.... |
GNU/Linux, Windows, Mac OS X (Java) | ||
| Geometric Supposer | |||
| Geometrix | Linux, Windows | ||
| Geometry Expert Geometry Expert Geometry Expert is a Chinese software for dynamic diagram drawing and automated geometry theorem proving and discovering.There's a new Chinese version of Geometry Expert, called MMP/Geometer.... (GEX) |
Windows, GNU/Linux, Mac OS X | ||
| Geometry Explorer | Windows, GNU/Linux, Mac OS X | ||
| Geometry Expressions Geometry Expressions Geometry Expressions is an Interactive Symbolic Geometry System.Geometry Expressions draws figures that can be defined by either Symbolic Constraints or numeric locations. Calculations can be made from these constraints and are presented numerically and also symbolically as mathematical expressions... |
Windows, GNU/Linux, Mac | ||
| Geometry Tutor | Windows/? | ||
| GeoNext | Windows, GNU/Linux, Mac OS X | ||
| Géoplan | Windows | ||
| GeoProof | Windows, GNU/Linux, Mac OS X | ||
| GeoView | Windows, GNU/Linux, Mac OS X | ||
| GEUP GEUP GEUP is a commercial interactive geometry software program.It lets you dynamically explore mathematics or build mathematical models of real world.OS: Windows 7/Vista/XP/2003/2000/NT4/Me/98/95-Main features:... |
Windows | ||
| GRACE | Windows, GNU/Linux, Mac OS X | ||
| iGeom | GNU/Linux, Windows, Mac OS X | ||
| Isard | Windows | ||
| Jeometry | Windows, GNU/Linux, Mac OS X | ||
| JSXGraph | Windows, GNU/Linux, Mac OS X | ||
| Kig Kig (software) Kig is free and open source interactive geometry software, which is part of theKDE edutainment project. It has some facilities for scripting in Python, as well as the creating macros from existing constructions.- Import and export :... |
GNU/Linux | ||
| Kgeo | GNU/Linux | ||
| KmPlot | GNU/Linux, Mac OS X | ||
| KSEG | Windows, GNU/Linux, Mac OS X | ||
| Live Geometry | Windows, Mac OS X (Silverlight & WPF) | ||
| MathKit | GNU/Linux, Windows, Mac OS X (Java) | ||
| Mentoniezh | |||
| OpenEuclide | Windows, GNU/Linux | ||
| Tabula | 19.95 US$ | Windows, Mac OS X (Silverlight) | |
| Tabulae | GNU/Linux, Windows, Mac OS X (Java) | ||
| WinGeom | Windows | ||
| WIRIS | GNU/Linux, Windows, Mac OS X (Java) |
3D Software
| Software | Cost (USD United States dollar The United States dollar , also referred to as the American dollar, is the official currency of the United States of America. It is divided into 100 smaller units called cents or pennies.... ) |
Licence | Platforms |
|---|---|---|---|
| Archimedes Geo3D Archimedes Geo3D Archimedes Geo3D is a software package for dynamic geometry in three dimensions. It was released in Germany in March 2006 and won a German government award for outstanding educational software in 2007 . -Basic features:... |
Windows/Mac OS X/Linux | ||
| Cabri 3D | Windows/Mac OS X | ||
| GeoGebra GeoGebra GeoGebra is an interactive geometry software for education in schools. Most parts of GeoGebra are free software. GeoGebra is written in Java and thus available for multiple platforms.... (from version 5.0) |
Windows, GNU/Linux, Mac OS X | ||
| Geometria | Windows, GNU/Linux, Mac OS X | ||
| GeomSpace | Windows, GNU/Linux, OpenSolaris, BSD | ||
| GeomView | Unix | ||
| Géospace | Windows | ||
| GEUP 3D | Windows | ||
| Yenka Yenka Yenka is a suite of educational software products which lets students simulate scientific experiments, create mathematical models, design electronic circuits or learn computer programming. Yenka is developed by Crocodile Clips Ltd.- Features :... 3D Shapes |
Windows | ||
| WIRIS | Windows, GNU/Linux, Mac OS X |
Any-dimensional Software
| Software | Cost (USD United States dollar The United States dollar , also referred to as the American dollar, is the official currency of the United States of America. It is divided into 100 smaller units called cents or pennies.... ) |
License | Platforms | Brief Info |
|---|---|---|---|---|
| SpaceFuncs | Windows, GNU/Linux, Mac OS X (Python) |
Uses FuncDesigner FuncDesigner FuncDesigner is a computer algebra system written as a Python module. It is cross-platform software , with a completely free license.... for parametrization and automatic differentiation Automatic differentiation In mathematics and computer algebra, automatic differentiation , sometimes alternatively called algorithmic differentiation, is a set of techniques to numerically evaluate the derivative of a function specified by a computer program... , OpenOpt OpenOpt OpenOpt is an open-source framework for numerical optimization, nonlinear equations and systems of them. It is licensed under the BSD license, making it available to be used in both open- and closed-code software. The package already has some essential .... 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 | (with plug-in) | (on relations) | Available on TI Calculator | ||||||||
| CaR | |||||||||||
| CaRMetal | (recursive) | (multiple) | (JavaScript) | (probabilistic) | Amodality, folder system, the Monkey | ||||||
| Cinderella | (PDF) | Probabilistic | Several geometries, Physics simulations | ||||||||
| GCLC | Readable proofs, support for 3D | ||||||||||
| GeoGebra | (JavaScript) | (JavaScript) | (PSTricks & PGF/TikZ) | (55 languages) | CAS, HTML5 Export (from version 4.2) 3D (from version 5.0) |
||||||
| Geometria | Two-role (teacher, student) model | ||||||||||
| Geometrix | Interactive proof, diagram checking, teacher/student models, labels with dynamic placeholders | ||||||||||
| GeoNext | Available as a web app | ||||||||||
| Géoplan-Géospace | (activeX) | Sequences, 2D & 3D, human readable file format | |||||||||
| GeoProof | Automatic formal proofs | ||||||||||
| GEUP | |||||||||||
| iGeom | Probabilist | Recurrent scripts | |||||||||
| Kig | (Python) | (PSTricks) | Labels with dynamic placeholders | ||||||||
| Live Geometry | Includes player. | ||||||||||
| Sketchpad | (limited) | Functions & function plots, symbolic differentiation, mathematical notation | |||||||||
| Tabula | Folding, cutting, taping, marker, and working instrument models. | ||||||||||
| Tabulae | Collaborative sessions over the internet. | ||||||||||
| Cabri 3D | (limited) | ||||||||||
| Archimedes Geo3D | (Eng De Fr) | Intersection of Loci | |||||||||
| GEUP 3D | |||||||||||
| Software | Calculations | Macros | Loci | Animations | Scripting | Assignments | LaTeX export | Web export | Multilingual | Proofs | Extra |
Macros
We detail here the features related to macro constructions. (TODO)| Software | Allows recursity | Allows saving |
|---|---|---|
| Cabri II Plus | ||
| GCLC | ||
| GeoGebra | ||
| Géoplan-Géospace | ||
| iGeom | ||
| Kig | ||
| KSEG | ||
| Sketchpad (GSP) | (via Iteration) |
Loci
We detail here the loci features. (TODO)| Software | Take a point of a locus | Intersection of two loci |
|---|---|---|
| Cabri II Plus | ||
| CaR | ||
| GeoGebra | ||
| Géoplan-Géospace | ||
| iGeom | ||
| Kig | ||
| Sketchpad (GSP) |
Proof
We detail here the proof related features. (TODO)| Software | Interactive Proofs | Automatic Proofs | Probabilist Proofs |
|---|---|---|---|
| Cabri II Plus | Feedback for | in Cabri I | |
| Cinderella | Using external CAS | ||
| GCLC | |||
| Geometrix | |||
| Géoplan-Géospace | |||
| GeoProof | |||
| iGeom | |||
| Jeometry |
Measurements and calculation
We detail here the measurements and calculation features. (TODO)| Software | Arbitrary Precision | Arithmetic expressions | Trigonometric functions | If | Object existence test |
|---|---|---|---|---|---|
| Cabri | |||||
| C.a.R. | |||||
| GCLC | |||||
| GeoGebra | (JavaScript) | ||||
| Geometria | |||||
| Géoplan-Géospace | (µ fonction) | ||||
| GeoProof | |||||
| Geometrix | |||||
| iGeom |
Graphics Export Formats
| Software | PNG | BMP | TIFF | GIF | SWF | SVG | EMF | Fig | Postscript | LaTeX/Eukleides | LaTeX/Pstricks | LaTeX/PGF/TikZ | Asymptote | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| C.a.R. | ||||||||||||||
| Cinderella | ||||||||||||||
| GCLC | ||||||||||||||
| GeoGebra | (animated) | |||||||||||||
| GeoProof | ||||||||||||||
| Kig | ||||||||||||||
| KmPlot | ||||||||||||||
| KSEG |  |
|||||||||||||
| Geometrix | ||||||||||||||
| iGeom |
Object attributes
| Software | Color | Filled/Not filled | Width | Transparency | Shown/Hidden | Layer | Shape of points | Type of line |
|---|---|---|---|---|---|---|---|---|
| Cabri | ||||||||
| C.a.R. | ||||||||
| GCLC | ||||||||
| GeoGebra | ||||||||
| Geometria | ||||||||
| Géoplan-Géospace | ||||||||
| Kig | ||||||||
| GeoProof | ||||||||
| Geometrix | ||||||||
| iGeom |
C.a.R.
C.a.R.C.a.R.
C.a.R.– Compass and Ruler – is a free and open source interactive geometry software that can do geometrical constructions in Euclidean and non-Euclidean geometry. The software is Java based. The author is R...
a free GPL
GNU General Public License
The GNU General Public License is the most widely used free software license, originally written by Richard Stallman for the GNU Project....
analog of GSP, written in Java
Java (programming language)
Java is a programming language originally developed by James Gosling at Sun Microsystems and released in 1995 as a core component of Sun Microsystems' Java platform. The language derives much of its syntax from C and C++ but has a simpler object model and fewer low-level facilities...
.
CaRMetal
CaRMetalCaRMetal
CaRMetal is an interactive geometry program which inherited the C.a.R. engine. The software has been created by Eric Hakenholz, in the Java . CaRMetal is free, under GNU GPL license. It keeps an amount of functionality of C.a.R. but uses a different graphical interface which purportedly eliminates...
a free GPL
GNU General Public License
The GNU General Public License is the most widely used free software license, originally written by Richard Stallman for the GNU Project....
software written in Java
Java (programming language)
Java is a programming language originally developed by James Gosling at Sun Microsystems and released in 1995 as a core component of Sun Microsystems' Java platform. The language derives much of its syntax from C and C++ but has a simpler object model and fewer low-level facilities...
.
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
CinderellaCinderella (software)
Cinderella is a proprietary interactive geometry software, written in Java programming language.- History :Cinderella was initially developed by Jürgen Richter-Gebert and Henry Crapo and was used to input incidence theorems and conjectures for automatic theorem proving using the binomial proving...
- very different from GSP, written in Java
Java (programming language)
Java is a programming language originally developed by James Gosling at Sun Microsystems and released in 1995 as a core component of Sun Microsystems' Java platform. The language derives much of its syntax from C and C++ but has a simpler object model and fewer low-level facilities...
.
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 DynaGeohttp://www.dynageo.com/eng/ is a sharewareShareware
The term shareware is a proprietary software that is provided to users without payment on a trial basis and is often limited by any combination of functionality, availability, or convenience. Shareware is often offered as a download from an Internet website or as a compact disc included with a...
analog of GSP for windows
Microsoft Windows
Microsoft Windows is a series of operating systems produced by Microsoft.Microsoft introduced an operating environment named Windows on November 20, 1985 as an add-on to MS-DOS in response to the growing interest in graphical user interfaces . Microsoft Windows came to dominate the world's personal...
.
Eukleides
Eukleideshttp://www.eukleides.org/, GPLGNU General Public License
The GNU General Public License is the most widely used free software license, originally written by Richard Stallman for the GNU Project....
, is a geometry drawing language.
Dr Genius
Dr Genius was an attempt to merge Dr. Geo and the Genius calculatorGenius (software)
Genius is a free open source numerical computing environment and programming language, similar in some aspects to MATLAB, GNU Octave, Mathematica and Maple. Genius is aimed at mathematical experimentation...
Dr. Geo
Dr. Geohttp://www.ofset.org/drgeo is a GPL interactive software especially valuable for younger students (7-15).Now Dr. Geo II complete rewrite of Dr. Geo for the Squeak/Smalltalk environment is available.
Gambol
Gambolhttp://gambol.sourceforge.net/ is a Euclidean, construction-based, drawing systemGCLC
GCLC 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
GeoGebraGeoGebra
GeoGebra is an interactive geometry software for education in schools. Most parts of GeoGebra are free software. GeoGebra is written in Java and thus available for multiple platforms....
is free software
Free software
Free software, software libre or libre software is software that can be used, studied, and modified without restriction, and which can be copied and redistributed in modified or unmodified form either without restriction, or with restrictions that only ensure that further recipients can also do...
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
Geometry Expressions
Geometry ExpressionsGeometry Expressions
Geometry Expressions is an Interactive Symbolic Geometry System.Geometry Expressions draws figures that can be defined by either Symbolic Constraints or numeric locations. Calculations can be made from these constraints and are presented numerically and also symbolically as mathematical expressions...
Does symbolic geometry. It uses symbolic inputs and returns symbolic outputs.
The Geometer's Sketchpad
The Geometer's SketchpadThe Geometer's Sketchpad
Arsh is a popular commercial interactive geometry software program for exploring Euclidean geometry, algebra, calculus, and other areas of mathematics. It was created by Nicholas Jackiw....
(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
Geometrixhttp://geometrix.free.fr/site a free interactive geometry software, written in PrologProlog
Prolog is a general purpose logic programming language associated with artificial intelligence and computational linguistics.Prolog has its roots in first-order logic, a formal logic, and unlike many other programming languages, Prolog is declarative: the program logic is expressed in terms of...
and Free Pascal
Free Pascal
Free Pascal Compiler is a free Pascal and Object Pascal compiler.In addition to its own Object Pascal dialect, Free Pascal supports, to varying degrees, the dialects of several other compilers, including those of Turbo Pascal, Delphi, and some historical Macintosh compilers...
(Lazarus).
Geonext
Geonext http://www.geonext.de/ free (GPLGNU General Public License
The GNU General Public License is the most widely used free software license, originally written by Richard Stallman for the GNU Project....
) analog of GSP written in Java and offers a view calculus features (parametric curves, functions) as well.
GeoProof
GeoProof a free GPLGNU General Public License
The GNU General Public License is the most widely used free software license, originally written by Richard Stallman for the GNU Project....
dynamic geometry software, written in Objective Caml
Objective Caml
OCaml , originally known as Objective Caml, is the main implementation of the Caml programming language, created by Xavier Leroy, Jérôme Vouillon, Damien Doligez, Didier Rémy and others in 1996...
.
GEUP
GEUPGEUP
GEUP is a commercial interactive geometry software program.It lets you dynamically explore mathematics or build mathematical models of real world.OS: Windows 7/Vista/XP/2003/2000/NT4/Me/98/95-Main features:...
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 JavaJava (programming language)
Java is a programming language originally developed by James Gosling at Sun Microsystems and released in 1995 as a core component of Sun Microsystems' Java platform. The language derives much of its syntax from C and C++ but has a simpler object model and fewer low-level facilities...
.
iGeom
iGeomhttp://www.matematica.br/igeom/ - Interactive Geometry on Internet is a freeware software for learning and teaching Geometry (analog of GSP and Cabri), written in JavaJava (programming language)
Java is a programming language originally developed by James Gosling at Sun Microsystems and released in 1995 as a core component of Sun Microsystems' Java platform. The language derives much of its syntax from C and C++ but has a simpler object model and fewer low-level facilities...
.
Isard
Isard is an interactive geometry software originally written in Smalltalk. The latest version only works under VisualWorks 7.Kig
KigKig (software)
Kig is free and open source interactive geometry software, which is part of theKDE edutainment project. It has some facilities for scripting in Python, as well as the creating macros from existing constructions.- Import and export :...
a free (GPL
GNU General Public License
The GNU General Public License is the most widely used free software license, originally written by Richard Stallman for the GNU Project....
) analog of GSP for KDE
KDE
KDE is an international free software community producing an integrated set of cross-platform applications designed to run on Linux, FreeBSD, Microsoft Windows, Solaris and Mac OS X systems...
, bit more to calculus-oriented, part of KDE Edutainment Project.
Kgeo
KgeoKGEO
KGEO is a radio station broadcasting a News/talk format. Licensed to Bakersfield, California, USA, it serves inland central California. The station was assigned the KGEO call letters by the Federal Communications Commission on May 18, 1981.- History :In the 1940s, 1950s and 1960s the station's...
http://kgeo.sourceforge.net/ a free (GPL
GNU General Public License
The GNU General Public License is the most widely used free software license, originally written by Richard Stallman for the GNU Project....
) analog of GSP for KDE
KDE
KDE is an international free software community producing an integrated set of cross-platform applications designed to run on Linux, FreeBSD, Microsoft Windows, Solaris and Mac OS X systems...
, bit more too calculus-oriented, its interface is similar to Kig
Kig (software)
Kig is free and open source interactive geometry software, which is part of theKDE edutainment project. It has some facilities for scripting in Python, as well as the creating macros from existing constructions.- Import and export :...
.
It is no more developed, replaced and improved by Kig
Kig (software)
Kig is free and open source interactive geometry software, which is part of theKDE edutainment project. It has some facilities for scripting in Python, as well as the creating macros from existing constructions.- Import and export :...
.
KmPlot
KmPlothttp://edu.kde.org/kmplot/ is a mathematical function plotter released under the free (GPLGNU General Public License
The GNU General Public License is the most widely used free software license, originally written by Richard Stallman for the GNU Project....
). 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 (GPLGNU General Public License
The GNU General Public License is the most widely used free software license, originally written by Richard Stallman for the GNU Project....
) 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 is a very basic JavaJava (programming language)
Java is a programming language originally developed by James Gosling at Sun Microsystems and released in 1995 as a core component of Sun Microsystems' Java platform. The language derives much of its syntax from C and C++ but has a simpler object model and fewer low-level facilities...
-IGS only for hyperbolic geometry
Hyperbolic geometry
In mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced...
in the Poincaré disk
Poincaré disk model
In geometry, the Poincaré disk model, also called the conformal disk model, is a model of n-dimensional hyperbolic geometry in which the points of the geometry are in an n-dimensional disk, or unit ball, and the straight lines of the hyperbolic geometry are segments of circles contained in the disk...
and the upper half-plane models
Poincaré half-plane model
In non-Euclidean geometry, the Poincaré half-plane model is the upper half-plane , together with a metric, the Poincaré metric, that makes it a model of two-dimensional hyperbolic geometry....
.
Live Geometry
Live Geometry http://livegeometry.codeplex.com/ 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
TracenPocheTracenPoche
TracenPoche is a free interactive geometry software, written in Adobe Flash language. It is very light weight.- Features :It is widely used in French secondary schools in the framework of the :fr:MathenPoche exerciser suite developed by the French association of mathematics teachers...
http://tracenpoche.sesamath.net completely Adobe Flash
Adobe Flash
Adobe Flash is a multimedia platform used to add animation, video, and interactivity to web pages. Flash is frequently used for advertisements, games and flash animations for broadcast...
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 http://www.tabulae.net is a dynamic geometry software written in Java. Under development from Federal University of Rio de Janeiro. Available in Brazilian Portuguese.Wingeom
Wingeom for high-precision geometric constructions in both two and three dimensionsEuler 3D
Euler 3DEuler 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.JavaView
JavaViewJavaView is a 3D geometry viewer and a mathematical visualization software. You can explore miscellaneous 3D models with it.
SingSurf
SingSurfBased on JavaView, this program can calculate and draw singular algebraic curves and surfaces.
Doorzien 4
Doorzien 4A very simple, online applet that allows one to view and bisect a cube in 3D space.
SpaceFuncs
a cross-platform (Linux, Windows, Mac etc) completely free (license: BSDBSD licenses
BSD licenses are a family of permissive free software licenses. The original license was used for the Berkeley Software Distribution , a Unix-like operating system after which it is named....
) Python
Python (programming language)
Python is a general-purpose, high-level programming language whose design philosophy emphasizes code readability. Python claims to "[combine] remarkable power with very clear syntax", and its standard library is large and comprehensive...
language module for 2D, 3D, N-dimensional space calculations with abilities of
- parametrized modeling (using FuncDesignerFuncDesignerFuncDesigner is a computer algebra system written as a Python module. It is cross-platform software , with a completely free license....
) - performing numerical optimization and solving geometrical systems of equations (possibly parametrized) by OpenOptOpenOptOpenOpt is an open-source framework for numerical optimization, nonlinear equations and systems of them. It is licensed under the BSD license, making it available to be used in both open- and closed-code software. The package already has some essential ....
, using FuncDesignerFuncDesignerFuncDesigner is a computer algebra system written as a Python module. It is cross-platform software , with a completely free license....
automatic differentiation, that yields more precise (and very often faster) results than finite-differences derivatives approximation - some graphic output using MatplotlibMatplotlibmatplotlib is a plotting library for the Python programming language and its NumPy numerical mathematics extension. It provides an object-oriented API which allows plots to be embedded into applications using generic GUI toolkits, like wxPython, Qt, or GTK...
(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 mid points (say A', B' C' ) between vertices and orthocenter.
Construct a circumcircle of A'B'C' .
This is the nine-point circle
Nine-point circle
In geometry, the nine-point circle is a circle that can be constructed for any given triangle. It is so named because it passes through nine significant points defined from the triangle...
, 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 mid point 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.
See also
- Mathematical softwareMathematical softwareMathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data.-Computer algebra systems:Many mathematical suites are computer algebra systems that use symbolic mathematics. They are designed to solve classical algebra equations and problems in human...
- Constructive solid geometryConstructive solid geometryConstructive solid geometry is a technique used in solid modeling. Constructive solid geometry allows a modeler to create a complex surface or object by using Boolean operators to combine objects...
(There's also a list of software.)
External links
- Links to other lists
- Links to the other programs
- Geometry Software Step-by-step problem solver, download available
- Geops Free perl script for performing compass and straightedge constructions in the manner of the Ancient Greeks.
- Geometria An online tool to compute lines, surfaces and volumes of the main plane and solid figures, through direct and indirect formulas.
- Interactive geometry on web:
- Cabri software editor website Available resources for teaching
- Geometry at cut-the-knotCut-the-knotCut-the-knot is a free, advertisement-funded educational website maintained by Alexander Bogomolny and devoted to popular exposition of many topics in mathematics. The site has won more than 20 awards from scientific and educational publications, including a Scientific American Web Award in 2003,...
- Sketchpad Resource Center Including classroom activities, research bibliography, demo version, etc.
- The Math Open Reference Project Collection of applets
- Math tools Catalog of applets
- Yenka 3D Shapes Free 3D geometry software available to download
- Interactive geometry examples in Mathematica The Wolfram Demonstrations Project
- Dynamic Geometry Sketches Includes student explorations and classroom demonstrations.
- Interactive Math And Geometry Applets Collection of java and Cabri 3D applets