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	Pdf	LaTeX/Eukleides	LaTeX/Pstricks	LaTeX/PGF/TikZ	Asymptote
C.a.R.	Yes	No	?	?	?	Yes	No	Yes	Yes	No	No	Yes	?	?
Cinderella	Yes	Yes	?	?	?	?	?	?	No	Yes	?	?	?	?
GCLC	No	Yes	?	?	?	Yes	No	No	Yes	No	No	Yes	?	?
GeoGebra	Yes	No	No	Yes (animated)	No	Yes	Yes	No	Yes	Yes	No	Yes	Yes	Yes
Geometry Expressions	Yes	Yes	Yes	Yes (animated)	No	No	Yes	No	Yes	No	?	?	?	?
GeoProof	Yes	No	?	?	?	Yes	No	No	No	No	Yes	No	?	?
Kig	Yes	Yes	?	?	?	Yes	No	Yes	Yes	Yes	No	Yes	?	?
KmPlot	Yes	Yes	?	?	?	Yes	?	?	?	?	?	?	?	?
KSEG	Yes	Yes	?	?	?	$\alpha$	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

Cabri 3D v2

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.

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

JavaView

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

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]

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

External links

A Comparison of Geometry Software for the Classroom

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