mathematics

List of interactive geometry software

List of interactive geometry software is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand List of interactive geometry software rather than just read about it. In short: 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.

Key takeaways

List of interactive geometry software belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect List of interactive geometry software to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of List of interactive geometry software from memory before moving on to harder problems.

Reference excerpt

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. 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. 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 table below provides a first comparison of the different software according to license and platform.

3D software

General features The following table provides a more detailed comparison:

Macros Features related to macro constructions: (TODO)

Loci Loci features related to IGS: (TODO)

Proof We detail here the proof related features. (TODO)

Measurements and calculation Measurement and calculation features related to IGS: (TODO)

Graphics export formats

Object attributes

2D programs

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

Cabri Cabri Cabri was developed by the French school of mathematics education in Grenoble (Laborde, 1993)

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

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

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

Dr. Geo Dr. Geo is a GPL interactive software intended for younger students (7-15). The later version, Dr. Geo II, is a complete rewrite of Dr. Geo, for the Squeak/Smalltalk environment.

GCLC 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 the abstract description. There are several output formats, including LaTeX, LaTeX/PStricks, LaTeX/Tikz, SVG and PostScript. There is a built-in geometry theorem prover (based on the area method). GCLC is available for Windows and Linux. WinGCLC is a Windows version of GCLC with a graphical interface that provides a range of additional functionalities. GCLC is open source software (licence CC BY-ND).

GeoGebra GeoGebra is software that combines geometry, algebra and calculus for mathematics education in schools and universities. It is available free of charge for non-commercial users.

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

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

Geolog Geolog is a logic programming language for finitary geometric logic.

Geometry Expressions Geometry Expressions does symbolic geometry. It uses real symbolic inputs and returns real and symbolic outputs. It emphasises use with a computer algebra system (CAS), and exporting and sharing via interactive HTML5, Lua, and macOS dashboard widget apps.

The Geometer's Sketchpad The Geometer's Sketchpad (GSP)

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

The Geometric Supposer

Géoplan-Géospace

Geonext Geonext was developed by the University of Bayreuth until 2007 and is completely implemented in Java. Its final version was 1.74.

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

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

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

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

Jeometry Jeometry is a dynamic geometry applet.

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

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with List of interactive geometry software

Start with the simplest possible case. Write down what List of interactive geometry software claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to List of interactive geometry software before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about List of interactive geometry software ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of List of interactive geometry software

In research: List of interactive geometry software appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses List of interactive geometry software in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: List of interactive geometry software is common in secondary-school and first-year university syllabi. It links to neighbouring topics Geometry education, Interactive geometry software, Lists of software, so understanding it makes those chapters shorter.
In everyday life: Look for List of interactive geometry software outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study List of interactive geometry software in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what List of interactive geometry software means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain List of interactive geometry software out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is List of interactive geometry software in simple terms?

Why does List of interactive geometry software matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study List of interactive geometry software?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on List of interactive geometry software.