A fractal landscape or fractal surface is generated using a stochastic algorithm designed to produce fractal behavior that mimics the appearance of natural terrain. In other words, the surface resulting from the procedure is not a deterministic, but rather a random surface that exhibits fractal behavior.
KSEG is a free (GPL) interactive geometry software for exploring Euclidean geometry. It was created by Ilya Baran. It runs on Unix-based platforms. It also compiles and runs on Mac OS X and should run on anything that Qt supports. Additionally, it was also ported to Microsoft Windows.
PSTricks is a set of macros that allow the inclusion of PostScript drawings directly inside TeX or LaTeX source code. It was originally written by Timothy Van Zandt and has been maintained in recent years by Denis Girou, Sebastian Rahtz and Herbert Voss.
GeoGebra is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level. GeoGebra is available on multiple platforms, with apps for desktops, tablets and web. It is presently owned by Indian edutech firm Byju's.
The Geometer's Sketchpad is a commercial interactive geometry software program for exploring Euclidean geometry, algebra, calculus, and other areas of mathematics. It was created as part of the NSF-funded Visual Geometry Project led by Eugene Klotz and Doris Schattschneider from 1986 to 1991 at Swarthmore College. Nicholas Jackiw, a student at the time, was the original designer and programmer of the software, and inventor of its trademarked "Dynamic Geometry" approach; he later moved to Key Curriculum Press, KCP Technologies, and McGraw-Hill Education to continue ongoing design and implementation of the software over multiple major releases and hardware platforms. Present versions run Microsoft Windows and MacOS Ventura. It also runs on Linux under Wine with a few bugs. There was also a version developed for the TI-89 and TI-92 series of Calculators. In June 2019, McGraw-Hill announced that it would no longer sell new licenses. Nonetheless, a license-free 64-bit version of Mac Sketchpad that is compatible with the latest Apple silicon chips is available. A license-free Windows version of the software is also available. The Sketchpad Repository contains over 200 videos, with Sketchpad and Web Sketchpad tutorials as well as an archive of Sketchpad webinars that were offered by Key Curriculum Press.
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 drawn on a blackboard. Relationships between points on a geometric object may easily be demonstrated, which can be useful in the learning process. There are also graphing and display functions which allow exploration of the connections between geometry and algebra. The program can be run under Windows or the Mac OS.
In plane geometry, Van Aubel's theorem describes a relationship between squares constructed on the sides of a quadrilateral. Starting with a given convex quadrilateral, construct a square, external to the quadrilateral, on each side. Van Aubel's theorem states that the two line segments between the centers of opposite squares are of equal lengths and are at right angles to one another. Another way of saying the same thing is that the center points of the four squares form the vertices of an equidiagonal orthodiagonal quadrilateral. The theorem is named after Belgian mathematician Henricus Hubertus (Henri) Van Aubel (1830–1906), who published it in 1878.
ImageJ is a Java-based image processing program developed at the National Institutes of Health and the Laboratory for Optical and Computational Instrumentation. Its first version, ImageJ 1.x, is developed in the public domain, while ImageJ2 and the related projects SciJava, ImgLib2, and SCIFIO are licensed with a permissive BSD-2 license. ImageJ was designed with an open architecture that provides extensibility via Java plugins and recordable macros. Custom acquisition, analysis and processing plugins can be developed using ImageJ's built-in editor and a Java compiler. User-written plugins make it possible to solve many image processing and analysis problems, from three-dimensional live-cell imaging to radiological image processing, multiple imaging system data comparisons to automated hematology systems. ImageJ's plugin architecture and built-in development environment has made it a popular platform for teaching image processing.
C.a.R.– Compass and Ruler — is a free and open source interactive geometry app that can do geometrical constructions in Euclidean and non-Euclidean geometry. The software is Java based. The author is René Grothmann of the Catholic University of Eichstätt-Ingolstadt. It is licensed under the terms of the GNU General Public License (GPL).
JTS Topology Suite is an open-source Java software library that provides an object model for Euclidean planar linear geometry together with a set of fundamental geometric functions. JTS is primarily intended to be used as a core component of vector-based geomatics software such as geographical information systems. It can also be used as a general-purpose library providing algorithms in computational geometry.
The Computational Geometry Algorithms Library (CGAL) is an open source software library of computational geometry algorithms. While primarily written in C++, Scilab bindings and bindings generated with SWIG are also available.
CaRMetal is an interactive geometry program which inherited the C.a.R. engine. The software has been created by Eric Hakenholz, in 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 some intermediate dialogs and provides direct access to numerous effects. Constructions are done using a main palette, which contains some useful construction shortcuts in addition to the standard compass and ruler tools. These include perpendicular bisector, circle through three points, circumcircular arc through three points, and conic section through five points. Also interesting are the loci, functions, parametric curves, and implicit plots. Element thickness, color, label, and other attributes can be set using a separate panel.
GNU Dr. Geo, and later Dr. Geo II, is interactive geometry software that allows its users to design & manipulate interactive geometric sketches. It is free software, created by Hilaire Fernandes, it is part of the GNU project. It runs over a Morphic graphic system. Dr. Geo was developed in C++ and Dr. Geo II is a complete rewrite using Pharo that happened in 2005.
In mathematics education, a representation is a way of encoding an idea or a relationship, and can be both internal and external. Thus multiple representations are ways to symbolize, to describe and to refer to the same mathematical entity. They are used to understand, to develop, and to communicate different mathematical features of the same object or operation, as well as connections between different properties. Multiple representations include graphs and diagrams, tables and grids, formulas, symbols, words, gestures, software code, videos, concrete models, physical and virtual manipulatives, pictures, and sounds. Representations are thinking tools for doing mathematics.
KIG is free and open-source interactive geometry software, which is part of the KDE Education Project. It has some facilities for scripting in Python, as well as the creating macros from existing constructions.
Desmos is an advanced graphing calculator implemented as a web application and a mobile application written in TypeScript and JavaScript.
PyX is a Python package for the creation of PostScript, PDF, and static SVG files. It combines an abstraction of the PostScript drawing model with a TeX/LaTeX interface. Complex tasks like 2d and 3d plots in publication-ready quality are built out of these primitives. Its goals are similar to those of other metalanguages for PDF drawing, such as TikZ or Asymptote.
