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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.
Geogebra (Geometry and Algebra) - combines geometric objects like circles and graphs of functions with its algebraic representation e.g. + = representing a circle with the radius . Designed for use in schools and educational settings.
Desmos was founded by Eli Luberoff, a math and physics double major from Yale University, [3] and was launched as a startup at TechCrunch's Disrupt New York conference in 2011. [4] As of September 2012 [update] , it had received around 1 million US dollars of funding from Kapor Capital , Learn Capital, Kindler Capital, Elm Street Ventures and ...
Before version 4.2, GeoGebra was published under the GNU General Public License (GPL-3.0-or-later). After version 4.2 the licensing was changed. [ 12 ] GeoGebra's source code, except the installers, web services, user interface image and style files, and documentation and language files, is licensed under the GNU General Public License (GPL-3.0 ...
The most efficient way to pack different-sized circles together is not obvious. In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap.
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A circle is tangent to a point if it passes through the point, and tangent to a line if they intersect at a single point P or if the line is perpendicular to a radius drawn from the circle's center to P. Circles tangent to two given points must lie on the perpendicular bisector. Circles tangent to two given lines must lie on the angle bisector.
The Möbius transformations of the plane preserve the shapes and tangencies of circles, and therefore preserve the structure of an Apollonian gasket. Any two triples of mutually tangent circles in an Apollonian gasket may be mapped into each other by a Möbius transformation, and any two Apollonian gaskets may be mapped into each other by a Möbius transformation.
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