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SageMath is designed partially as a free alternative to the general-purpose mathematics products Maple and MATLAB. It can be downloaded or used through a web site. SageMath comprises a variety of other free packages, with a common interface and language. SageMath is developed in Python.
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.
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 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.
The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.
Figure 3: Two given circles (black) and a circle tangent to both (pink). The center-to-center distances d 1 and d 2 equal r 1 + r s and r 2 + r s, respectively, so their difference is independent of r s. The solution of Adriaan van Roomen (1596) is based on the intersection of two hyperbolas. [13] [14] Let the given circles be denoted as C 1, C ...
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Kissing circles. Given three mutually tangent circles (black), there are, in general, two possible answers (red) as to what radius a fourth tangent circle can have. In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this ...
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