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Exact Drawing and Geometry


Mathematica 8 compatible Geometrica is designed to be an encyclopedia of geometry. Because it uses the symbolic engine of Mathematica, the drawing is exact, many theorems are integrated, and tests of validity can be performed. List processing is embedded in most functions so that complex commands can be performed with concise statements. Adding legends to a figure is an example of that feature.

Euclidean geometry is thoroughly covered for two and three dimensions. Whenever possible, a unified design is adopted for 2D and 3D, and plane objects can easily be immersed into space. Geometric objects are systematically represented by their Cartesian or parametric forms and defined by a variety of Euclidean functions. Basic objects such as lines, planes, conics, and quadrics are manipulated using their Cartesian equations. To simplify these manipulations, default definitions are available so that an object's shape can be visualized without using all the equation's coefficients. For instance, HyperbolicParaboloid[] returns a quadric that can be immediately visualized using the function Draw3D.

Differential geometry is treated through the parametric form of an object. A catalog of curves and surfaces is available. Distances, areas, and volumes are evaluated. Thick objects are readily obtained using the functions Wall and Pipe.

Geometrica is used by mathematics educators at the high school and college level, by researchers for drawing exact diagrams of any complexity, and by graphical designers, architects, and engineers for CAD applications.

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Geometrica09 requires Mathematica 7.0 or 8.0 and is available for Windows, Mac OS X, and Linux.