Exact Drawing and Geometry
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
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
Developed and supported by MuSoftware.
Le Clot des Sources
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requires Mathematica 7.0 or 8.0 and is available for Windows, Mac OS X, and Linux.