Geometrica

# What's New

MuSoftware's new version of Geometrica lets users perform a wider range of geometrical operations and analysis using Mathematica's list processing, symbolic, and functional programming facilities.

### New in Geometrica09

Geometrica09 features full integration with the interactivity of Mathematica, serves as an ideal tool for demonstrations, includes enhanced documentation and additional tutorials, and contains a new palette.

• The new Geometrica palette fully uses Mathematica's graphical interactivity and maintains a concise format.
• Differential geometry is introduced with the Frenet moving system and its derivative with respect to curvilinear abscissa.
• Curvature, torsion, and evolute of curves can be determined. As a test bench for differential geometry, a catalog of curves and surfaces is provided with links to MathWorld, by Eric Weisstein.
• The concept of thick geometry, a unique feature of Geometrica, is now available. Paraxial curves or surfaces have been merged with parallel constructs. Simply, the distance that defines the parallel object is either fixed or variable. Another aspect of thick geometry is the notion of walls and pipes. Walls can be defined for 2D curves and surfaces; pipes are surfaces.
• Most 3D functions, especially Draw3D, convert 2D input into 3D automatically.
• Games are introduced with a Sudoku grid.
• Intersections are upgraded using a new intersection test.

### New in Geometrica05

Geometrica05 represented a significant step in elaborating an encyclopedia of geometry and expanding the functions for exact drawing.

• The variables of shape and position are systematically distinguished. This way, it is possible to get an object such as a sphere using the simple syntax Sphere[].
• The treatment of conics and quadrics is fully unified using the algebraic representation of quadrics. Intersections and tests are thus greatly simplified. New constructs (pole, polar, conjugate directions, and others) and metric notions (areas and volumes) are now available.
• General volumes are introduced using parametric points depending on three variables.
• CAD applications have been expanded with new and faster Bezier functions for curves and surfaces and with special objects such as helix, helicoid, and staircases.
• Graphics have also been improved with, in particular, an automatic painting of surfaces.