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What's New

New in GeometricaPlus

GeometricaPlus is a fully refurbished version of the previous releases of the Geometrica program and includes documentation for 250 functions. It takes the recent developments of Mathematica into consideration and introduces interactivity in animated examples, access to libraries, and precise intersections. Although GeometricaPlus is not compatible with the previous Geometrica versions, it maintains and deepens the three approaches: Cartesian, Euclidean, and parametric. Differential geometry has also been expanded.

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.

Features added in Geometrica02

Geometrica02 introduced two major innovations with respect to Geometrica97: the functions had been reorganized to express more clearly the three ways of defining a geometrical object (Cartesian, Euclidean, and parametric) and 3D geometry was introduced.

  • In Cartesian or analytical geometry, a point is defined by two or three coordinates and curves and surfaces by their equation which is a unique relation between the coordinates of the points which compose the curve or the surface. Such a definition is noted with the capital letter C at the beginning of the function every time a confusion with another definition may occur. This is the case for CPoint, CLine, CConic or CPlane which denote a Cartesian point, line, conic or plane.
  • In Euclidean or synthetic geometry, the point is a primitive and there is a variety of ways of defining geometrical objects. This great variety is very helpful in practical applications and is unified by theorems. Basic functions specifically related to Euclidean geometry start with a capital E such as ELine or ECircle. This way, any confusion with other definitions related to the same object is avoided.
  • Parametric or explicit definitions are well adapted for the representation of geometrical objects and for elements of objects such as bound points, segments, arcs or limited surfaces. It is however not unique. The parametric representation chosen in Geometrica is given by the function Pointer. The capital P in PPoint or PRange denotes the parametric definition. A curve or a surface in Geometrica is an object of head PPoint depending on one or two parameters in intervals defined by the option PRange.