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Kompatibel zu Mathematica 10

GeometricaPlus

Exaktes Zeichnen und Geometrie

Geometrica ist eine Toolbox zum Erstellen von exakten Zeichnungen mit Mathematica. Entwickelt für Lehrer naturwissenschaftlicher Disziplinen an Schulen, Gymnasien und akademischen Einrichtungen, für Forscher, die exakte Zeichnungen benötigen, für Grafikdesigner, Architekten und Ingenieure im CAD-Bereich. Geometrica nutzt die symbolische Rechenengine Mathematica (ab V4) zur Definition der Geometrieregeln, damit Sie perfekte Figuren und Zeichnungen erzeugen und anhand analytischer Regeln testen können.

In Geometrica werden die geometrischen Objekte systematisch durch ihre kartesische, euklidische und parametrische Definition beschrieben. Funktionen für die dreidimensionale Geometrie wurden, wenn möglich, als Verallgemeinerung von zweidimensionalen Funktionen beschrieben und zweidimensionale Objekte können leicht in die dritte Dimension erweitert werden. Das Drittentwicklerpaket bietet eine vollständige Dokumentation mit zahlreichen farbig gedruckten und online abrufbaren Beispielen.

Features

Features von Geometrica PLUS

Zeichnen

  • Basic functions in 2 D and 3 D
  • Animation
  • Origin of lines and planes
  • Range of variations of the parameters
  • Arrow
  • Legend
  • Painting
  • Canonical view point
  • Control of display

Points

  • Cartesian point
  • Parametric point
  • Bound point
  • Barycenter
  • Brianchon point
  • Center
  • Center of curvature, of gravity and of perspective
  • Circumcenter
  • Excenters
  • Fermat point
  • Foci
  • Incenter
  • Line and plane origin
  • Orthocenter
  • Pole
  • Vertices

Lines and Planes

  • Cartesian line and plane
  • Pencil
  • Euclidean line and plane
  • Conjugate line
  • Conjugate plane
  • Parallel
  • Normal plane
  • Tangent
  • Altitudes
  • Asymptotes
  • Axes
  • Axis of perspective
  • Bisector
  • Diagonals
  • Directrices
  • Euler's line
  • Generators
  • Imaginary, infinity and indeterminate line
  • Imaginary, infinity and indeterminate plane
  • Medians
  • Normals
  • Pascal line
  • Polar
  • Symmetry planes

Conics

  • Cartesian conic in 2 D and 3 D
  • Pencil
  • Euclidean conic
  • Conic elements
  • Normal conic
  • Imaginary and real circle
  • Circumcircle
  • Euler's circle
  • Excircles
  • Incircle
  • Imaginary and real ellipse
  • Parabola
  • Hyperbola

Quadrics

  • Cartesian quadric
  • Euclidean quadric
  • Quadric elements
  • Sphere
  • Circumsphere
  • Edge sphere
  • Exspheres
  • Insphere
  • Ellipsoid
  • Quadric cone
  • Elliptic cylinder
  • Hyperbolic cylinder
  • Parabolic cylinder
  • Elliptic paraboloid
  • Hyperbolic paraboloid
  • Hyperboloid of one sheet
  • Hyperboloid of two sheets

Curves, surfaces and volumes

  • General definitions
  • Parameter range
  • Libraries of curves and surfaces
  • Arc and strip
  • Evolute of a curve
  • Isolines of a surface
  • Axisymmetric and ruled surfaces
  • Cubic or Bezier fits
  • Transformation into regions
  • Wall and pipe
  • Cardioid
  • Cassini's ovals
  • Cissoid
  • Conchoid
  • Cycloid
  • Hypotrochoid
  • Petal
  • Racetrack
  • Spiral
  • Trochoid General cone and cylinder
  • Helix
  • Helicoid
  • Helicoidal staircase
  • Möbius' strip
  • Torus
  • Viviani's window

Polygons and Polyhedra

  • General definitions
  • Cartesian and generalized segments
  • Operations on segments
  • Elements of polygons and polyhedra
  • Orthogonal and parallel polygons
  • Special polygons and polyhedra
  • Graphics complex
  • Oriented segments : 2D and 3D Frenet systems

Transformations

  • Affine
  • Homothety
  • Symmetries and inversion
  • Projection and inverse projection
  • Rotation
  • Translation
  • Shear
  • Embedding a 2 D object into 3 D
  • Creation of regions

Intersections

  • 2 D intersections : Line, conic or polygonal line
  • Line and general curve
  • General curves using an interactive technique
  • 3 D intersections : Coplanar lines or conics
  • Plane with line, plane, polygonal line, polyhedron, quadric, cone, cylinder, general curve or surface

Affine Notions

  • Barycentric coordinates
  • Cartesian coordinates
  • Cross and section ratios
  • Sorting points on lines and conics

Metric Notions

  • Angle of vectors, lines and planes
  • Distance between points, parallel lines and parallel planes
  • Length, curvature and torsion of curves
  • Radius of circles and spheres
  • Eccentricity of conics
  • Areas of closed curves and surfaces
  • Volume limited by a surface

Tests and Theorems

  • Collinear points, segments, and straight lines
  • Coplanar points, segments, straight lines and planes
  • Congruent and similar triangles
  • Regular polygon
  • Platonic solid
  • Point on line, conic, polygonal line, plane, or quadric
  • Line on plane or quadric
  • Segment on line, plane, or quadric
  • Conic on plane or quadric
  • Type of special surfaces and polyhedra
  • Line, polygonal line or conic tangent to a conic
  • Plane or line tangent to a quadric. Identical objects
  • Theorems : Brianchon
  • Desargues
  • Euler
  • Pappus
  • Pascal
  • Thales
  • Villarceaux