Geometrica09 Products
 Geometrica

# Contents

#### Getting Started

• Calling Geometrica | Mathematica notations | Tour of Geometrica | More on quadrics

#### Points

• Cartesian point | Parametric point | Bound point
• Barycenter | Brianchon point | Center | Center of gravity | Center of perspective | Circumcenter | Excenters | Fermat point | Foci | Incenter | Orthocenter | Pole | Vertices

#### Lines and Planes

• Cartesian line and plane | Pencil | Euclidean line and plane | Conjugate line | Conjugate plane | Parallel | Normal plane
• Altitudes | Asymptotes | Axes | Axis of perspective | Bisector | Diagonals | Directrices | Generators | Medians | Normals | Pascal line | Polar | Symmetry planes

#### Conics

• Cartesian conic in 2D and 3D | Pencil | Euclidean conic | Conic elements
• Circle | Circumcircle | Euler circle | Excircles | Incircle | Ellipse | Parabola | Hyperbola

• 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 and Surfaces

• General definitions | Parameter range | Cubic or Bezier fits | Parallel | Ribbon | Offset or paraxial Arc | Helix | Petal | Racetrack | Solid angle
• General cone and cylinder | Helicoid | Helicoidal staircase | Solid angle 3D | Solid of revolution

#### Polygons and Polyhedra

• General definitions | Segment | Elements of polygons and polyhedra | Orthogonal and parallel polygons
• Triangle | Isosceles | Right angled | Diamond | Parallelogram | Rectangle | Regular polygon | Reference systems
• Cube | Parallelepiped | Platonic solid | Prismoid | Pyramid | Tetrahedron

#### Drawing

• Basic functions in 2D and 3D | Origin of lines and planes | Range of variations of the parameters | Arrow | Legend | Painting a figure | Canonical view point | Control of display
• Movies and story boards in two and three dimensions

#### Transformations

• Affine | Symmetries and inversion | Projection and inverse projection | Rotation | Translation | Zooming | Shear | Splitting a segment | Embedding a 2D object into 3D

#### Intersections

• 2D intersections: Line, conic or polygonal line | Line and general curve
• 3D 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 ratio | Ratio | Sorting points on lines and conics

#### Metric Notions

• Angle of vectors, lines and planes | Areas in 2D and of surfaces | Distance between points, parallel lines and parallel planes | Length of curves | Radius of circles and spheres | Eccentricity of conics

#### Tests and Theorems

• Collinear points, segments, and lines | Coplanar points, segments, and lines
• Congruent triangles | 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
• Surface of type cone, cylinder or sphere
• Line, polygonal line, or conic tangent to a conic | Plane or line tangent to a quadric
• Identical objects
• Theorems: Brianchon | Desargues | Euler | Pascal