Contents
Getting Started
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Calling Geometrica | Mathematica notations | Tour
of Geometrica | More on quadrics
Points
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Cartesian point | Parametric point | Bound point
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Barycenter | Brianchon point | Center | Center of gravity | Center of
perspective | Circumcenter | Excenters | Fermat point | Foci |
Incenter | Orthocenter | Pole | Vertices
Lines and Planes
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Cartesian line and plane | Pencil | Euclidean line and plane |
Conjugate line | Conjugate plane | Parallel | Normal plane
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Altitudes | Asymptotes | Axes | Axis of perspective | Bisector |
Diagonals | Directrices | Generators | Medians | Normals | Pascal line
| Polar | Symmetry planes
Conics
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Cartesian conic in 2D and 3D | Pencil | Euclidean conic | Conic elements
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Circle | Circumcircle | Euler circle | Excircles | Incircle | Ellipse
| Parabola | Hyperbola
Quadrics
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Cartesian quadric | Euclidean quadric | Quadric elements
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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
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General definitions | Parameter range | Cubic or Bezier fits |
Parallel | Ribbon | Offset or paraxial Arc | Helix | Petal | Racetrack
| Solid angle
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General cone and cylinder | Helicoid | Helicoidal staircase | Solid
angle 3D | Solid of revolution
Polygons and Polyhedra
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General definitions | Segment | Elements of polygons and polyhedra |
Orthogonal and parallel polygons
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Triangle | Isosceles | Right angled | Diamond | Parallelogram |
Rectangle | Regular polygon | Reference systems
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Cube | Parallelepiped | Platonic solid | Prismoid | Pyramid | Tetrahedron
Drawing
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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
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Movies and story boards in two and three dimensions
Transformations
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Affine | Symmetries and inversion | Projection and inverse projection
| Rotation | Translation | Zooming | Shear | Splitting a segment |
Embedding a 2D object into 3D
Intersections
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2D intersections: Line, conic or polygonal line | Line and general curve
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3D intersections: Coplanar lines or conics | Plane with line, plane,
polygonal line, polyhedron, quadric, cone, cylinder, general curve or
surface
Affine Notions
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Barycentric coordinates | Cartesian coordinates | Cross ratio | Ratio
| Sorting points on lines and conics
Metric Notions
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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
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Collinear points, segments, and lines | Coplanar points, segments, and lines
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Congruent triangles | Similar triangles | Regular polygon | Platonic solid
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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
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Surface of type cone, cylinder or sphere
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Line, polygonal line, or conic tangent to a conic | Plane or line tangent
to a quadric
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Identical objects
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Theorems: Brianchon | Desargues | Euler | Pascal
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