Plane Geometry
The Wolfram Language provides fully integrated support for plane geometry, including basic regions such as points, lines, triangles, and disks; functions for computing basic properties such as arc length and area; and nearest points to solvers to find the intersection of regions or integrals over regions.
Geometrical Objects »
Point ▪ Line ▪ HalfLine ▪ InfiniteLine ▪ HalfPlane ▪ InfinitePlane
Rectangle ▪ Parallelogram ▪ RegularPolygon ▪ Polygon
Geometric Constructions »
SSSTriangle — triangle specified by the length of its sides
SASTriangle ▪ ASATriangle ▪ AASTriangle ▪ Triangle
Midpoint ▪ AngleBisector ▪ PerpendicularBisector ▪ CircleThrough ▪ ...
TriangleConstruct — incircle, circumcircle, altitude, ... of triangles
TriangleCenter — orthocenter, circumcenter, incenter, ... of triangles
Polygons »
Polygon — polygon or collections of polygons with or without holes
PolygonCoordinates ▪ OuterPolygon ▪ InnerPolygon ▪ ...
Visualization
Graphics — visualize regions with different styles
Region — standard region visualization
Measures & Tests »
Area ▪ Perimeter ▪ ArcLength ▪ PlanarAngle ▪ PolygonAngle
TriangleMeasurement — circumradius, height, ... of triangles
RegionMember — test whether a point is in a region
RegionNearest — nearest point in a region to a given point
RegionQ ▪ RegionDimension ▪ RegionDistance ▪ ...
CollinearPoints ▪ PositivelyOrientedPoints ▪ NegativelyOrientedPoints
Geometric Reasoning »
GeometricScene — symbolic representation of a geometric scene
RandomInstance — find and display a random instance of a geometric scene
FindGeometricConjectures — find conjectures about a geometric scene
GeometricAssertion — assert geometric properties or relations (convex, parallel, congruent, ...)
GeometricTest — test whether geometric objects satisfy given properties or relations
GeometricStep — representation of a step in the construction of a geometric scene
GeometricScene — entities representing notable theorems and constructions
Solving with Regions »
FindInstance — find examples of points in a region
Solve — find curve crossings etc.
NSolve ▪ Reduce ▪ Minimize ▪ NMinimize ▪ ...
Solid Geometry »
CSGRegion — constructive solid geometry region
Polygon ▪ Polyhedron ▪ Sphere ▪ Ball ▪ Cylinder ▪ ...
General Geometry »
ImplicitRegion ▪ MeshRegion ▪ RegionUnion ▪ ...