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

Circle  ▪  Disk

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  ▪  ...


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  ▪  ...

Geometric Data

PlaneCurve Lamina Polyhedron Solid