The Geometry Engine
CoreGX is powered by the same constraint solver and symbolic algebra system at the heart of Geometry Expressions, a commercial symbolic geometry tool with decades of development behind it. The engine is exposed here as a REST API, making precise geometric computation available to any application or LLM that can make an HTTP request.
Describe relationships, not coordinates
Most geometry tools require you to place objects at explicit positions. CoreGX works the other way: you describe the relationships between objects, and the engine determines where everything goes.
Specify that a triangle has a right angle at B, that sides AB and BC have lengths 3 and 4, and that a circle passes through all three vertices. The engine resolves the full figure from those constraints alone, without you ever naming a coordinate.
This makes CoreGX well suited to tasks where the geometry is defined by rules rather than measurements: proofs, constructions, and figures that need to hold under symbolic parameters.
# No x/y coordinates needed. # Describe the figure by its rules. anglemode degree triangle A B C angle A B C 90 distance AB 3 distance BC 4 circumcircle C0 O A B C measure distance(O,A) measure area(A,B,C)
Exact, symbolic results
Numerical solvers approximate. CoreGX computes exactly. When a measurement depends on a symbolic parameter, the result is a symbolic expression, not a rounded decimal. Distances, angles, areas, perimeters, and curve equations are returned in closed algebraic form when possible.
A right triangle with legs a and b returns a hypotenuse
of sqrt(a^2 + b^2),
not 5.000.
This precision is preserved through the full computation, making results
suitable for mathematical publishing, LLM reasoning, or downstream symbolic computation.
# Legs are symbolic: a and b anglemode degree triangle A B C angle A B C 90 distance AB a distance BC b measure distance(A,C) measure area(A,B,C) # Response equations: # sqrt(a^2+b^2) # (1/2)*a*b
What the engine handles
A summary of supported constructions and constraints.
Points, lines, segments, circles, triangles, polygons, vectors, and cyclic polygons.
Midpoints, intersections, altitudes, medians, angle bisectors, perpendicular bisectors, projections, circumcircles, incircles, and excircles.
Distance, angle, radius, parallelism, perpendicularity, congruence, incidence, tangency, and side/orientation constraints.
Ellipses, parabolas, hyperbolas, loci, envelopes, Cartesian functions, polar functions, and parametric curves.
Reflection, rotation, dilation, and translation, applied to any object. Transforms may depend on parameters, enabling locus and envelope constructions.
Distance, angle, area, perimeter, radius, slope, direction, coordinates, line and circle equations, parametric equations, centroids, and moments of inertia.