Plane and solid geometry, coordinate geometry, conic sections, polygons and polyhedra, computational geometry (convex hulls, Voronoi, triangulation) and curves and surfaces.
Geometry (geometry-ai999x) is an offline Python package for geometry. It covers plane and solid geometry, coordinate geometry, conic sections, polygons and polyhedra, computational geometry (convex hulls, Voronoi, triangulation) and curves and surfaces.
It has 76 capabilities — 76 computational procedures — in 13 topics, the largest being Computational geometry, Coordinate geometry, Plane figures, Solids, Solid coordinate geometry and Polygons. Ask a question in words with ask(), or call a capability by name with typed inputs with solve(). Every answer carries its value and unit, the steps that produced it and the formula in LaTeX.
When a question is not determined — a value is missing, an input is out of range, or the request is outside the package — it says so and names what it needs, instead of guessing. It runs on an ordinary CPU without a network connection (Python >=3.10), and the same question always gets the same answer.
pip install geometry-ai999x hf download AI999X/geometry-ai999x --local-dir geometry-ai999x
Each question below was put to geometry-ai999x and the answer shown is the one it returned, with the steps it took.
Find the circumcenter and circumradius of the triangle with vertices (0, 0), (4, 0) and (0, 3).
points = [0, 0, 4, 0, 0, 3]cx = 2, cy = 1.5, radius = 2.5Find the convex hull of the points (0, 0), (2, 1), (4, 0), (3, 3), (1, 2), (2, 4).
points = [0, 0, 2, 1, 4, 0, 3, 3, 1, 2, 2, 4]hull = [[0, 0], [4, 0], [3, 3], [2, 4]], n_vertices = 4, area = 9, perimeter = 13.04862718Where does the line y = x + 1 intersect the circle x^2 + y^2 = 25?
cx = 0, cy = 0, r = 5, a = -1, b = 1, c = -1count = 2, x1 = -4, y1 = -3, x2 = 3, y2 = 4Find the volume and surface area of a regular icosahedron with edge 2.
solid = icosahedron, edge = 2vertices = 12, edges = 30, faces = 20, euler_characteristic = 2, volume = 17.45355993, surface_area = 34.64101615, circumradius = 1.902113033, inradius = 1.511522628m.solve("great_circle_distance", lat1=51.5074, lon1=-0.1278, lat2=40.7128, lon2=-74.006) lat1 = 51.5074, lon1 = -0.1278, lat2 = 40.7128, lon2 = -74.006central_angle = 50.09421156, distance = 5570.22218Classify the conic x^2 + 4y^2 - 4 = 0.
A = 1, B = 0, C = 4, D = 0, E = 0, F = -4type = ellipseFind the curvature of y = x^2 at x = 0.
coefficients = [1, 0, 0], x0 = 0curvature = 2, radius_of_curvature = 0.5, slope = 0Find the area of an annulus with outer radius 5 and inner radius 3.
outer = 5, inner = 3area = 50.26548246Every snippet was run as shown; the output under it is what it printed.
import geometry_ai999x as m
a = m.ask("Find the circumcenter and circumradius of the triangle with vertices (0, 0), (4, 0) and (0, 3).")
print(a.outcome)
print(a.values)
for step in a.steps:
print(step["name"])SOLVED
{'cx': 2.0, 'cy': 1.5, 'radius': 2.5}
Circumcircle: the circle through three points
import geometry_ai999x as m
a = m.solve("great_circle_distance", lat1=51.5074, lon1=-0.1278, lat2=40.7128, lon2=-74.006)
print(a.outcome)
print(a.values)SOLVED
{'central_angle': 50.0942115601, 'distance': 5570.22217974}
import geometry_ai999x as m
# an input is missing: the answer says what it needs instead of guessing
a = m.solve("great_circle_distance")
print(a.outcome)
print(a.message)NEEDS_INPUT
great_circle_distance needs lat1, lon1, lat2, lon2 (latitude of point 1, degrees; longitude of point 1, degrees; latitude of point 2; longitude of point 2). Example: solve('great_circle_distance', lat1=0, lon1=0, lat2=0, lon2=90, radius=1).
geometry-ai999x "Find the circumcenter and circumradius of the triangle with vertices (0, 0), (4, 0) and (0, 3)."
cx = 2, cy = 1.5, radius = 2.5 1. Circumcircle: the circle through three points: intersection of the perpendicular bisectors, solved in coordinates relative to the first point with points = [0, 0, 4, 0, 0, 3] -> cx = 2, cy = 1.5, radius = 2.5 Assumptions: exactly 3 points; not collinear …
Every value in these figures was computed by the package, each point a run of solve(); in a notebook, plot() and plot_relation() draw a capability's curves the same way.
12 of its 76 formulas; every one is in the capability browser below.
Search by name, formula, input or topic. Each capability opens to show what it takes, what it returns, when it applies, and a question it answered.
convex_polygon_intersectionThe area common to two convex polygons given by their vertices.
p first convex polygon's vertices in order vectorq second convex polygon's vertices in order vectorarea area of the intersection (0 if they do not overlap)closest_pairThe smallest distance between any two of a set of points in the plane.
points the points: x1 y1, x2 y2, ... vectordistance smallest pairwise distanceconvex_hullThe convex hull of a set of points: its vertices (counterclockwise), their number, its area and perimeter.
points the points: x1 y1, x2 y2, ... vectorhull hull vertices [x, y], counterclockwise from the smallest x (then smallest y)n_vertices number of hull verticesarea area of the hullperimeter perimeter of the hulldelaunay_voronoi_countsNumbers of Delaunay triangles and edges, hull vertices, Voronoi vertices and unbounded Voronoi cells of points in general position.
points the points: x1 y1, x2 y2, ... (3 to 25) vectortriangles Delaunay triangles 2n - 2 - hedges Delaunay edges 3n - 3 - hhull_vertices h, vertices of the convex hullvoronoi_vertices Voronoi vertices (one per triangle)unbounded_cells unbounded Voronoi cells (one per hull vertex)point_segment_distanceThe shortest distance from a point to the segment AB and the closest point of the segment.
px x of the pointpy y of the pointx1 x of Ay1 y of Ax2 x of By2 y of Bdistance shortest distanceqx x of the closest pointqy y of the closest pointfarthest_pairThe largest distance between any two of a set of points in the plane.
points the points: x1 y1, x2 y2, ... vectordistance largest pairwise distancehausdorff_distanceThe Hausdorff distance between two finite point sets and both directed distances.
a first set: x1 y1, x2 y2, ... vectorb second set vectordistance max of the two directed distancesfrom_a max over A of the distance to the nearest point of Bfrom_b max over B of the distance to the nearest point of Asegment_intersectionWhether segments AB and CD meet, and where: at one point, along an overlap, or not at all.
points the endpoints A, B, C, D: xA yA, xB yB, xC yC, xD yD vectorstatus point / overlap / nonex x of the common point (point only)y y of the common point (point only)min_area_rectangleThe area (and sides) of the smallest-area rectangle, in any orientation, enclosing the points.
points the points: x1 y1, x2 y2, ... vectorarea minimum areawidth shorter side of that rectanglelength longer sidenearest_neighborWhich of a list of points is nearest to a query point, and how far it is.
px x of the query pointpy y of the query pointpoints the candidate points: x1 y1, x2 y2, ... vectorindex position of the nearest point in the list (1 = first)distance its distancenx its xny its ypoint_in_polygonWhether a point lies inside, outside or on the boundary of a simple polygon.
px x of the pointpy y of the pointpoints polygon vertices in order: x1 y1, x2 y2, ... vectorlocation inside / outside / boundarymin_enclosing_circleCentre and radius of the smallest circle that contains every given point.
points the points: x1 y1, x2 y2, ... vectorcx x of the centrecy y of the centreradius radiusconic_classifyWhether A x^2 + B xy + C y^2 + D x + E y + F = 0 is a circle, ellipse, parabola, hyperbola, a degenerate conic or has no real points.
A coefficient of x^2B coefficient of xyC coefficient of y^2D coefficient of xE coefficient of yF constant termtype circle / ellipse / parabola / hyperbola / degenerate / emptyellipse_perimeterThe exact perimeter (circumference) and area of an ellipse with semi-axes a and b.
a one semi-axisb the other semi-axisperimeter 4 a E(e^2), a the larger semi-axisarea pi a bangle_between_linesThe acute (or right) angle between two lines given by equations.
a1 coefficient of x in line 1 (a1 x + b1 y + c1 = 0)b1 coefficient of y in line 1c1 constant of line 1a2 coefficient of x in line 2 (a2 x + b2 y + c2 = 0)b2 coefficient of y in line 2c2 constant of line 2angle angle between the lines, degrees, 0 to 90barycentric_coordinatesThe barycentric coordinates (l1, l2, l3) of a point with respect to triangle ABC: P = l1 A + l2 B + l3 C, l1 + l2 + l3 = 1.
px x of the pointpy y of the pointpoints the triangle's vertices A, B, C vectorl1 weight of Al2 weight of Bl3 weight of Ctriangle_circumcircleCircumcentre and circumradius of a triangle given by its vertices (the circle through three points).
points the three points: x1 y1, x2 y2, x3 y3 vectorcx x of the circumcentrecy y of the circumcentreradius circumradiustriangle_incircleIncentre and inradius of the triangle with the given vertices.
points the vertices: xA yA, xB yB, xC yC vectorix x of the incentreiy y of the incentreradius inradiuscircle_line_intersectionThe points where the line a x + b y + c = 0 meets the circle with centre (cx, cy) and radius r (0, 1 or 2 points).
cx x of the centrecy y of the centrer radiusa coefficient of x of the lineb coefficient of y of the linec constant of the linecount number of intersection points (0, 1 or 2)x1 x of the first point (ordered by x, then y)y1 y of the first pointx2 x of the second pointy2 y of the second pointcircle_circle_intersectionThe points where two circles meet (0, 1 or 2 points).
x1 x of the first centrey1 y of the first centrer1 first radiusx2 x of the second centrey2 y of the second centrer2 second radiuscount number of intersection points (0, 1 or 2)x1 x of the first point (ordered by x, then y)y1 y of the first pointx2 x of the second pointy2 y of the second pointline_intersectionThe point where two lines a1 x + b1 y + c1 = 0 and a2 x + b2 y + c2 = 0 meet.
a1 coefficient of x in line 1 (a1 x + b1 y + c1 = 0)b1 coefficient of y in line 1c1 constant of line 1a2 coefficient of x in line 2 (a2 x + b2 y + c2 = 0)b2 coefficient of y in line 2c2 constant of line 2x x of the intersectiony y of the intersectionpolyline_lengthThe total length of the open path that visits the points in the order given.
points the points in order: x1 y1, x2 y2, ... vectorlength sum of the segment lengthssegments number of segmentstriangle_orthocenterThe orthocentre (common point of the three altitudes) of the triangle with the given vertices.
points the vertices: xA yA, xB yB, xC yC vectorhx x of the orthocentrehy y of the orthocentretangent_from_pointThe tangent length from an external point to a circle and the two points of tangency.
cx x of the centrecy y of the centrer radiuspx x of the external pointpy y of the external pointlength tangent length sqrt(d^2 - r^2)x1 x of the first tangency point (ordered by x, then y)y1 y of the first tangency pointx2 x of the second tangency pointy2 y of the second tangency pointtriangle_coordinatesArea, perimeter, centroid and the angles at A, B, C of the triangle with vertices A, B, C.
points the vertices A, B, C: xA yA, xB yB, xC yC vectorarea area (shoelace)perimeter perimetergx x of the centroidgy y of the centroidangle_A angle at A, degreesangle_B angle at B, degreesangle_C angle at C, degreesparabola_arc_lengthThe length of the curve y = a x^2 + b x + c between x = x0 and x = x1.
a coefficient of x^2b coefficient of xx0 start xx1 end xc constant (does not affect the length) optionallength arc lengthcurvature_of_graphThe curvature and radius of curvature of y = p(x) at x = x0 for a polynomial p.
coefficients coefficients from the highest power down: a_n, ..., a_1, a_0 vectorx0 the x-coordinate of the pointcurvature |y''| / (1 + y'^2)^(3/2)radius_of_curvature 1 / curvature (none where the curvature is 0)slope y'(x0)ellipse_curvatureThe curvature and radius of curvature of the ellipse (a cos t, b sin t) at parameter t (eccentric anomaly).
a semi-axis along xb semi-axis along yt parameter t (eccentric anomaly), degreescurvature ab / (a^2 sin^2 t + b^2 cos^2 t)^(3/2)radius_of_curvature 1 / curvaturex x of the pointy y of the pointhelix_measuresCurvature, torsion and arc length per turn of the circular helix of radius r and pitch p (rise per turn).
radius radius r of the helixpitch pitch p: rise per full turn (negative: left-handed)curvature r / (r^2 + c^2), c = p / (2 pi)torsion c / (r^2 + c^2)length_per_turn sqrt((2 pi r)^2 + p^2)triangle_area_base_heightThe area of a triangle from a base and the height (altitude) to that base.
base length of the baseheight height perpendicular to the basearea area b*h/2annulus_areaThe area between two concentric circles.
outer outer radiusinner inner radiusarea pi (R^2 - r^2)circle_measuresArea, circumference and diameter of a circle from its radius (or diameter).
radius radius of the circlearea area pi r^2circumference circumference 2 pi rdiameter diameter 2rsector_measuresArc length, sector area and chord of a circular sector from the radius and central angle.
radius radiusangle central angle in degreesarc_length r theta (theta in radians)sector_area r^2 theta / 2chord 2 r sin(theta/2)circular_segmentArea, chord, height (sagitta) and arc length of the circular segment cut off by a chord with a given central angle.
radius radiusangle central angle in degreesarea r^2 (theta - sin theta)/2chord 2 r sin(theta/2)height r (1 - cos(theta/2))arc_length r thetatriangle_classifyWhether a triangle with sides a, b, c is equilateral, isosceles or scalene, and acute, right or obtuse.
a side ab side bc side cby_sides equilateral / isosceles / scaleneby_angles acute / right / obtusetriangle_ceviansThe lengths of the three medians, three altitudes and three internal angle bisectors of a triangle from its sides.
a side a (opposite A)b side b (opposite B)c side c (opposite C)median_a median from vertex A (to side a)median_b median from vertex B (to side b)median_c median from vertex C (to side c)altitude_a altitude from vertex A (to side a)altitude_b altitude from vertex B (to side b)altitude_c altitude from vertex C (to side c)bisector_a bisector from vertex A (to side a)bisector_b bisector from vertex B (to side b)bisector_c bisector from vertex C (to side c)rectangle_measuresArea, perimeter and diagonal of a rectangle (a square when length = width).
length length of the rectanglewidth width of the rectanglearea area l*wperimeter perimeter 2(l + w)diagonal diagonal sqrt(l^2 + w^2)rhombus_measuresArea, side and perimeter of a rhombus from its two diagonals.
d1 first diagonald2 second diagonalarea d1 d2 / 2side sqrt(d1^2 + d2^2)/2perimeter 4 * sidetrapezoid_measuresArea and midsegment (median) of a trapezoid from its parallel sides and height.
a first parallel sideb second parallel sideheight distance between the parallel sidesarea (a + b) h / 2midsegment (a + b) / 2polygon_centroidThe centroid (centre of mass of the uniform region) of a simple polygon given its vertices in order.
points vertices in order: x1 y1, x2 y2, ... vectorcx x of the centroidcy y of the centroidpolygon_interior_anglesThe interior angle at every vertex of a simple polygon (reflex angles included), their sum and the number of reflex vertices.
points vertices in order: x1 y1, x2 y2, ... vectorangles interior angle at each vertex, degrees, in the order givenangle_sum (n - 2) 180reflex_vertices number of angles above 180 degreespolygon_is_convexWhether a simple polygon given by its vertices is convex.
points vertices in order: x1 y1, x2 y2, ... vectorconvex yes / nopick_lattice_pointsArea, boundary lattice points and interior lattice points of a simple polygon with integer vertices.
points integer vertices in order: x1 y1, x2 y2, ... vectorarea areaboundary_points lattice points on the boundaryinterior_points lattice points strictly insideregular_polygon_anglesEach interior and exterior angle of a regular n-gon, the interior angle sum of any n-gon and its number of diagonals.
n number of sides integerinterior_angle each interior angle of the regular polygon, degreesexterior_angle each exterior angle, degreesinterior_sum sum of the interior angles, degreesdiagonals number of diagonals n(n-3)/2polygon_areaArea (shoelace formula), perimeter and orientation of a simple polygon given its vertices in order.
points vertices in order: x1 y1, x2 y2, ... vectorarea enclosed areaperimeter sum of the edge lengthsorientation counterclockwise or clockwiseregular_polygon_measuresArea, perimeter, apothem (inradius) and circumradius of a regular n-gon from its side length.
n number of sides integerside side lengtharea n s a / 2perimeter n sapothem s / (2 tan(pi/n))circumradius s / (2 sin(pi/n))platonic_solidVertices, edges, faces, Euler characteristic, volume, surface area, circumradius and inradius of a regular polyhedron of edge a.
solid which Platonic solid choiceedge edge length avertices Vedges Efaces Feuler_characteristic V - E + Fvolume volumesurface_area surface areacircumradius radius of the circumscribed sphereinradius radius of the inscribed sphereangle_between_planesThe acute (dihedral) angle between two planes given by their equations (only the normals matter).
a1 x-coefficient of plane 1b1 y-coefficient of plane 1c1 z-coefficient of plane 1a2 x-coefficient of plane 2b2 y-coefficient of plane 2c2 z-coefficient of plane 2angle angle between the planes, degrees, 0 to 90skew_lines_distanceThe shortest distance between the lines P1 + s d1 and P2 + t d2 in three dimensions.
p1 a point on line 1 vectord1 direction of line 1 vectorp2 a point on line 2 vectord2 direction of line 2 vectordistance shortest distanceparallel yes / no (exact test)point_plane_distanceThe distance from a point to the plane a x + b y + c z + d = 0 and the foot of the perpendicular.
px x of the pointpy y of the pointpz z of the pointa coefficient of xb coefficient of yc coefficient of zd constant termdistance |a px + b py + c pz + d| / sqrt(a^2 + b^2 + c^2)fx x of the footfy y of the footfz z of the footline_plane_intersectionThe point where the line P0 + t v meets the plane a x + b y + c z + d = 0.
x0 x of a point on the liney0 y of the pointz0 z of the pointdx x of the directiondy y of the directiondz z of the directiona coefficient of xb coefficient of yc coefficient of zd constant termx x of the intersectiony yz zt line parameter at the intersectionplane_through_pointsThe equation a x + b y + c z + d = 0 of the plane through three points, with (a, b, c) a unit normal.
points the three points: x y z for each vectora x-component of the unit normalb y-componentc z-componentd constant termsphere_four_pointsCentre and radius of the sphere through four non-coplanar points.
points the four points: x y z for each vectorcx x of the centrecy y of the centrecz z of the centreradius radiustetrahedron_measuresVolume and total surface area of the tetrahedron with four given vertices.
points the four vertices: x y z for each vectorvolume |det(B - A, C - A, D - A)| / 6surface_area sum of the four face areastriangle_area_3dArea and perimeter of the triangle with vertices A, B, C in three-dimensional space.
points the vertices: xA yA zA, xB yB zB, xC yC zC vectorarea areaperimeter perimetersolid_angle_coneThe solid angle (steradians) subtended at the apex by a right circular cone of given half-angle.
half_angle half-angle of the cone (axis to side), degreessolid_angle 2 pi (1 - cos a) steradiansfraction_of_sphere solid angle / (4 pi)solid_angle_triangleThe solid angle (steradians) that the triangle with vertices A, B, C subtends at the origin.
points the vertices as seen from the origin: x y z for each vectorsolid_angle solid angle, steradianscone_measuresVolume, slant height, lateral area and total surface area of a right circular cone.
radius radius of the baseheight perpendicular heightvolume pi r^2 h / 3slant_height sqrt(r^2 + h^2)lateral_area pi r ltotal_area pi r (r + l)cuboid_measuresVolume, total surface area and space diagonal of a rectangular box (a cube when all edges are equal).
length lengthwidth widthheight heightvolume l w hsurface_area 2(lw + lh + wh)space_diagonal sqrt(l^2 + w^2 + h^2)cylinder_measuresVolume, lateral (curved) area and total surface area of a right circular cylinder.
radius radius of the baseheight heightvolume pi r^2 hlateral_area 2 pi r htotal_area 2 pi r (r + h)frustum_measuresVolume, slant height, lateral and total surface area of a frustum of a right circular cone.
r1 radius of one baser2 radius of the other baseheight perpendicular heightvolume pi h (R^2 + R r + r^2)/3slant_height sqrt(h^2 + (R - r)^2)lateral_area pi (R + r) stotal_area lateral + pi (R^2 + r^2)regular_prismVolume, base area, lateral and total surface area of a right prism whose base is a regular n-gon.
n number of sides of the base integerside side length of the baseheight height (length) of the prismvolume base area * heightlateral_area n s htotal_area lateral + 2 * basebase_area n s^2 / (4 tan(pi/n))pyramid_measuresVolume, lateral area and total surface area of a right pyramid on a rectangular base (apex above the base centre).
length base lengthwidth base widthheight perpendicular heightvolume l w h / 3lateral_area area of the four triangular facestotal_area lateral + basesphere_measuresVolume and surface area of a sphere from its radius (or diameter).
radius radiusvolume 4/3 pi r^3surface_area 4 pi r^2spherical_capVolume, curved surface area and base radius of a cap of height h cut from a sphere of radius R.
radius radius R of the sphereheight height h of the capvolume pi h^2 (3R - h)/3cap_area 2 pi R hbase_radius sqrt(h (2R - h))spheroid_measuresSurface area and volume of an oblate or prolate spheroid with equatorial radius a and polar radius c.
a equatorial radius (semi-axis in the equator)c polar radius (semi-axis along the axis)surface_area surface areavolume 4/3 pi a^2 cshape oblate / prolate / spheretorus_measuresVolume and surface area of a ring torus with major radius R (centre to tube centre) and tube radius r.
major major radius Rminor tube (minor) radius rvolume 2 pi^2 R r^2surface_area 4 pi^2 R rspherical_triangle_areaThe spherical excess and area of the triangle with three vertices given by latitude and longitude on a sphere of radius R.
points the vertices (lat lon): lat1 lon1, lat2 lon2, lat3 lon3, degrees vectorradius sphere radius (default 1; 'Earth' means 6371 km) optionalexcess spherical excess A + B + C - 180, degreesarea area E R^2 (E in radians)great_circle_distanceThe central angle and great-circle distance between two points given by latitude and longitude (on the Earth unless a radius is given).
lat1 latitude of point 1, degreeslon1 longitude of point 1, degreeslat2 latitude of point 2lon2 longitude of point 2radius sphere radius (default 6371, the mean Earth radius in km) optionalcentral_angle central angle, degreesdistance great-circle distance (radius units)initial_bearingThe initial compass bearing from point 1 to point 2 along the great circle, degrees clockwise from north.
lat1 latitude of the start, degreeslon1 longitude of the startlat2 latitude of the destinationlon2 longitude of the destinationbearing initial bearing, degrees in [0, 360), clockwise from northtorus_curvatureGaussian, mean and principal curvatures of a ring torus at tube angle v (v = 0 on the outer equator, 180 on the inner).
major major radius Rminor tube radius rv tube angle v, degrees (0 = outer equator)gaussian K = cos v / (r (R + r cos v))mean H = (R + 2 r cos v) / (2 r (R + r cos v))k1 principal curvature around the tube, 1/rk2 principal curvature along the ring, cos v / (R + r cos v)surface_curvatureGaussian curvature K and mean curvature H of z = A x^2 + B xy + C y^2 + D x + E y + F at the point above (x0, y0).
A coefficient of x^2B coefficient of xyC coefficient of y^2D coefficient of xE coefficient of yx0 x of the pointy0 y of the pointF constant term (does not affect curvature) optionalgaussian Gaussian curvature Kmean mean curvature H (upward normal: positive where the surface opens upward)dilate_pointThe image of a point under a dilation with scale factor k about a centre (the origin unless given).
px x of the pointpy y of the pointk scale factor (negative: through the centre)cx x of the centre (default 0) optionalcy y of the centre (default 0) optionalx x of the imagey y of the imagereflect_point_lineThe mirror image of a point in the line a x + b y + c = 0 (including the axes and y = x).
px x of the pointpy y of the pointa coefficient of x of the lineb coefficient of y of the linec constant of the linex x of the imagey y of the imagerotate_pointThe image of a point rotated by an angle about a centre (the origin unless given); counterclockwise is positive.
px x of the pointpy y of the pointangle rotation angle in degrees, counterclockwise positivecx x of the centre (default 0) optionalcy y of the centre (default 0) optionalx x of the imagey y of the imagerotate_point_3dThe image of a point rotated by an angle about an axis through the origin (right-hand rule).
point the point x y z vectoraxis axis direction (through the origin) vectorangle angle in degrees (right-hand rule)x x of the imagey y of the imagez z of the image15 files, 44.1 MB in total. The largest:
| File | Size |
|---|---|
| model.safetensors | 18.9 MB |
| dist/geometry_ai999x-1.0.0-py3-none-any.whl | 16.8 MB |
| onnx/search/encoder.int8.onnx | 4.9 MB |
| docs/geometry_ai999x_capabilities.pdf | 2.6 MB |
| onnx/search/index.json | 403.3 KB |
| docs/geometry_ai999x_capabilities.html | 202.7 KB |
| onnx/search/tokenizer.json | 176.4 KB |
| docs/geometry_ai999x_capabilities.md | 147.8 KB |
| README.md | 21.7 KB |
| LICENSE | 11.4 KB |
| evaluation/release_gate.md | 2.3 KB |
| evaluation/KNOWLEDGE_CARD.md | 1.4 KB |
Geometry answers questions in geometry: plane and solid geometry, coordinate geometry, conic sections, polygons and polyhedra, computational geometry (convex hulls, Voronoi, triangulation) and curves and surfaces. Each answer gives the value with its unit, the steps and the formula in LaTeX.
With pip: pip install geometry-ai999x. The same files are on Hugging Face (hf download AI999X/geometry-ai999x --local-dir geometry-ai999x) and GitHub.
Yes. It is a Python package that runs on an ordinary CPU without a network connection (Python >=3.10); no GPU and no API key are needed.
76 capabilities in 13 topics, including Computational geometry, Coordinate geometry, Plane figures, Solids, Solid coordinate geometry.
Field: Mathematics & Statistics. Tasks: Question Answering, Token Classification, Text Classification, Sentence Similarity, Feature Extraction.
Asked "Find the circumcenter and circumradius of the triangle with vertices (0, 0), (4, 0) and (0, 3).", it answers: cx = 2, cy = 1.5, radius = 2.5.
It says so and names what is missing or out of range, instead of guessing a number.