📐 Geometry

Constructive and analytic geometry — points, lines, curves, angles, and 2D shapes. This is our biggest growth area.

✓ 12 Implemented ⏳ 41 Coming Soon

Measurement — Implemented

Abstand( <PunktA>, <PunktB> )

Aliases: distance, Distance

✓ Done

Euclidean distance between two points, or between a point and a line.

Abstand((1,2), (4,6))   → 5
Abstand((0,0), (3,4))   → 5

Winkel( , <v> ) / Winkel( <A>, , <C> )

Aliases: angle, Angle

✓ Done

Angle between two vectors, or angle at vertex B in triangle ABC.

Winkel((1,0), (0,1))         → 90°
Winkel((1,1), (0,0), (1,0))  → 45°

Flächeninhalt( <Vieleck> ) / Umfang( <Objekt> )

Aliases: area / perimeter

✓ Done

Area and perimeter of polygons, circles, or other geometric shapes.

Flächeninhalt(Kreis((0,0), 5))   → 78.54
Umfang(Kreis((0,0), 5))          → 31.42

Radius( <Kreis> )

Aliases: radius

✓ Done

Returns the radius of a circle object.

Radius(Kreis((0,0), 5))   → 5

Steigung( <Gerade> )

Aliases: slope, Slope

✓ Done

Slope (gradient) of a line object.

Steigung(Gerade((0,0), (2,4)))   → 2

Constructions — Implemented

Mittelpunkt( <A>, )

Aliases: midpoint, Midpoint

✓ Done

Midpoint of a segment or between two points.

Mittelpunkt((1,0), (3,4))   → (2, 2)

Gerade( <A>, ) / Strecke( <A>, ) / Strahl( <A>, )

✓ Done

Line through two points / segment from A to B / ray starting at A through B.

Gerade((0,0), (1,2))   → line: y = 2x
Strecke((0,0), (3,4))  → length 5

Kreis( <Mittelpunkt>, <Radius> ) / Kreis( <A>, , <C> )

✓ Done

Circle from center+radius, or circumscribed circle through 3 points.

Kreis((0,0), 5)              → circle x²+y²=25
Kreis((0,0), (5,0), (0,5))  → circumscribed circle

Vieleck( <P1>, <P2>, ... ) / RegelmaessigesVieleck( <A>, , <n> )

✓ Done

Polygon from vertex list, or regular n-gon from two base points.

Vieleck((0,0),(4,0),(4,3),(0,3))  → rectangle
RegelmaessigesVieleck((0,0),(1,0),6)  → hexagon

Senkrechte( <Punkt>, <Gerade> ) / Parallele( <Punkt>, <Gerade> )

✓ Done

Perpendicular or parallel line through a given point.

Senkrechte((2,1), y=3x+1)   → y = -x/3 + 5/3

Schneide( <Obj1>, <Obj2> )

Aliases: intersect, Intersect

✓ Done

Intersection point(s) of two geometric objects (lines, curves, circles).

Schneide(y=x^2, y=x+2)   → {(-1,1), (2,4)}

Coming Soon — High Priority

Länge( <Objekt> )

⏳ Soon

Length of a segment, vector, or arc. Also arc length along a curve.

Länge(Strecke((0,0),(3,4)))   → 5

Schwerpunkt( <Vieleck> ) / Massenmittelpunkt( <Punkte>, <Massen> )

⏳ Soon

Centroid of a polygon, or center of mass with weighted points.

Scheitel( <Kegelschnitt> )

⏳ Soon

Vertex of a conic section (parabola, ellipse, hyperbola).

Tangente( <Punkt>, <Kurve> )

⏳ Soon

Tangent line to a curve at a given point.

Tangente((1,1), x^2)   → y = 2x - 1

Mittelsenkrechte( <Strecke> ) / Winkelhalbierende( <A>, , <C> )

⏳ Soon

Perpendicular bisector of a segment / angle bisector at vertex B.

SindParallel / SindNormal / SindGleich / SindKongruent

⏳ Soon

Predicate functions to test geometric relationships between objects.

SindParallel(Gerade1, Gerade2)  → true/false
SindNormal(v1, v2)              → true/false

Kreisbogen / Kreissektor / Bogen

⏳ Soon

Arc along a circle and circular sector (pie slice) shapes.

Spiegelung( <Objekt>, <Achse> ) / Drehung( <Obj>, <Zentrum>, <Winkel> )

⏳ Soon

Reflect an object across an axis, or rotate it around a center by an angle.

Spiegelung((3,2), y=x)       → (2, 3)
Drehung((1,0), (0,0), 90°)   → (0, 1)

Verschiebung( <Objekt>, <Vektor> ) / Streckung( <Obj>, <Zentrum>, <Faktor> )

⏳ Soon

Translate by a vector or scale from a center point.

Doppelverhältnis / Teilverhältnis

⏳ Soon

Cross-ratio and division ratio — projective geometry operations on collinear points.

Ortslinie( <Punkt>, <Bedingung> ) / Ortsliniengleichung

⏳ Soon

Locus of points satisfying a dynamic condition. Fundamental for GeoGebra-style constructions.

Einhüllende( <Kurve>, <Parameter> )

⏳ Soon

Envelope of a family of curves parametrized by a slider.

NächsterPunkt( <Kurve>, <Punkt> )

⏳ Soon

Closest point on a curve to a given point (projection).

Schwerpunkt( <ThreePoints> ) — Triangle Centroid

⏳ Soon

Centroid of a triangle at (x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3.