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GeometricStep[{hyp1,hyp2,…}]

gives a symbolic representation of a step in the definition of a geometric scene, in which the hypotheses hypi are introduced.

GeometricStep[hyps,label]

labels the step with label when displaying an instance of the geometric scene.

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GeometricStep

GeometricStep[{hyp1,hyp2,…}]

gives a symbolic representation of a step in the definition of a geometric scene, in which the hypotheses hypi are introduced.

GeometricStep[hyps,label]

labels the step with label when displaying an instance of the geometric scene.

Details

Examples

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Basic Examples  (2)

Display an interactive scene that constructs, in steps, a square equal in area to a given polygon:

Wolfram Language code: GeometricScene[{{, , , , , , , , , , , , }, {}}, {GeometricStep[{GeometricAssertion[{Polygon[{, , , }]}, "Convex"]}], GeometricStep[{GeometricAssertion[{Polygon[{, , , }]}, "Equiangular", "Clockwise"], Area[Polygon[{, , , }]] == Area[Polygon[{, , , }]]}], GeometricStep[{Line[{, , }], EuclideanDistance[, ] == EuclideanDistance[, ]}], GeometricStep[{ == Midpoint[Line[{, }]]}], GeometricStep[{GeometricAssertion[{Line[{, , }], CircleThrough[{}, ]}, {"Concurrent", }]}], GeometricStep[{GeometricAssertion[{Polygon[{, , , }]}, "Regular"]}]}, {Area[Polygon[{, , , }]] == Area[Polygon[{, , , }]]}]//RandomInstance

Label the steps in a scene constructing an equilateral triangle from a given line segment:

Wolfram Language code: RandomInstance[GeometricScene[{a, b, c}, {GeometricStep[{Line[{a, b}]}, Row[{"Let ", Line[{a, b}], " be given."}]], GeometricStep[{CircleThrough[{b, c}, a], CircleThrough[{a, c}, b]}, "Draw circles centered at each endpoint passing through the other endpoint."], GeometricStep[{Triangle[{a, b, c}]}, Row[{Triangle[{a, b, c}], " is equilateral"}]]}]]

Scope  (1)

Display an interactive scene that constructs, in steps, the bisector of a given angle:

Wolfram Language code: GeometricScene[{{a, b, c, d, e, f}, {}}, { GeometricStep[{PlanarAngle[{b, a, c}]}], GeometricStep[{d∈Line[{a, b}]}], GeometricStep[{e∈Line[{a, c}], EuclideanDistance[a, d] == EuclideanDistance[a, e]}], GeometricStep[{GeometricAssertion[Triangle[{e, f, d}], "Equilateral"], GeometricAssertion[{{f}, {a}}, {"OppositeSides", Line[{d, e}]}]}], GeometricStep[{Line[{a, f}]}] }]//RandomInstance

Add textual descriptions to each step:

Wolfram Language code: GeometricScene[{{a, b, c, d, e, f}, {}}, { GeometricStep[{PlanarAngle[{b, a, c}]}, "Let bac be the given angle."], GeometricStep[{d∈Line[{a, b}]}, "Take a point d on ab."], GeometricStep[{e∈Line[{a, c}], EuclideanDistance[a, d] == EuclideanDistance[a, e]}, "Find a point e on ac such that ad=ae."], GeometricStep[{GeometricAssertion[Triangle[{e, f, d}], "Equilateral"], GeometricAssertion[{{f}, {a}}, {"OppositeSides", Line[{d, e}]}]}, "Construct an equilateral triangle efd with base de and with vertex f falling on the opposite side of de from a."], GeometricStep[{Line[{a, f}]}, "Join af to bisect bac."] }]//RandomInstance

Properties & Relations  (2)

If there is a GeometricStep, consecutive hypotheses are grouped into geometric steps:

Wolfram Language code: GeometricScene[{a, b, c}, {Line[{a, b}], GeometricStep[{CircleThrough[{b, c}, a], CircleThrough[{a, c}, b]}], Triangle[{a, b, c}], CircleThrough[{a, b, c}]}]

The presence of a GeometricStep adds a menu for selecting stages of a GeometricScene:

Wolfram Language code: RandomInstance /@ {GeometricScene[{a, b, c}, {Line[{a, b}], CircleThrough[{b, c}, a], CircleThrough[{a, c}, b], Triangle[{a, b, c}], CircleThrough[{a, b, c}]}], GeometricScene[{a, b, c}, {Line[{a, b}], GeometricStep[{CircleThrough[{b, c}, a], CircleThrough[{a, c}, b]}], Triangle[{a, b, c}], CircleThrough[{a, b, c}]}]}

Possible Issues  (1)

If constraints are added to objects after the step in which those objects are introduced, the scene may be unsatisfiable:

Wolfram Language code: RandomInstance[GeometricScene[{a, b}, {GeometricStep[{Line[{a, b}]}], GeometricStep[{EuclideanDistance[a, b] == 1}]}]]

Adding the constraints to the same step in which the objects are introduced may allow the scene to be satisfiable:

Wolfram Language code: RandomInstance[GeometricScene[{a, b}, {GeometricStep[{Line[{a, b}], EuclideanDistance[a, b] == 1}]}]]
Wolfram Research (2020), GeometricStep, Wolfram Language function, https://reference.wolfram.com/language/ref/GeometricStep.html.

Text

Wolfram Research (2020), GeometricStep, Wolfram Language function, https://reference.wolfram.com/language/ref/GeometricStep.html.

CMS

Wolfram Language. 2020. "GeometricStep." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeometricStep.html.

APA

Wolfram Language. (2020). GeometricStep. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeometricStep.html

BibTeX

@misc{reference.wolfram_2026_geometricstep, author="Wolfram Research", title="{GeometricStep}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/GeometricStep.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_geometricstep, organization={Wolfram Research}, title={GeometricStep}, year={2020}, url={https://reference.wolfram.com/language/ref/GeometricStep.html}, note=[Accessed: 12-June-2026]}