GeometricScene

GeometricScene[{p1,p2,},{hyp1,hyp2,}]

represents an abstract 2D geometric scene defined by the hypotheses hypi in terms of the symbolic points pi.

GeometricScene[{{p1,p2,},{k1,k2,}},hyps]

represents a scene whose hypotheses depend on the symbolic scalar quantities ki.

GeometricScene[{{p1{x1,y1},},{k1v1,}},hyps]

represents a specific instance with explicit values for all points and scalar quantities.

GeometricScene[params,hyps,{con1,con2,}]

represents a scene together with some conclusions coni about it.

GeometricScene[{{{p1{x1,y1},},{k1v1,}},},hyps]

represents a collection of specific instances of the same scene.

GeometricScene[{scene1,scene2,}]

combines several scene instances into one scene object.

Details and Options

Examples

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Basic Examples  (4)

Represent a symbolic geometric scene containing a triangle with points a, b, c and a 30° angle:

RandomInstance fills in explicit coordinates for the points:

Retrieve the rules giving coordinates for the points:

Represent a geometric scene with explicit coordinates for points:

Display an interactive scene that constructs an equilateral triangle in steps:

Consider a scene featuring a right triangle with its leg lengths specified but its hypotenuse unknown:

Use GeometricSolveValues to solve for the hypotenuse :

Scope  (4)

Find multiple instances of a scene depicting a triangle, one of whose sides is a diameter of its circumcircle:

Combine the instances into a single GeometricScene object:

Find the coordinates for the points in the scene corresponding to each instance:

Represent a scene depicting line-circle tangency using a GeometricAssertion:

Find conjectures about the scene:

Extract the conclusions from the GeometricScene object:

Represent the construction of the infinite line bisecting the angle formed by points points a, b, c with GeometricStep:

Style can be used to apply styles to objects in a geometric scene:

Options  (6)

Axes  (1)

Draw a medial triangle with coordinate axes shown:

Background  (1)

Draw a polygon on a yellow background:

GeometricStylingRules  (1)

Specify how primitives in a scene are to be styled:

PlotLabel  (1)

Draw the nine-point circle of a triangle with a plot label:

PlotTheme  (1)

Style the entire scene in pre-defined ways:

UnconstrainedParameters  (1)

Represent a scene where the points a, b, c are unconstrained, and the remaining points must conform to the triangle made by the unconstrained points:

Applications  (7)

Solve for a missing radius, given the radii of four pairwise tangent circles:

Represent a scene with a triangle circumscribed by a circle whose diameter forms an edge:

Find conjectures:

Extract Thales's theorem:

Represent a scene with two sets of collinear points:

Find conjectures:

Discover Pappus's hexagon theorem:

Iteratively take circumcenters:

Find conjectures:

Discover Kosnita's theorem:

Solve for missing angles:

Describe a scene with two squares and a quadrilateral formed by taking midpoints:

Find conjectures:

Discover the FinslerHadwiger theorem:

Bisect a given arc, as specified by Euclid's Book 3, Proposition 30:

Properties & Relations  (2)

Geometric scenes with symbolic points do not format:

Geometric scenes where all points have numerical values format graphically:

The conditions for a GeometricScene to hold can be extracted with the subvalue "AlgebraicFormulation":

GeometricTest directly finds these conditions:

These are the same conditions as were returned by the GeometricScene subvalue "AlgebraicFormulation":

Neat Examples  (1)

Decompose a polygon into similar triangles:

Wolfram Research (2019), GeometricScene, Wolfram Language function, https://reference.wolfram.com/language/ref/GeometricScene.html (updated 2024).

Text

Wolfram Research (2019), GeometricScene, Wolfram Language function, https://reference.wolfram.com/language/ref/GeometricScene.html (updated 2024).

CMS

Wolfram Language. 2019. "GeometricScene." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/GeometricScene.html.

APA

Wolfram Language. (2019). GeometricScene. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeometricScene.html

BibTeX

@misc{reference.wolfram_2024_geometricscene, author="Wolfram Research", title="{GeometricScene}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/GeometricScene.html}", note=[Accessed: 11-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_geometricscene, organization={Wolfram Research}, title={GeometricScene}, year={2024}, url={https://reference.wolfram.com/language/ref/GeometricScene.html}, note=[Accessed: 11-December-2024 ]}