# GeometricSolveValues

GeometricSolveValues[scene,expr]

solves for the symbolic geometric quantity expr defined by the GeometricScene object scene.

GeometricSolveValues[scene,{expr1,expr2,}]

returns a list containing the solutions of scene for expr1,expr2, .

# Details

• If a single quantity is specified, the result is a list of values of the quantity that can occur in valid instances of scene.
• If a list of quantities is specified, the result is a list of lists of values of the quantities that can occur in valid instances of scene. »
• If all point coordinates and quantities in scene are assigned numerical values (such as if scene were returned by RandomInstance), then output will be based solely on those values. »
• If not all point coordinates and quantities in scene are assigned numerical values and expr cannot be determined to be an invariant of the scene, then output may not be numerical. »
• Symbolic representations of coordinates use Indexed. »

# Examples

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## Basic Examples(3)

Solve for the hypotenuse of a right triangle:

Compute the area of a specific triangle:

Create a geometric scene:

Find the area of the quadrilateral :

Visualize an instance of the scene:

## Scope(6)

Consider a triangle where two of the three vertices are fixed:

Compute the area of the triangle for any position of the third vertex :

Compute the area of the particular triangle pictured above:

Construct an isosceles triangle with the segments from the vertices to the opposite sides forming the inner angles:

Solve for the measure of the inner angle :

Visualize an instance of the scene:

Construct a scene with two triangles embedded inside a third triangle:

Solve for a ratio of areas of the two inner triangles:

Consider a shaded region defined by a square and a circle:

Compute the fraction of the square covered by the shaded region:

Construct a geometric scene:

Find the area of the triangle and the measure, in radians, of the angle :

Visualize the triangle:

Find an instance of a scene:

Solve for the point a, the distance between points a and c and the area of the triangle in this scene instance:

Solving with a different instance will give different results:

## Properties & Relations(4)

If expr in GeometricSolveValues[scene,expr] is not a list, the result is a list of possible values:

If expr is a list, even a list of one element, the result is a list of lists of possible values:

Results using coordinates of points are represented with Indexed:

Results for abstract scenes, even if they uniquely describe the geometry, are based solely on the description:

Results for concrete scenes are expressed in terms of the coordinates of the scene:

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

The subvalue "AlgebraicFormulation" of a GeometricScene object gives a conjunction of constraints for that scene to be valid:

The hypotenuse can be solved for using SolveValues on the algebraic formulation or using GeometricSolveValues directly on the scene:

## Possible Issues(1)

For a generic triangle, there are two possible solutions for the area, only one of which will have the correct sign for a specific numeric instantiation of the parameters:

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

#### Text

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

#### CMS

Wolfram Language. 2024. "GeometricSolveValues." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeometricSolveValues.html.

#### APA

Wolfram Language. (2024). GeometricSolveValues. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeometricSolveValues.html

#### BibTeX

@misc{reference.wolfram_2024_geometricsolvevalues, author="Wolfram Research", title="{GeometricSolveValues}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/GeometricSolveValues.html}", note=[Accessed: 02-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_geometricsolvevalues, organization={Wolfram Research}, title={GeometricSolveValues}, year={2024}, url={https://reference.wolfram.com/language/ref/GeometricSolveValues.html}, note=[Accessed: 02-August-2024 ]}