Function Repository Resource:

GeometricSolve

Source Notebook

Solve for a given quantity in a geometric scene

Contributed by: Daniel McDonald

ResourceFunction["GeometricSolve"][scene,expr]

solves for the quantity expr defined by the GeometricScene scene.

ResourceFunction["GeometricSolve"][scene,{expr₁,expr₂,…}]

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

Details and Options

Each separate solution is returned as a List.

Solution components are returned in the form expr₁→value₁, expr₂→value₂, ….

Examples

Basic Examples (3)

Solve for the hypotenuse of a right triangle:

In[1]:=

$ResourceFunction["GeometricSolve"][ GeometricScene[{a, b, c}, {Triangle[{a, b, c}], PlanarAngle[{a, b, c}] == 90 \[Degree], EuclideanDistance[a, b] == 3, EuclideanDistance[b, c] == 4}], EuclideanDistance[a, c] ]$

Out[1]=

Compute the area of a specific triangle:

In[2]:=

ResourceFunction["GeometricSolve"][
GeometricScene[{a, b, c}, {a == {0, 0}, b == {0, 4}, c == {5, 3}, p == Polygon[{a, b, c}]}],
Area[p]
]

Out[2]=

Compute the area of a triangle where one point has an unknown but positive x value:

In[3]:=

ResourceFunction["GeometricSolve"][
GeometricScene[{a, b, c}, {a == {0, 0}, b == {0, 4}, c == {d, 5}, d > 0, p == Polygon[{a, b, c}]}],
Area[p]
]

Out[3]=

Scope (2)

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:

In[4]:=