Function Repository Resource:

ErikssonCornerAngle

Evaluate the multidimensional corner angle

Contributed by: Michael Reed
 ResourceFunction["ErikssonCornerAngle"][o,{p1,…,pd}] gives the corner angle at the point o and spanned by the vectors p1,…,pd.

Details

ResourceFunction["ErikssonCornerAngle"] generalizes the law of sines for d-dimensional Euclidean simplices.

Examples

Basic Examples (2)

The corner angle at the origin for vectors in two dimensions:

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The corner angle at the origin for vectors in three dimensions:

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Scope (1)

ErikssonCornerAngle works in any number of dimensions:

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Applications (2)

Compute the corner angle for various Platonic solids:

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Generate a random simplex:

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Compute all the corner angles of the simplex:

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Properties and Relations (2)

In two dimensions, ErikssonCornerAngle is similar to the results of SolidAngle and PlanarAngle:

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In three dimensions, the difference between ErikssonCornerAngle and SolidAngle is more apparent:

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Michael Reed

Version History

• 1.0.0 – 20 July 2022