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Square-densities, and volume forms

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arxiv 2012.06210 v3 pith:SO2GWWON submitted 2020-12-11 math.DG

classification math.DG
keywords infinitesimalvolumeantiquityareacertainformformsformula
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Heron's formula from antiquity, for the area of a triangle, is used to relate volume form and infinitesimal square-volume of certain infinitesimal simplices in a Riemannian manifold

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Cited by 1 Pith paper

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  1. Measuring Distortion in the Empty Regions of Dimensionality Reduction Scatterplots with the Gap Index

    cs.LG 2026-07 conditional novelty 5.0 of 10

    The Gap Index quantifies visual distortion in empty regions of DR scatterplots via Delaunay triangle area deformation and is more sensitive to salient gap artifacts than stress or trustworthiness.

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