What question did this study set out to answer?

To prove that in any set of points intersecting a convex region of area 1, pairs must exist at arbitrarily small distances.

April 4, 20260 citationsOpen Access

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ANARVIND N

Key Points

To prove that in any set of points intersecting a convex region of area 1, pairs must exist at arbitrarily small distances.
Used a packing argument to analyze spatial arrangements of points.
Applied interval analysis to assess distances between points.
Employed scaling techniques to derive contradictions regarding minimum distances.
Demonstrated that arbitrary point sets interacting with convex regions require close distances.
Proved that the minimum distance between some pairs of points must be zero.

Abstract

"This paper proves that any set of points in the plane intersecting every convex region of area 1 must contain pairs of points at arbitrarily small distances. The proof uses a packing argument, interval analysis, and scaling to derive a contradiction unless the minimum distance is zero."

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Cite This Study

ARVIND N (Thu,) studied this question.

synapsesocial.com/papers/69d0afc7659487ece0fa5e50 https://doi.org/https://doi.org/10.5281/zenodo.19382340

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