Solution to the Dead Fly Problem

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-04-02
DOI
https://doi.org/10.5281/zenodo.19382340
Primary Topic
Computational Geometry and Mesh Generation
Type
article
Field-Weighted Citation Impact
0.00
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article

Solution to the Dead Fly Problem

ARVIND N
Zenodo (CERN European Organization for Nuclear Research)
Computational Geometry and Mesh Generation
article

Solution to the Dead Fly Problem

ARVIND N
article en

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.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Openalex Percentile: Top 3%
Computational Geometry and Mesh Generation
DOIOpen Access PDFOpenAlex
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Solution to the Dead Fly Problem — ARVIND N · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS