On the relative distances of nine points in the boundary of a plane convex body

DOI10.1007/s00025-021-01398-2zbMath1467.52005OpenAlexW3149195286MaRDI QIDQ2038634

Cen Liu, Zhanjun Su

Publication date: 7 July 2021

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-021-01398-2

zbMATH Keywords

homothetical copyrelative distanceplane convex body

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15) Convex sets in (2) dimensions (including convex curves) (52A10)

Cites Work

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• On the relative distances of eleven points in the boundary of a plane convex body
• On the relative distances of nine or ten points in the boundary of a plane convex body
• The relative lengths of sides of convex hexagons and octagons
• Self-packing of centrally symmetric convex bodies in \(\mathbb{R}{}^ 2\)
• Covering the boundary of a convex body with its smaller homothetic copies
• On five points in the boundary of a plane convex body pairwise in at least unit relative distances
• On relatively short and long sides of convex pentagons
• On the relative distances of seven points in a plane convex body
• On the relative lengths of the sides of convex polygons
• On the relative lengths of sides of convex polygons
• On the relative distances of six points in a plane convex body
• On a conjecture about nine points in the boundary of a plane convex body at pairwise relative distances not greater than \({4 \sin \frac{\pi}{18}}\)

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