The Kakeya problem for circular arcs
Korn\'elia H\'era, Mikl\'os Laczkovich
TL;DR
This paper demonstrates that very short circular arcs can be moved continuously to any position within an arbitrarily small area, revealing new geometric flexibility properties of such arcs.
Contribution
It establishes a new result on the mobility of short circular arcs within small regions, extending understanding of geometric transformations.
Findings
Short circular arcs can be moved freely within small areas.
The movement is continuous and can reach any prescribed position.
The result applies to arcs with sufficiently small angles.
Abstract
We prove that if a circular arc has angle short enough, then it can be continuously moved to any prescribed position within a set of arbitrarily small area.
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