Invisibility in billiards is impossible in an infinite number of directions

TL;DR

This paper proves that in a two-dimensional billiard system outside a piecewise smooth body, the number of directions in which the body is invisible is finite, establishing a fundamental limitation on invisibility.

Contribution

It introduces a new result showing the maximum number of invisible directions in such billiards is finite, advancing understanding of geometric invisibility constraints.

Findings

Maximum number of invisible directions is finite.

Invisibility in billiards is fundamentally limited.

Provides a mathematical proof for the finiteness of invisibility directions.

Abstract

We consider the billiard in the exterior of a piecewise smooth body in two-dimensional Euclidean space and show that the maximum number of directions of invisibility in such billiard is at most finite.