Geometriae Dedicata

, Volume 5, Issue 1, pp 51–70

n-bathycenters

  • Bruce Hedman
Article
  • 11 Downloads

Abstract

Does there exist a polygon with the property that for a suitable point p in the plane every ray with endpoint p intersects the polygon in exactly n connected components? Does there exist a polygon with the property that there are two such points, or three, or a segment of such points?

For polygon P call a point p with the property that every ray from p intersects P in exactly n connected components n-isobathic with respect to P. Define the n-bathycenter of a polygon P as the set of all points p that are n-isobathic with respect to P. Further define a set S to be an n-bathycenter if there exists a polygon P of which S is the n-bathycenter. This paper deals with the characterization of 2- and 3-bathycenters, together with some results on the general case.

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Copyright information

© D. Reidel Publishing Company 1976

Authors and Affiliations

  • Bruce Hedman
    • 1
  1. 1.2625 Graduate CollegePrinceton UniversityPrincetonU.S.A.

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