Geometriae Dedicata

, Volume 5, Issue 1, pp 51–70 | Cite as

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.

Keywords

Suitable Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. 1.
    Guggenheimer, H., Am. Math. Monthly 80 (1973), 211–212.Google Scholar

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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