Balanced lines, halving triangles, and the generalized lower bound theorem

  • Authors:

  • Micha Sharir;Emo Welzl

  • Affiliations:

  • School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel and Courant Institute of Mathematical Sciences, New York University, New York, NY;Theoretical Computer Science, ETH Zürich, CH-8092 Zürich, Switzerland

  • Venue:
  • SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
  • Year:
  • 2001

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Abstract

A recent result by Pach and Pinchasi on so-called balanced lines of a finite two-colored point set in the plane is related to other facts on halving triangles in 3-space and to a special case of the Generalized Lower Bound Theorem for convex polytopes.