The Midpoint Locus of a Triangle in a Corner

  • Daniel Lichtblau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6877)


We are given an equilateral triangle with vertices constrained to lie in each of the three positive octant coordinate planes (colloquially, “a triangle in a corner”). We wish to describe the locus of points covered by the midpoint of the triangle, as the vertices range over configurations allowed by the above constraint. This locus comprises a solid region. We use numerical and graphical methods, and also computational algebra, to find the boundary surface and visualize this locus.


Constraint geometry implicit surfaces nonlinear systems 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Daniel Lichtblau
    • 1
  1. 1.Wolfram Research, Inc.ChampaignUSA

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