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UFOs -- Unidentified Figurative Objects. A Geometric Challenge

C. Bruschek·S. Gann·H. Hauser·D. Wagner·D. Zeillinger
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Abstract

Choose a polynomial in three variables with not more than three or four monomials of moderate degree. Take simple coefficients as 1 and -1. Then draw a picture of the solution variety in real three space using a ray-tracing program like POV-Ray, Surf or Spicy. Go to your colleague in the next room, show her/him the picture and ask for a suitable equation. This is the theme of the article: The problem of recognizing the algebraic definition of a geometric object, in this case a real algebraic surface. We do not offer any answers or results. 24 surfaces are presented, each in two different views, but without equations. The reader may try to find them -- or consult the calendar at http://www.hh.hauser.cc, where the equations are displayed one per day together with a short animation of the surface.

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C. Bruschek, S. Gann, H. Hauser, D. Wagner, D. Zeillinger. 2005-12-07. UFOs -- Unidentified Figurative Objects. A Geometric Challenge. https://arxiv.org/abs/math/0512160

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