On Napoleon's theorem in the isotropic plane]{On Napoleon's theorem in
the isotropic plane |
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| Authors: | Horst Martini Margarita Spirova |
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| Institution: | (1) Faculty of Mathematics, University of Technology Chemnitz, 09107 Chemnitz, Germany;(2) Faculty of Mathematics and Informatics, University of Sofia, James Bourchier, 1164 Sofia, Bulgaria |
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| Abstract: | Summary Napoleon's original theorem refers to arbitrary triangles in the
Euclidean plane. If equilateral triangles are externally erected on the sides
of a given triangle, then their three corresponding circumcenters form an
equilateral triangle. We present some analogous theorems and related statements
for the isotropic (Galilean) plane. |
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| Keywords: | dual numbers Napoleon configuration Cayley--Klein geometries Napoleon's theorem Galilean plane isotropic plane |
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