Napoleon\'s Theorem with Weights in n-Space

by Martini, H.; Weißbach, B.


Preprint series: 98-20, Preprints

51N10 Affine analytic geometry
51N20 Euclidean analytic geometry


Abstract: The famous theorem of Napoleon was recently extended to higher dimensions. With the help of weighted vertices of an n-simplex T in E n , n >= 2, we present a weighted version of this generalized theorem, leading to a natural configuration of (n-1)-speres corresponding with T by an almost arbitrarily chosen point. Besides the Euclidean point of view, also affine aspects of the theorem become clear, and in addition a critical discussion on the role of the Fermat-Tooicelli point in this framework is given.

Keywords: Napoleon\'s Theorem, Torricelli\'s configuration

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