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Napoleon's Theorem with Weights in n-Space

by Martini, H., Weißbach, B..

Series: 1998-20, Preprints

51N10 Affine analytic geometry
51N20 Euclidean analytic geometry

The famous theorem of Napoleon was recently extended
to higher dimensions.
With the help of weighted vertices of an n-simplex T in
En, 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.

Napoleon's Theorem, Torricelli's configuration