by Martini, H., Weißbach, B..
Series: 1998-20, Preprints
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
Napoleon's Theorem, Torricelli's configuration