### 1998-20

by Martini, H., Weißbach, B..

**Series:** 1998-20, Preprints

- MSC:
- 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