# The Monge Point and the 3(n+1) Point Sphere of an n-Simplex

@inproceedings{BubaBrzozowa2005TheMP, title={The Monge Point and the 3(n+1) Point Sphere of an n-Simplex}, author={Małgorzata Buba-Brzozowa}, year={2005} }

The hyperplanes through the centroids of the (ni 2)-dimensional faces of an n-simplex and perpendicular to the respectively opposite 1-dimensional edges have a point in common. As a consequence, we deflne an analogue of the nine-point circle for any n-simplex.

## 7 Citations

### Circumcenter of Mass and Generalized Euler Line

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- 2014

The Circumcenter of Mass (CCM) is an affine combination of the circumcenters of the simplices in a triangulation of a polytope, weighted by their volumes, and it is shown that it satisfies an analog of Archimedes’ Lemma, a familiar property of the center of mass.

### Monge points, Euler lines, and Feuerbach spheres in Minkowski spaces

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### OLD AND NEW GENERALIZATIONS OF CLASSICAL TRIANGLE CENTRES TO TETRAHEDRA

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The classical triangle centres, namely centroid, circumcentre, incentre, excentre, orthocentre and Monge point, will be generalized to tetrahedra in a unified approach as points of concurrence of…

### A Characterization by Optimization of the Monge Point of a Tetrahedron

- MathematicsJ. Optim. Theory Appl.
- 2016

It is shown that it is also the case for the classical “centres” of a tetrahedron, more specifically for the so-called Monge point (the substitute of the notion of orthocentre for a tetstrahedron) by optimization.

### The Triangle

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### Orthocentric Simplices as the True Generalizations of Triangles

- MathematicsThe Mathematical Intelligencer
- 2013

S tudents taking a first course in elementary linear algebra may end up with the impression that the various Euclidean spaces R ; d 3, are routine generalizations ofR and that whatever can be proved…

## References

SHOWING 1-4 OF 4 REFERENCES

### Modern Pure Solid Geometry

- GeologyNature
- 1936

AbstractTHE scope of this book is more limited than its title indicates. The nine chapters deal respectively with preliminary ideas, trihedral angles, skew quadrilaterals, tetrahedra, transversals,…

### Gaspard Monge and the Monge Point of the Tetrahedron

- History
- 2003

Gaspard Monge (1746-1818) was a man of extraordinary talent. Despite humble origins, he founded one new branch of mathematics, made major early contributions to a second, and became a close friend of…

### Ceva, Menelaus, and the Area Principle

- Philosophy
- 1995

(1995). Ceva, Menelaus, and the Area Principle. Mathematics Magazine: Vol. 68, No. 4, pp. 254-268.

### The n-sphere of the 3(n+1) points

- Proc. of Graphica
- 2001