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Title of Journal: Result Math

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Abbravation: Results in Mathematics

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SP Birkhäuser Verlag Basel

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DOI

10.1016/1010-6030(91)85081-q

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1420-9012

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Orthocentric Simplices and Biregularity

Authors: Allan L Edmonds Mowaffaq Hajja Horst Martini
Publish Date: 2008/07/21
Volume: 52, Issue: 1-2, Pages: 41-50
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Abstract

It is well known that the incenter of a Euclidean triangle lies on its Euler line connecting the centroid and the circumcenter if and only if the triangle is isosceles The analogue of this result in higher dimensions is studied for orthocentric simplices It is shown that the incenter of an orthocentric simplex of any dimension lies on its Euler line if and only if this simplex can be expressed as the join of two regular simplices with all edges connecting the two corresponding components having the same length These are precisely the orthocentric simplices whose group of isometries has as fixed point set a line or a point in the special case of a regular simplex

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Other Papers In This Journal:
  1. Attracting and Invariant Sets of Nonlinear Stochastic Neutral Differential Equations with Delays
  2. L p -L q Estimates For Solutions To The Damped Plate Equation In Exterior Domains
  3. Defect and Area in Beltrami–Klein Model of Hyperbolic Geometry
  4. Limits of integrals involving almost periodic functions
  5. Asymptotische LÖsungen Der Translationsgleichung
  6. Representation Formulas of Curves in a Two- and Three-Dimensional Lightlike Cone
  7. Decompositions of para-complex vector bundles and para-complex affine immersions
  8. Smooth Stable Planes
  9. Blaschke Dupin hypersurfaces and equiaffine tubes
  10. Matrix Representations of Sturm–Liouville Problems with Finite Spectrum
  11. On the Variation-Diminishing Property
  12. Real Hypersurfaces in Complex Two-plane Grassmannians with $${\mathfrak{D}^{\bot}}$$-Parallel Shape Operator
  13. Point-Reflection Geometries, Geometric K-Loops and Unitary Geometries
  14. Stability of Two Types of Cubic Fuzzy Set-Valued Functional Equations
  15. Pedal Curves Part I: Homogeneous Differential Equation
  16. Regelflächen von Strahlensystemen Mit Demselben SphÄrischen Bild
  17. On the de la Vallée-Poussin Means on the Sphere
  18. Type $${\mathcal{}}$$ Sets and the ttractors of Infinite Iterated Function Systems
  19. Conditions for Starlikeness of Multivalent Functions
  20. Rigidity of Complete Minimal Hypersurfaces in the Euclidean Space
  21. On the Rate of Almost Everywhere Convergence of Abel-Cartwright means on L p ( R n )
  22. A Class of Nonlocal Impulsive Problems for Integrodifferential Equations in Banach Spaces
  23. Minimal Submanifolds in S p+3 with Constant Scalar Curvature
  24. Closed form of the Fourier–Borel Kernel in the Framework of Clifford Analysis
  25. Approximation by Linear Combinations of Complex Phillips Operators in Compact Disks
  26. Liouville Theorems for F -Harmonic Maps and Their Applications
  27. A Theorem on Homogeneous Differential Polynomials
  28. Recent Developments In Harmonic Approximation, With Applications
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