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- Title
REFINED EULER’S INEQUALITIES IN PLANE GEOMETRIES AND SPACES.
- Authors
VELJAN, DARKO
- Abstract
Refined famous Euler’s inequalities R ≥ nr of an ndimensional simplex for n = 2, 3 and 4 as well as of non-Euclidean triangles in terms of symmetric functions of edge lengths of a triangle or a simplex in question are shown. Here R is the circumradius and r the inradius of the simplex. We also provide an application to geometric probabilities of our results and an example from astrophysics to the position of a planet within the space of four stars. We briefly discuss a recursive algorithm to get similar inequalities in higher dimensions.
- Subjects
TETRAHEDRA; MATHEMATICS; NON-Euclidean geometry; ALGEBRA; POLYNOMIALS
- Publication
Rad HAZU: Matematicke Znanosti, 2023, Vol 27, p167
- ISSN
1845-4100
- Publication type
Article
- DOI
10.21857/y6zolb6ldm