Related papers: Some inequalities for tetrahedra

Some inequalities for different types of convexity are established.

We present a complete system of inequalities for the inradius, circumradius, and diameter in the $3$-dimensional Euclidean space. To do so, we prove quasiconcavity of the inradius evaluated over $n$-simplices with a common facet…

We study tetrahedra and the space of tetrahedra from the viewpoint of local and global maxima for intrinsic distance functions.

We give a geometric proof of the Routh's theorem for tetrahedra.

In this paper, we prove some inequalities for the differences and ratios of the beta function.

We consider the problem of enumerating integer tetrahedra of fixed perimeter (sum of side-lengths) and/or diameter (maximum side-length), up to congruence. As we will see, this problem is considerably more difficult than the corresponding…

We give three new proofs of the triangle inequality in Euclidean Geometry. There seems to be only one known proof at the moment. It is due to properties of triangles, but our proofs are due to circles or ellipses. We aim to prove the…

We prove that the geodesic complexity of a regular tetrahedron exceeds its topological complexity by 1 or 2. The proof involves a careful analysis of minimal geodesics on the tetrahedron.

We prove three inequalities relating some invariants of sets of matrices, such as the joint spectral radius. One of the inequalities, in which proof we use geometric invariant theory, has the generalized spectral radius theorem of Berger…

In the article we prove some inequalities that contain relations between altitudes and medians in triangle. At least one of these inequalities has not been considered in the literature before and the main theorem has also not been proved…

The difference between the (squared) sides of the Grace-Danielsson inequality for tetrahedra will be represented as a sum of two nonnegative terms. This gives another proof of the inequality. Examining the denominator allows us to…

We prove a Hardy inequality for ultraspherical expansions by using a proper ground state representation. From this result we deduce some uncertainty principles for this kind of expansions. Our result also implies a Hardy inequality on…

In this note we characterize all regular tetrahedra whose vertices in R^3 have integer coordinates. The main result is a consequence of the characterization of all equilateral triangles having integer coordinates contained in previous work.…

In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.

We study the perimeter inequality under circular symmetrisation, and we provide a full geometric characterisation of equality cases. A careful inspection of the proof shows that a similar characterisation holds true also for the perimeter…

New Hardy type inequalities in sectorial area and as a limit in an exterior of a ball are proved. Sharpness of the inequalities is shown as well.

We define the notions of outer medians and outer median triangles. We show that outer median triangles enjoy similar properties to that of the median triangle.

As a consequence of the Integral Test we find a triple inequality which bounds up and down both a series with respect to its corresponding improper integral, and reciprocally an improper integral with respect to its corresponding series.

We review some convexity inequalities for Hermitian matrices an add one more to the list.

We obtain some new inequalities of Chebyshev Type.