Related papers: Outer median triangles
We establish a characterization of the extraordinary dimension of perfect maps between metrizable spaces.
In this article we obtain an improved upper bound for the regularity of binomial edge ideals of trees.
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 several congruences for trinomial coefficients.
We establish two comparison results between the solutions of a class of mean curvature equations and pieces of arcs of circles that satisfy the same Neumann boundary condition. Finally we present a number of examples where our estimates can…
In this paper, we develop the theory of symmetric triads with multiplicities. First, we classify abstract symmetric triads with multiplicities. Second, we determine the symmetric triads with multiplicities corresponding to commutative…
Any four mutually tangent spheres in R^3 determine three coincident lines through opposite pairs of tangencies. As a consequence, we define two new triangle centers.
A description of solutions of some integral equations has been obtained. A two-radii theorem is obtained as well.
The classical inner and outer billiards can be formulated in variational terms, with length and area as the respective generating functions. The other two combinations, ``inner with area'' and ``outer with length,'' are more recently…
We study equivalence relation of the set of triangles generated by similarity and operation on a triangle to get a new one by joining division points of three edges with the same ratio. Using the moduli space of similarity classes of…
We introduce the concept of pseudo-trisections of smooth oriented compact 4-manifolds with boundary. The main feature of pseudo-trisections is that they have lower complexity than relative trisections for given 4-manifolds. We prove…
We characterize conservative median algebras and semilattices by means of forbidden substructures and by providing their representation as chains. Moreover, using a dual equivalence between median algebras and certain topological…
We give an explicit description of cubic rings over a discrete valuation ring, as well as a description of all ideals of such rings.
A perfect triangle is a triangle with rational sides, medians, and area. In this article, we use a similar strategy due to Pocklington to show that if $\Delta$ is a perfect triangle, then it cannot be an isosceles triangle. It gives a…
We construct 3-manifolds which have at least two inequivalent embeddings such that both complementary regions have abelian fundamental group.
In a previous paper we have introduced the ortho-homological triangles, which are triangles that are orthological and homological simultaneously. In this article we call attention to two remarkable ortho-homological triangles (the given…
The median principle is applied for different integral inequalities of Gruss and Ostrowski type.
We prove that the Eulerian polynomial satisfies certain polynomial congruences. Furthermore, these congruences characterize the Eulerian polynomial.
We generalize the classical Ceva's and Menelaus's theorems to curvilinear triangles bounded by circular arcs. We introduce trilinear coordinates associated with such triangles and develop several geometric constructions. In particular, for…
We find a one-to-one correspondence between full extrinsic symmetric spaces in (possibly degenerate) inner product spaces and certain algebraic objects called (weak) extrinsic symmetric triples. In particular, this yields a description of…