Displaying similar documents to “Triangulation of subanalytic sets”

Whitney triangulations of semialgebraic sets

Masahiro Shiota (2005)

Annales Polonici Mathematici

Similarity:

A compact semialgebraic set admits a semialgebraic triangulation such that the family of open simplexes forms a Whitney stratification and is compatible with a finite number of given semialgebraic subsets.

Distinct equilateral triangle dissections of convex regions

Diane M. Donovan, James G. Lefevre, Thomas A. McCourt, Nicholas J. Cavenagh (2012)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We define a proper triangulation to be a dissection of an integer sided equilateral triangle into smaller, integer sided equilateral triangles such that no point is the vertex of more than three of the smaller triangles. In this paper we establish necessary and sufficient conditions for a proper triangulation of a convex region to exist. Moreover we establish precisely when at least two such equilateral triangle dissections exist. We also provide necessary and sufficient conditions for...

Altitude, Orthocenter of a Triangle and Triangulation

Roland Coghetto (2016)

Formalized Mathematics

Similarity:

We introduce the altitudes of a triangle (the cevians perpendicular to the opposite sides). Using the generalized Ceva’s Theorem, we prove the existence and uniqueness of the orthocenter of a triangle [7]. Finally, we formalize in Mizar [1] some formulas [2] to calculate distance using triangulation.

Combinatorial lemmas for polyhedrons I

Adam Idzik, Konstanty Junosza-Szaniawski (2006)

Discussiones Mathematicae Graph Theory

Similarity:

We formulate general boundary conditions for a labelling of vertices of a triangulation of a polyhedron by vectors to assure the existence of a balanced simplex. The condition is not for each vertex separately, but for a set of vertices of each boundary simplex. This allows us to formulate a theorem, which is more general than the Sperner lemma and theorems of Shapley; Idzik and Junosza-Szaniawski; van der Laan, Talman and Yang. A generalization of the Poincaré-Miranda theorem is also...