Approximating the Volume of Convex Bodies.
Approximation from the exterior of Carathéodory multifunctions
Approximation of Convex Bodies by Polytopes with Uniformly Bounded Valences.
Approximation of convex bodies by sums of line segments
Approximation of Convex Discs by Polygons.
Approximation of spherical caps by polygons
Approximation of symmetric convex bodies.
Approximation of the Euclidean ball by polytopes
There is a constant c such that for every n ∈ ℕ, there is an Nₙ so that for every N≥ Nₙ there is a polytope P in ℝⁿ with N vertices and where B₂ⁿ denotes the Euclidean unit ball of dimension n.
Approximation of Zonoids by Zonotopes in Fixed Directions.
Approximation on convex bodies by random polytopes.
Approximation under an arc length constraint.
Approximation under an arc length constraint. (Short Communiaction).
Aproximación aleatoria de cuerpos convexos.
Problems related to the random approximation of convex bodies fall into the field of integral geometry and geometric probabilities. The aim of this paper is to give a survey of known results about the stochastic model that has received special attention in the literature and that can be described as follows:Let K be a d-dimensional convex body in Eucliden space Rd, d ≥ 2. Denote by Hn the convex hull of n independent random points X1, ..., Xn distributed identically and uniformly in the interior...
Area and coarea formulas for the mappings of Sobolev classes with values in a metric space.
Area preserving pl homeomorphisms and relations in
To any compactly supported, area preserving, piecewise linear homeomorphism of the plane is associated a relation in of the smallest field whose elements are needed to write the homeomorphism.Using a formula of J. Morita, we show how to calculate the relation, in some simple cases. As applications, a “reciprocity” formula for a pair of triangles in the plane, and some explicit elements of torsion in of certain function fields are found.
Areas of lattice polygons, applied to computer graphics
Areas of Polygons Inscribed in a Circle.
Around the proof of the Legendre-Cauchy lemma on convex polygons.
Around the Razumov-Stroganov conjecture: proof of a multi-parameter sum rule.
Around the Rogers-Shepard inequality.