Add to ORKGFrom among � � n triangles with vertices chosen from n points in the unit square, 3 let T be the one with the smallest area, and let A be the area of T. Heilbronn’s triangle problem asks for the maximum value assumed by A over all choices of n points. We consider the average-case: If the n points are chosen independently and at random (with a uniform distribution), then there exist positive constants c and C such that c/n3 <µ n < C/n3 for all large enough values of n, where µ n is the expectation of A. Moreover, c/n3 <A<C/n3, with probability close to one. Our proof uses the incompressibility method based on Kolmogorov complexity; it actually determines the area of the smallest triangle for an arrangement i
Ensino Médio::MatemáticaThe general Heilbronn problem finds maxima for points in unit objects. In th...
Ensino Médio::MatemáticaThe general Heilbronn problem finds maxima for points in unit objects. In th...
In this paper we study the following problem: we are given a set of imprecise points modeled as para...
From among (n/3) triangles with vertices chosen from n points in the unit square, let T be the one w...
Heilbronn's triangle problem asks for the least \Delta such that n points lying in the unit dis...
AbstractWe consider a variant of Heilbronn's triangle problem by asking for a distribution of n poin...
noneFor n points in a square of side length one, find the three points that make the triangle with m...
Heilbronn conjectured that given arbitrary n points form R"2, located in the unit square (or ci...
AbstractFor given integers d,j≥2 and any positive integers n, distributions of n points in the d-dim...
AbstractGiven 3n points in the unit square, n ⩾ 2, they determine n triangles whose vertices exhaust...
Pick n points independently at random in R , according to a prescribed probability measure , and l...
Problem. Let ABC be a triangle in which ∡B and ∡C are acute, and let PQRS be a rectangle inscribed ...
AbstractThe study of extremal problems on triangle areas was initiated in a series of papers by Erdő...
AbstractFor given integers d,j≥2 and any positive integers n, distributions of n points in the d-dim...
AbstractWe consider a variant of Heilbronn's triangle problem by asking for a distribution of n poin...
Ensino Médio::MatemáticaThe general Heilbronn problem finds maxima for points in unit objects. In th...
Ensino Médio::MatemáticaThe general Heilbronn problem finds maxima for points in unit objects. In th...
In this paper we study the following problem: we are given a set of imprecise points modeled as para...
From among (n/3) triangles with vertices chosen from n points in the unit square, let T be the one w...
Heilbronn's triangle problem asks for the least \Delta such that n points lying in the unit dis...
AbstractWe consider a variant of Heilbronn's triangle problem by asking for a distribution of n poin...
noneFor n points in a square of side length one, find the three points that make the triangle with m...
Heilbronn conjectured that given arbitrary n points form R"2, located in the unit square (or ci...
AbstractFor given integers d,j≥2 and any positive integers n, distributions of n points in the d-dim...
AbstractGiven 3n points in the unit square, n ⩾ 2, they determine n triangles whose vertices exhaust...
Pick n points independently at random in R , according to a prescribed probability measure , and l...
Problem. Let ABC be a triangle in which ∡B and ∡C are acute, and let PQRS be a rectangle inscribed ...
AbstractThe study of extremal problems on triangle areas was initiated in a series of papers by Erdő...
AbstractFor given integers d,j≥2 and any positive integers n, distributions of n points in the d-dim...
AbstractWe consider a variant of Heilbronn's triangle problem by asking for a distribution of n poin...
Ensino Médio::MatemáticaThe general Heilbronn problem finds maxima for points in unit objects. In th...
Ensino Médio::MatemáticaThe general Heilbronn problem finds maxima for points in unit objects. In th...
In this paper we study the following problem: we are given a set of imprecise points modeled as para...