Editing Heilbronn triangle problem (section)

{{good article}}
{{Short description|On point sets with no small-area triangles}}
{{unsolved|mathematics|What is the asymptotic growth rate of the area of the smallest triangle determined by three out of <math>n</math> points in a square, when the points are chosen to maximize this area?}}
[[File:Heilbronn square n=6.svg|thumb|300px|Six points in the unit square, with the smallest triangles (red) having area 1/8, the optimal area for this number of points. Other larger triangles are colored blue. These points are an [[affine transformation]] of a [[regular hexagon]], but for larger numbers of points the optimal solution does not form a convex polygon.]]
In [[discrete geometry]] and [[discrepancy theory]], the '''Heilbronn triangle problem''' is a problem of placing points in the plane, avoiding [[triangle]]s of small [[area]]. It is named after [[Hans Heilbronn]], who [[conjecture]]d that, no matter how points are placed in a given area, the smallest triangle area will be at most [[Proportionality (mathematics)#Inverse proportionality|inversely proportional]] to the [[Square (algebra)|square]] of the number of points. His conjecture was proven false, but the [[Asymptotic analysis|asymptotic growth]] rate of the minimum triangle area remains unknown.