The article presents the Heilbronn Triangle Problem, a classic problem in discrete geometry. The goal is to place nn points inside a region of area 1 so that the smallest triangle determined by any three points is as large as possible. In other words, we want to distribute the points as evenly as possible while avoiding three points becoming nearly collinear. The page examines three settings: points restricted to a unit square, points inside a unit-area triangle, and points inside an arbitrary convex region whose area is 1.
The site provides the best-known values of A(n)A(n) for n=3n=3 through 3535, together with exact coordinates for the corresponding point configurations, symmetry information, proofs where available, and an online verifier. A key feature is that only some values are marked as proven optimal; many others are merely the best configurations currently known.
The numerical values decrease rapidly as nn increases—for example, in the square the value falls from 0.50.5 for n=3n=3 to about 0.004100.00410 for n=35n=35. Thus, the page serves both as an introduction to the Heilbronn problem and as a catalogue of computational and mathematically verified progress on an optimization problem that remains difficult for larger numbers of points.
ARTICLE
The site provides the best-known values of A(n)A(n) for n=3n=3 through 3535, together with exact coordinates for the corresponding point configurations, symmetry information, proofs where available, and an online verifier. A key feature is that only some values are marked as proven optimal; many others are merely the best configurations currently known.
The numerical values decrease rapidly as nn increases—for example, in the square the value falls from 0.50.5 for n=3n=3 to about 0.004100.00410 for n=35n=35. Thus, the page serves both as an introduction to the Heilbronn problem and as a catalogue of computational and mathematically verified progress on an optimization problem that remains difficult for larger numbers of points.
ARTICLE
┌────────────────────────────────┐
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘