What is the asymptotic growth rate of the area of the smallest triangle determined by three out of points in a square, when the points are chosen to maximize this area?
(more unsolved problems in mathematics)
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 triangles of small area. It is named after Hans Heilbronn, who conjectured that, no matter how points are placed in a given area, the smallest triangle area will be at most inversely proportional to the square of the number of points. His conjecture was proven false, but the asymptotic growth rate of the minimum triangle area remains unknown.
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area? (more unsolved problems in mathematics) In discrete geometry and discrepancy theory, the Heilbronntriangleproblem is a problem of placing points...
for his research on sums of powers, on the large sieve, on the Heilbronntriangleproblem, and on square packing in a square. He was a coauthor of the book...
Solving the happy ending problem for arbitrary n {\displaystyle n} Improving lower and upper bounds for the Heilbronntriangleproblem. Kalai's 3d conjecture...
unsolved problems relating to discrepancy theory include: Axis-parallel rectangles in dimensions three and higher (folklore) Komlós conjecture Heilbronn triangle...
number problem Deuring–Heilbronn phenomenon Heilbronn triangleproblemHeilbronn set Heilbronn Institute for Mathematical Research List of German Canadians...
coinage, and the thrackle conjecture. Heilbronntriangleproblem, on sets of points that do not form triangles of small area Minkowski's theorem, that...
the Heilbronntriangleproblem, throw n {\displaystyle n} points in the unit square and determine the maximum of the minimal area of a triangle formed...
Hamming distance Hash function Hash collision Perfect hash function Heilbronntriangleproblem Helly family Hypergeometric function identities Hypergeometric...
Europaminister, 15./16.07.2013, Heilbronn/ Bad Wimpfen Federal Foreign Office, press release of 9 July 2013. "Weimar Triangle – Amélie de Montchalin's meeting...
literature, such problems are sometimes considered to be direct problems as well. Examples of this type include the Erdős–Heilbronn Conjecture (for a...
doi:10.1145/272991.272995. S2CID 3332028. Roth, K.F. (1951). "On a problem of Heilbronn". Journal of the London Mathematical Society. Second Series. 26 (3):...
sister ten years before. The episode is partly based on the Phantom of Heilbronn case. 123–124 "Domestica" Anthony Byrne Richard Davidson Anthony Flanagan...
within this framework. Davenport–Schmidt theorem Duffin–Schaeffer theorem Heilbronn set Low-discrepancy sequence Khinchin 1997, p. 21 Cassels 1957, p. 2 Lang...
Siegle of the Department of Research and Development, AEG-Telefunken, Heilbronn, Germany for what they called a "three-state signaling system". Reportedly...
First and the Ninth US Army. The target of the unit was the industrial triangle at Eschweiler-Weisweiler and the Eschweiler woods at Stolberg. This part...
bombing campaign on Milan, Turin and Genoa (the so-called 'industrial triangle') during the autumn of 1942. All three cities suffered heavy damage and...
metres wide at its base beyond the Leopold Canal (described as a long triangle with its base on the Maldegem-Aardenburg road and its apex near the village...
Kilowatt series symmetrical antenna coupler] (product manual) (in German). Heilbronn, DE: Annecke HF - Techn. Bauelemente. DJ 6 00. Westerman, Richard M. (DJ0IP)...
close up to the Rhine in the British section was the clearing of the Roer Triangle (codename Operation Blackcock). The XIII Corps removed German forces from...
Strauss's exhaustive Heidelberg dissertation on the POW and internment in the Heilbronn camp. The mountain of evidence has been building that Bacque's charge...
"Tallest Smokestack in the World El Paso, TX". www.cardcow.com. Inco Triangle sudburymuseums.ca "Our History in Canada". www.vale.com. "Schilling Power...
Commission. As an urban planner, he has worked o in the cities of Stuttgart, Heilbronn, Ulm, Würzburg, Jena, Potsdam, Stralsund, Lübeck and Flensburg, Paris...
Dietrich Höppner and Kurt Hintzmann of AEG-Telefunken Halbleiterwerk [de], Heilbronn. The chip contained more than 500 transistors. With minimal changes in...
Göppingen, to be taken into operation, so that through trains could run from Heilbronn to Friedrichshafen. Thus, the first railway line across Württemberg was...
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