[HN Gopher] The Biggest Smallest Triangle Just Got Smaller
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       The Biggest Smallest Triangle Just Got Smaller
        
       Author : rbanffy
       Score  : 11 points
       Date   : 2023-09-11 11:49 UTC (10 hours ago)
        
 (HTM) web link (www.quantamagazine.org)
 (TXT) w3m dump (www.quantamagazine.org)
        
       | alexander2002 wrote:
       | Can someone explain the headline in laymen terms
        
         | _Microft wrote:
         | There are sets of triangles and in each one there will be a
         | smallest triangle by area. Now look at all of these possible
         | sets for a given number of points. There's a value for the area
         | that this smallest triangle cannot exceed. That's the biggest
         | smallest triangle. The researchers here showed that this value
         | was so far overestimated.
        
         | eigenket wrote:
         | Take a 1 meter by 1 meter square, and scatter a bunch of points
         | inside. Every 3 of those points forms a triangle with those
         | points as its vertices. Take the smallest one of those
         | triangles and compute its area.
         | 
         | This process (consider every triangle and compute the smallest
         | area) gives you a function which takes an arrangement of points
         | and returns a number. Now ask which arrangement of points gives
         | the biggest such number. This is the biggest smallest triangle
         | problem and it appears to be very (very very very) difficult.
        
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       (page generated 2023-09-11 22:02 UTC)