OFFSET
1,1
COMMENTS
"Enclosing" means that each edge lies outside the circle or is tangent to it.
The area of a "grid triangle" with integer vertex coordinates is a multiple of 1/2. If (0,0) is the center of the circle, a grid triangle exists with a vertex (x0,y0), 0 <= x0 <= y0 (because of the grid symmetry) such that the area is minimized.
The basic idea of finding the minimum: Generate triangles with vertices (x0,y0), (x1,y1), (x2,y2) such that all edges are tangents and replace (x1,y1) and (x2,y2) with points with integer coordinates in the neighborhood.
Limit_{n->oo} a(n)/n^2 = 6*sqrt(3). - Jon E. Schoenfield, Nov 19 2022
LINKS
Gerhard Kirchner, Examples and algorithm
Gerhard Kirchner, Visual Basic program
Gerhard Kirchner, Diagrams
EXAMPLE
See link.
PROG
(Visual Basic) ' See links.
CROSSREFS
KEYWORD
nonn
AUTHOR
Gerhard Kirchner, Nov 18 2022
STATUS
approved