OFFSET
1,1
COMMENTS
"Enclosing" means that any edge runs outside the circle or is a tangent.
Such a polygon does not need to be symmetrical, but the partial areas in the four quadrants are equal. Therefore it is sufficient to find the least area of a quarter polygon (multiplied by 2). The half area is an integer because the area of any convex polygon whose vertex coordinates are integers is a multiple of 1/2. The least number of polygons minimizing the area is 16 if x=y is not an axis of symmetry (2 solutions for each quadrant).
LINKS
Gerhard Kirchner, Closest polygons around a circle
EXAMPLE
For n=1: 2 X 2 square: a(1) = 4/2 = 2.
For n=2: Octagon with vertices (1,2) and (2,1) in the first quadrant: a(2) = 14/2 = 7.
For further examples, see "Closest polygons around a circle".
PROG
(Visual Basic) ' See "Closest polygons around a circle"
CROSSREFS
KEYWORD
nonn
AUTHOR
Gerhard Kirchner, Oct 17 2022
STATUS
approved