A269156 Smallest sum of length of edges and diagonals of an integer polygon with n vertices.

3, 19, 60, 90

Offset

3,1

Comments

An integer polygon is a convex polygon such that the distance between every pair of vertices is an integer (in some length units).

Links

Table of n, a(n) for n=3..6.

B. E. Peterson and J. H. Jordan, Integer geometry: some examples and construction, The Mathematical Gazette, Volume 81, Number 490, 1997, pages 18-28.

Example

An equilateral triangle with sides of length 1 has the smallest perimeter. Hence a(3)=3.
The integer quadrilateral with the smallest sum of lengths of edges and diagonals is a trapezium with bases of length 3 and 4, legs of length 2 and diagonals of length 4. Hence a(4)=19.

Crossrefs

Cf. A096872 for minimum diameter.

Sequence in context: A215646 A182353 A012863 * A370434 A041015 A378115

Adjacent sequences: A269153 A269154 A269155 * A269157 A269158 A269159

Keyword

nonn,more

Author

Dmitry Kamenetsky, Feb 20 2016

Status

approved