New Results about Minimum Number of Lattice Points, when the Condition for the Midpoints of the Connecting Segments Are Given
International Conference Pioneers of Bulgarian Mathematics, Sofia University St Kliment Ohridski, July 8-10, 2006, Sofia, 39-40
Objects of examination are lattice points in the plane and n-dimensional space. The basis of this work is the problem for determining the minimum number of lattice points in the plane, among which there always exists at least a couple of them that satisfies the following conditions: the midpoint of the connecting segment is also a point from the lattice. A summary is made by the requirement for existing of given number of couples of points that satisfy condition about the midpoint of the connecting segment. The value formula is proved by determining of another minimum number of lattice points - minimum number of couples of points for given number of lattice points, so that for every couple of points, the midpoint of the connecting segment is a point from the lattice.
And finally the statements are summarized and proved for a lattice in the n-dimensional space.
lattice points, conditions of minimality
Природни науки, математика и информатика
Natural sciences, mathematics and informatics