Matematické Fórum

Skrytý text:

Suppose the contrary:
Let's denote the centre of the circle S, choose 6 equally distanced points A1-A6 (define A7 as A1) on its perimeter (ie. is constant for all i=1..6). Subdivide circle (without S) into six regions Ri with the border S-Ai-A(i+1) (where Ai-A(i+1) is an arc of the circle) not containing line S-A(i+1). Every two points in every region Ri has distance less then 1 so every region has to be occupied by at most 1 point, one more point is S - so at most 7 points can be placed to satisfy the condition that no two points has distance less than 7. This is contradiction.