fiftyonepointslieinsideasquareofside1.provethatitispossibletocoversomethreeofthembyacircleofradius1/7.用pigeonhole来证明

Question

fifty one points lie inside a square of side 1.prove that it is possible to cover some three of them by a circle of radius 1/7.
用pigeonhole 来证明

Answer 1

1.divide the square into 5x5 small squares,that is 25 in total.
2.and every small square can be covered by a disk with radius 1/7,since sqrt(2)/5 < 2/7.
3.show that there is a small square in which there are more than 3 points,so they can be covered by a disk with radius 1/7