These are based on a similar problem on this forum

http://www.mathhelpforum.com/math-he...principal.html

1. Let there be 'some' points in a plane such that distance between any two them is < 1. What is the minimum area/shape which can inscribe all these points?

2. You grab an area by putting infinite points on a plane. Only condition - any two points you put should be <1 apart. What is the maximum area you can grab?

Any pointers? I think I know the answer but am struggling to justify it.

Thanks