ABSTRACT
A new set of fascinating questions arises when we focus on circles and other non-tessellating shapes in the plane. Since circles do not tile the plane, we look for arrangements of circles with the smallest possible gaps. How small can we make the gaps and still have no overlaps? We will explore this question as well as many others on the topic of packing areas of the plane. In mathematics, packing means filling a given space with a given set of objects allowing no overlaps. We will focus on packing areas of the plane with copies of one geometrical shape. There are two main questions to study. How many copies of the shape can be arranged with no overlaps onto a given space? How much of the space can be covered by copies of the shape?
