The Coordination Number of Equal Disks in Two-dimensional Random Packing

The three-dimensional random packing of particles has attracted physicists, chemists, sedimentologists, materials scientists and mathematicians for more than a century. The study focuses on the packing density, porosity, the packing concentration, coordination number and the effect of the particle’s shape, density on the packing etc. For the metals and crystallized rocks with equigranular texture without porosity, there exists the"triple-point junction" with an angle of 120掳 in two dimensions. Every particle is adjacent to another six particles. To explain this texture, scientists proposed the definition of"Voronoi polygon". J. A. Dodds tried to demonstrate this conclusion by