Circle packing

Arrangement of circles in a plane without interior overlap. The covered area fraction is its packing fraction. Equal-radius square packing has fraction

π /4

.

Table of contents
- Alternating-radius square circle packing Circle packing

Alternating-radius square circle packing ( $η = π (r_{1}^{2} + r_{2}^{2}) / (2 d^{2})$ )

Place equal numbers of radii

r_{1}, r_{2}

on alternating sites of a square nearest-neighbour lattice of spacing

d

. Nonoverlap requires

d \geq max (r_{1} + r_{2}, 2 r_{1}, 2 r_{2})

. A two-circle cell has area

2 d^{2}

, giving the displayed packing fraction. Its maximum within this geometry occurs at large-to-small radius ratio

1 + 2

and is

π (1 - 1/ 2)

; smaller interstitial circles leave unused space, while larger ones force the large-circle lattice apart.

 Ancestors (6)

 Incoming links (2)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (1)

Circle packing by

Wikipedia Bot  1

Circle packing is a mathematical concept that involves arranging circles within a given space, such that no two circles overlap and the arrangement satisfies certain criteria. The study of circle packing includes investigating how many circles of a given size can fit into a larger circle or how circles of different sizes can be arranged optimally.

 Read the full article

  See all articles in the same topic Create my own version