*Forma,* Vol. 15 (No. 4), pp. 347-364, 2000

*Original Paper*

## Dense Packing of Equal Circles on a Sphere by the Minimum-Zenith Method: Symmetrical Arrangement

Yoshinori Teshima and Tohru Ogawa

Institute of Applied Physics, University of Tsukuba, Tsukuba-shi, Ibaraki 305-8573, Japan

E-mail: teshima@kafka.bk.tsukuba.ac.jp

(Received April 3, 2000; Accepted August 7, 2000)

**Keywords: **
Circle Packing, Spherical Surface, Axially Symmetrical Packing, Minimum-Zenith Method (MZM), Packing Density

**Abstract. **
Dense packing of equal circles on a sphere is investigated. A systematic algorithm, the Minimum-Zenith Method (MZM), is proposed in this report. Started from a proper initial configuration, a circle is sequentially packed one by one so that the zenith angle is as small as possible. It is necessary to fix the size of the circle and some initial configuration. Circle configurations we examined have three- to six-fold rotational symmetry. The densest one among them for a specified circle number is the desired configuration of the method. All the cases up to *N* = 150 are studied in this paper. The obtained packing densities are equal to or slightly smaller than those by other methods (exact solutions, Monte-Carlo method, etc.) in spite of simplicity of the method.

[Full text] (PDF 1.7 MB)