*Forma,* Vol. 24 (No. 3), pp. 87-92, 2009

*Original Paper*

## A Simple Mathematical Model for Chamber Arrangement
of Planktic Foraminifera

Takashi Yoshino^{1}*, Katsunori Kimoto^{2}, Naoko Kishimoto^{3}, Atsushi Matsuoka^{4}, Toshiyuki Kurihara^{5}, Naoto Ishida^{5} and Shu Matsuura^{6}

^{1}Department of Mechanical Engineering, Toyo University, Kujirai 2100, Kawagoe, Saitama 350-8585, Japan

^{2}Research Institute for Global Change (RIGC), Japan Agency for Marine-Earth Science and Technology (JAMSTEC), Japan

^{3}Graduate School of Engineering, Kyoto Univiersity, Japan

^{4}Department of Geology, Faculty of Science, Niigata University, Japan

^{5}Graduate School of Science and Technology, Niigata University, Japan

^{6}Faculty of Education, Tokyo Gakugei University, Japan

*E-mail address: tyoshino@toyonet.toyo.ac.jp

(Received March 16, 2009; Accepted January 12, 2010)

**Abstract. **
We propose a simple mathematical model for chamber arrangement of planktic foraminifera. The arrangement
is approximated using connection of spheres. It is represented by combination of four sequences: they correspond
to radius of chamber, horizontal/vertical distance of connected chambers, and angle of horizontally projected two
lines constructed by connection of centers of adjacent spheres. We assumed that the sequences of the radius and
horizontal/vertical distances are geometric series and that of the angle is constant. We succeeded in reproducing
the chamber configuration of all recent planktic foraminifera at the level of family in taxonomy. We also point
out that some other parameters are required in order to classify the chamber arrangement in detail. The model
enables us to consider an optimization problem of the volume-surface area ratio which corresponds to the cost
of chamber forming materials. Using the simplest case of our models, we obtain an optimized radius-distance
relation.

**Keywords: **
Planktic Foraminifera, Chamber Arrangement, Mathematical Model

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