*Forma,* Vol. 14 (No. 3), pp. 213-219, 1999

*Original Paper*

## On Example of Inverse Problem of Variation Problem
in Case of Columnar Joint

Yoshihiro Shikata

Department of Mathematics, Meijo University, Tempaku-ku, Nagoya 468-8502, Japan

E-mail address: shikat@meijo-u.ac.jp

(Received December 21, 1998; Accepted August 13, 1999)

**Keywords: **
Inverse Variation Problem, Columnar Joint, Euclidean Motion Group, Evaluation Function, Curvature of a Plane Curve

**Abstract. **
Taking the columnar joint as example, we illustrate how we solve the inverse problem to the variation problem posed by Nature giving the hexagonal shape to the joint. We notice that the joint is formed by straight line segments, three of which crosses at one vertices. From this geometric information, we characterize a class of evaluation function for the joint. We prove that the subset consists essentially of the functions only in the length. Since the hexagonal shape is known to minimize the length, we see that the hexagonal shape of the joint is a necessary consequence of the geometric information under the assumption that the joint is the solution to the variation problem satisfying several mathematical coditions.

[Full text] (PDF 200 KB)